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© Zeta Maths Ltd.
ZETA MATHS ZETA MATHS
z ZETA MATHS
Fourth Level Mathematics
DEVELOPMENT AND CONSOLIDATION
Homework Exercises
© Zeta Maths Ltd.
© ZETA MATHS LTD.
The contents of this book are copyright of Zeta Maths Limited and are for the use of the pupils and teachers of the licensed school only. The book may be printed or photocopied for the use of those to whom it is licensed and it may also be posted on a secured website for digital use. If photocopying this book, ensure that this page is attached.
Note that if posting the book digitally as a pdf file, this may only be via a website that is only accessible by staff and pupils of the licensed school (such as Glow or Edmodo).
It is prohibited to digitally copy or to edit any part of this book, any photocopies or prints produced must contain the copyright and licensing information.
It is prohibited to post this book on an unsecured website that is accessible via the public domain.
INTRODUCTION
The aim of this book is to support learners in their pursuit of excellence in Mathematics. Curriculum for Excellence offers learners breadth in learning; this resource is intended to assist learners in developing depth and consolidation of skills.
The resource can be used in a variety of ways: It may be used systematically as learners work through the book progressively doing each of the four exercises from each homework on consecutive days of the week, or it may be used in a more flexible way. The contents page is intended for learners and teachers to keep track of progress through the resource. Learners may use a traffic light system for each of the exercises to monitor progression through each of the experiences and outcomes.
© Zeta Maths Ltd.
Homework Contents Ex 1 Ex 2 Ex 3 Ex 4
1 Mixed Third Level Review 2 Mixed Homework 1 3 Mixed Third Level Review 4 Mixed Homework 1 5 Mixed Homework 4 6 Mixed Homework 2 7 Mixed Homework 2 8 Mixed Homework 4 9 Speed, Distance, Time 10 Mixed Homework 1 11 Volume and Surface Area 1 12 Mixed Homework 4 13 Volume and Surface Area 2 14 Straight Line – Gradient 15 Straight Line – Equation from Graph 16 Straight Line – Mixed 17 Sequences, Fractions, Algebra 18 Expanding Brackets 19 Factorising 20 Solving Equations -‐ Brackets 21 Mixed Homework 1 22 Solving Equations -‐ Brackets 23 Solving Equations -‐ Fractions 24 Mixed Homework 2 25 Mixed Homework 3 26 Solving Inequations 27 Circles – Area and Perimeter 28 Mixed Homework 2 29 Mixed Homework 1 30 Mixed Homework 5 31 Mixed Homework 3 32 Mixed Homework 6 33 Pythagoras 1 34 Pythagoras 2 35 Mixed Homework 3 36 Trigonometry 1 37 Mixed Homework 1 38 Trigonometry 2 39 Similar Shapes 40 Angles, Pythagoras 41 Angles, Pythagoras 42 Mixed Homework 2 43 Mixed Homework 1 44 Coordinates 45 Mixed Homework 3
CONTENTS CONTENTS
1
© Zeta Maths Ltd.
Homework Contents Ex 1 Ex 2 Ex 3 Ex 4 46 Mixed Homework 6 47 Mixed Homework 2 48 Mixed Homework 3
CONTENTS Contd. CONTENTS Contd.
Exercise 1 Exercise 2
Exercise 4
1 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find 55 x 30
2. Solve 6a – 2 = a + 9
3. 3 + 9 x 2 - 82
4. Find 18 000 ÷ 60
5. Find 1675 x 8 (show working)
6. Find the HCF of 32 and 18
7. Change 5.5m into mm. 8. Find the LCM of 5 and 12
9. Change 65cm to km
1. Find 27 x 600 2. Solve 9a – 5 = 2a + 8 3. 2 x 42 – 3 x (8 + 7)
4. Find 6400 ÷ 400
5. Find 2791 x 9 (show working)
6. Find the HCF of 57 and 24 7. Change 40.5m into mm 8. Find the LCM of 7 and 12
9. Change 80cm to km
1. Find 1452 x 200
2. Solve 12a – 17 = 9 –a
3. 3 + 12 x 2 - 72
4. Find 452 000 ÷ 400
5. Find 17 984 x 6 (show working)
6. Find the HCF of 45 and 108
7. Change 312mm to m 8. Find the LCM of 9 and 6
9. Change 142km to mm
1. Find 245 x 500 2. Solve 4 – 5a = 9a + 7 3. 5 + 62 – 3(3 + 9) 4. Find 49 000 ÷ 70
5. Find 7984 x 7 (show working)
6. Find the HCF of 24 and 36
7. Change 670mm to m
8. Find the LCM of 3 and 13
9. Change 0.04km to mm
CfE Outcomes 3-03a, 3-03b 3-15a, 2-03c, 2-01a, 2-03a, 3-07a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
2 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 72 as a product of prime factors.
2. Solve 4a – 2 = 3a + 8
3. 42 – 2 x 3 + 9
4. Simplify: 3a + 2a x 4a – a
5. Round the following to 2 significant figures:
a. 0.000405 b. 45 214
6. Find 0.002 x 0.4
7. Find 31
43+
8. Find the supplement of 76º.
1. Express 96 as a product of prime factors. 2. Solve 6a – 2 = 8a + 8 3. 3 x 22 – 2 x (3 + 9) 4. Simplify 4a x 2a - 4a2 5. Round the following to 2 significant figures:
a. 0.007695 b. 785 415 6. Find 23 x 0.9
7. Find 31
52−
8. Find the supplement of 108º.
1. Express 69 as a product of prime factors.
2. Solve 7a – 2 = 9 – 3a
3. 8 – 2 x 7
4. Simplify 3a + 2a – 17a
5. Round the following to 2 significant figures:
a. 0.09099 b. 147 015
6. Find 0.002 x -0.8
7. Find 43
61+
8. Find the complement of 56º.
1. Express 56 as a product of prime factors. 2. Solve 4 – 3a = 5a + 7 3. 2 + 52 – 2(3 + 9) 4. Simplify 5a x 3 – 4a + 9 5. Round the following to 2 significant figures:
a. 0.06709 b. 999 999 6. Find 0.002 x -0.0005
7. Find 51
65−
8. Find the complement of 76º.
CfE Outcomes 3-05a, 3-15a, 4-03b, 4-01a, 3-07a, 3-07b, 3-17a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
3 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find 46 x 30
2. Solve 3a – 2 = a + 8
3. Find 52 – 6 x 3 + 9
4. Find 18 000 ÷ 900.
5. Find 2539 x 8 (show working)
6. Find the HCF of 64 and 18.
7. Change 2m into mm. 8. Find the LCM of 4 and 6.
9. Change 45cm to km.
1. Find 27 x 40 2. Solve 6a – 2 = 2a + 8 3. Find 3 x 32 – 4 x (3 + 7)
4. Find 4200 ÷ 600.
5. Find 1781 x 9 (show working)
6. Find the HCF of 36 and 24. 7. Change 3.5m into mm. 8. Find the LCM of 3 and 17.
9. Change 69cm to km.
1. Find 132 x 200.
2. Solve 7a – 2 = 9 –a
3. Find 8 – 2 x 7
4. Find 48 000 ÷ 600.
5. Find 1973 x 6 (show working)
6. Find the HCF of 72 and 18.
7. Change 3mm to m. 8. Find the LCM of 4 and 14.
9. Change 16km to mm.
1. Find 245 x 500. 2. Solve 4 – 3a = 8a + 7 3. Find 2 + 52 – 2(3 + 9) 4. Find 420 000 ÷ 7000.
5. Find 4537 x 7 (show working)
6. Find the HCF of 24 and 96.
7. Change 15mm to m.
8. Find the LCM of 8 and 15.
9. Change 41km to mm
CfE Outcomes 3-03a, 3-03b 3-15a, 2-03c, 2-01a, 2-03a, 3-07a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
4 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 48 as a product of prime factors.
2. Solve 5t – 3 = 2t + 12
3. 62 – 5 x 4 + 12
4. Simplify: 7y + y x 4y – 5y
5. Round the following to 2 significant figures:
a. 0.08715 b. 614,709
6. Find 0.012 x 0.3
7. Find 15+34
8. Find the supplement of 13º
1. Express 125 as a product of prime factors. 2. Solve 9g – 4 = 4g + 31 3. 8 x 32 – 2 x (5 + 6) 4. Simplify: 8p x 5p – 3p2 5. Round the following to 2 significant figures:
a. 0.10367 b. 3,791 6. Find 31 x 0.6
7. Find 57−18
8. Find the supplement of 163º
1. Express 52 as a product of prime factors.
2. Solve 8h – 4 = 20 – 2h
3. 102 – 5 x 8
4. Simplify: 7f + 4f – 15f
5. Round the following to 2 significant figures:
a. 0.006362 b. 535,193
6. Find 0.0006 x -0.03
7. Find 15+37
8. Find the complement of 19.5º
1. Express 200 as a product of prime factors. 2. Solve 3 – 2r = 5r + 16 3. 3 + 62 – 4(8 - 2) 4. Simplify: 7n x 2 – 3n + 10 5. Round the following to 2 significant figures:
a. 0.07610 b. 1,090,907 6. Find 0.005 x -0.0008
7. Find 1316
−38
8. Find the complement of 170.5º
CfE Outcomes 3-05a, 3-15a, 4-03b, 4-01a, 3-07a, 3-07b, 3-17a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
5 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Write the following in scientific notation: (a) 14,920 (b) 265,000 (c) 0.004572
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from £1.28 to £1.35, calculate the % increase to 1 decimal place.
4. Four apples cost £1.32, how much do 7 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 26,420 (b) 1,365,000 (c) 0.0009472
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from $3.30 to $4.00, calculate the % increase to 1 decimal place.
4. Five apples cost £1.25, how much do 7 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation: (a) 89,520 (b) 1,999,000 (c) 0.00009872
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from €1.15 to €1.30, calculate the % increase to 1 decimal place.
4. Four apples cost £1.32, how much do 7 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 65,920 (b) 26,000 (c) 0.004
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from £1.32 to £1.43, calculate the % increase to 1 decimal place.
4. Six apples cost £1.68, how much do 7 cost?
5. Find the volume of the shape, give your answer
in litres:
CfE Outcomes 4-06b, 4-01a, 4-03a, 3-11a, 3-11b
5cm
15cm
12cm
16cm 6cm
12cm
18cm
15cm
9cm
12cm
10cm
15cm 7cm
8cm
12cm
10cm
5cm 5cm
6cm 4cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
6 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x = 4, y = -2 and z = 3 find:
a. 4x +3y −2z b. x 2 − 4y +6z
2. Solve 7x – 4 = 3x + 8
3. Evaluate: 62 – 2 x (5 - 6) showing working
4. Simplify 5a – 3 - 4a + 6
5. Round the following to 2 significant figures:
a. 0.0000936 b. 178,764
6. Find 0.0625 ÷ 0.005
7. Find 34×17
1. If x = 4, y = -2 and z = 2 find:
a. 5x +3y 2 −3z b. x 2 +2y +5z
2. Solve 4x – 2 = 6x + 3
3. Evaluate: 22 – 2 x (7 - 7) showing working 4. Simplify 4a + 8 – 10a – 5 5. Round the following to 3 significant figures:
a. 0.01064 b. 5,784,984 6. Find 180 ÷ 0.02
7. Find 27×45
1. If x = -5, y = -2 and z = 3 find:
a. zx +2y 2 b. 2x − 4y 2 + 4z
2. Solve 7x – 5 = 9 - 6x
3. Evaluate: 92 – 2 x (4 - 7) showing working
4. Simplify 12a – 6 – 16a + 16
5. Round the following to 3 significant figures:
a. 0.004809 b. 606,486
6. Find 0.032 ÷ 0.0004
7. Find 16×34
1. If x = -5, y = -3 and z = 5 find:
a. 2xy +3z b. 3xyz
2. Solve 4 – 3x = 8x + 7 3. E valuate: 72 – 4 x (5 - 7) showing working 4. Simplify 8a + 16 – 10 – 2a 5. Round the following to 3 significant figures:
a. 6.5073 b. 1,086,483 6. Find 0.002 ÷ 0.00004
7. Find 56×15
CfE Outcomes 3-14a, 3-15a, 4-03b, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
7 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x = 5, y = -1 and z = 6 find:
a. x − y −2z b. 2x − y 2 +3z 2
2. Solve 2x – 1 = 5x + 8
3. Evaluate: 32 – 12 x (2 - 6) showing working
4. Simplify a – 12 + 2a + 10
5. Round the following to 2 significant figures:
a. 0.0006032 b. 2,252,394
6. Find 0.0675 ÷ 0.005
7. Find 25×34
1. If x = -2, y = -3 and z = -4 find:
a. 2x +3y 2 −z b. x − 4x 2 −7z
2. Solve 8x – 2 = 6x + 14
3. Evaluate: 62 – 2 x (1 - 3) showing working 4. Simplify 4a – 8 – 6a – 3 5. Round the following to 3 significant figures:
a. 0.0001105 b. 799,901 6. Find 3600 ÷ 0.009
7. Find 47×512
1. If x = 10, y = -3 and z = 2 find:
a. zx +zy 2 b. 2x + y 2 −8z
2. Solve 4x – 7 = 14 - 3x
3. Evaluate: 102 – 2 x (8 - 13) showing working
4. Simplify -2a – 9 + 15a - 16
5. Round the following to 1 significant figure:
a. 0.00804 b. 166,786
6. Find 0.042 ÷ 0.0006
7. Find 29×34
1. If x = -10, y = 2 and z = -5 find:
a. xy −2z 2 b. −xyz
2. Solve 4 – x = 8x + 22 3. E valuate: 112 – 3 x (1 - 6) showing working 4. Simplify 14a + 1 – 10a – 9 – 2a 5. Round the following to 4 significant figures:
a. 11.5076 b. 1,026,491 6. Find 0.00024 ÷ 0.0000004
7. Find 37×712
CfE Outcomes 3-14a, 3-15a, 4-03b, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
8 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Write the following in scientific notation: (a) 61,200 (b) 651,000 (c) 0.0000805
2. Round the numbers above to 2 significant
figures.
3. Diesel prices increased from £1.26 to £1.34, calculate the % increase to 1 decimal place.
4. Seven pears cost £2.03, how much do 5 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 19,700,000 (b) 134 (c) 0.001883
2. Round the numbers above to 2 significant
figures.
3. Diesel prices increased from $4.20 to $4.80, calculate the % increase to 1 decimal place.
4. Four apples cost £1.24, how much do 7 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation: (a) 16,000 (b) 9,004 (c) 0.020071
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from €1.15 to €1.32, calculate the % increase to 1 decimal place.
4. Six peaches cost £2.52, how much do 9 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 17,250 (b) 341,000 (c) 0.005111
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from £1.38 to £1.48, calculate the % increase to 1 decimal place.
4. Eight kiwis cost £3.84, how much do 4 cost?
5. Find the volume of the shape, give your answer
in litres:
CfE Outcomes 4-06b, 4-01a, 4-03a, 3-11a, 3-11b
4cm
12cm
11cm
14cm 8cm
14cm
17cm
20cm
8cm
13cm
13cm
12cm 7cm
8cm8cm
11cm
9cm
4cm 9cm
7cm 7cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
9 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Convert each of these times to hours and minutes. (a) 2.3 hours (b) 3.6 hours
2. Convert each of these times to hours as a
decimal (a) 5 hours 42 minutes (b) 9 hours 18 minutes
3. A plane travels at 520mph for 2.2 hours.
Calculate the total distance travelled.
4. A car covers 220 miles in 4 hours 42 minutes. Calculate the average speed of the journey.
5. A boat travels 30miles at an average speed of
8mph. Calculate the time taken in hours and minutes.
1. Convert each of these times to hours and
minutes. (a) 8.7 hours (b) 1.5 hours
2. Convert each of these times to hours as a
decimal (a) 4 hours 54 minutes (b) 2 hours 6 minutes
3. A plane travels at 480mph for 5.4 hours.
Calculate the total distance travelled.
4. A car covers 240 miles in 5 hours 36 minutes. Calculate the average speed of the journey.
5. A boat travels 20.4miles at an average speed of
6mph. Calculate the time taken in hours and minutes.
1. Convert each of these times to hours and minutes.
(a) 5.25 hours (b) 823
hours
2. Convert each of these times to hours as a
decimal (a) 7 hours 36 minutes (b) 4 hours 3 minutes
3. A plane travels at 486mph for 3.6 hours.
Calculate the total distance travelled.
4. A car covers 280 miles in 6 hours 18 minutes. Calculate the average speed of the journey.
5. A boat travels 34.2miles at an average speed of
9mph. Calculate the time taken in hours and minutes.
1. Convert each of these times to hours and
minutes.
(a) 4 13
hours (b) 6.9 hours
2. Convert each of these times to hours as a
decimal (a) 1 hour 9 minutes (b) 3 hours 12 minutes
3. A plane travels at 544mph for 5.9 hours.
Calculate the total distance travelled.
4. A car covers 300 miles in 6 hours 54 minutes. Calculate the average speed of the journey.
5. A boat travels 16.1miles at an average speed of
7mph. Calculate the time taken in hours and minutes.
CfE Outcomes 4-10b
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
10 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 128 as a product of prime factors.
2. Solve 18t – 4 = 12t + 20
3. 92 – 2 x 3 - 13
4. Simplify: 20k + k x 3k – 5k
5. Round the following to 3 significant figures:
a. 0.0028634 b. 91,542
6. Find 0.012 x 0.3
7. Find 12+23+15
8. Find the supplement of 25º
1. Express 400 as a product of prime factors. 2. Solve 50g – 7 = 44g + 35 3. 7 x 22 – 3 x (2 + 3) 4. Simplify: 7h x 5h x 2h 5. Round the following to 3 significant figures:
a. 6.0362 b. 158,342 6. Find 31 x 0.6
7. Find 89−38
8. Find the supplement of 154º
1. Express 180 as a product of prime factors.
2. Solve 15h – 9 = 51 – 5h
3. 202 – 5 x 10 + 102
4. Simplify: 7f + 4f – 15f
5. Round the following to 3 significant figures:
a. 0.028763 b. 1,987,862
6. Find 0.002 x 0.009
7. Find 25+49
8. Find the complement of 22.7º
1. Express 250 as a product of prime factors. 2. Solve 5 – 3v = 8v - 28 3. 7 + 32 – 6(5 - 2) 4. Simplify: 7n x 2 – 3n + 10 5. Round the following to 3 significant figures:
a. 0.49999 b. 14,810,109 6. Find 0.12 x 0.005
7. Find 1217
−334
8. Find the supplemplement of 120.6º
CfE Outcomes 3-05a, 3-15a, 4-03b, 4-01a, 3-07a, 3-07b, 3-17a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
11 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Find (i) the volume and (ii) the surface area of the following shapes: 1.
2. 3.
Find (i) the volume and (ii) the surface area of the following shapes: 1.
2. 3.
Find (i) the volume and (ii) the surface area of the following shapes: 1.
2. 3.
Find (i) the volume and (ii) the surface area of the following shapes: 1.
2. 3.
CfE Outcomes 4-11b, 4-11c, 4-16b
12cm
8cm
10cm
15cm
10cm
10cm
25cm
12cm
15cm
40cm
15cm
20cm
120mm
100mm
90mm
18mm
20mm
50mm
9m
8m
4m
50cm
9cm
11cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
12 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Write the following in scientific notation: (a) 85,600 (b) 333,000 (c) 0.0000701
2. Round the numbers above to 2 significant
figures.
3. Diesel prices decreased from £1.41 to £1.37, calculate the % increase to 1 decimal place.
4. Five pears cost £1.35, how much do 8 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 12,600,000 (b) 225 (c) 0.003460
2. Round the numbers above to 2 significant
figures.
3. Diesel prices increased from $4.15 to $4.35, calculate the % increase to 1 decimal place.
4. Four apples cost £1.52, how much do 6 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation: (a) 19,000 (b) 13,007 (c) 0.034001
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from €1.36 to €1.52, calculate the % increase to 1 decimal place.
4. Six bananas cost £1.14, how much do 12 cost?
5. Find the volume of the shape, give your answer
in litres:
1. Write the following in scientific notation:
(a) 18,650 (b) 918,000 (c) 0.006999
2. Round the numbers above to 2 significant
figures.
3. Petrol prices increased from £1.32 to £1.40, calculate the % increase to 1 decimal place.
4. Seven plums cost £3.71, how much do 11 cost?
5. Find the volume of the shape, give your answer
in litres:
CfE Outcomes 4-06b, 4-01a, 4-03a, 3-11a, 3-11b
4cm
7cm
6cm
5cm 17cm
13cm
30cm
30cm
50cm
70cm
80cm
90cm 30cm
42cm
54cm
50cm
3cm 14cm
22cm 40cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
13 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. The Khufu Pyramid has a square base of approximate length 230m and sloped height 186m as in the net below: (a) Calculate its surface
area
(b) Its vertical height is 140m. Calculate its volume to the nearest thousand.
2. An ice-cream cone has a radius of 5cm and a
height of 16cm, calculate the volume of the cone, give your answer to 2 significant figures.
1. An unused toilet roll has a
radius of 16cm and a height of 14cm. The empty roll has a radius of 6cm. Find the volume of toilet paper on the roll.
2. Find the volume of the composite shape below.
1. The glass pyramid at the Louvre has a square base of approximate length 35m and sloped height 28m as in the net below: (a) Calculate its surface
area
(b) Its vertical height is 22m. Calculate its volume to the nearest thousand.
2. An ice-cream cone has a radius of 8cm and a height of 18cm, calculate the volume of the cone, give your answer to 2 significant figures.
1. An unused kitchen roll has
a radius of 24cm and a height of 26cm. The empty roll has a radius of 6cm. Find the volume of kitchen paper on the roll.
2. Find the volume of the composite shape below.
CfE Outcomes 4-11b, 4-11c, 4-16b
25cm
22cm
30cm 38cm
230m
186m
35m
28m
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
14 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Plot the points on a Cartesian diagram (x and y graph) and determine the gradient of the line passing through them: (a) (0,4), (1,4), (3,4)
(b) (-1,-3), (1,1), (3,5)
(c) (5,-2), (5,3), (5,7)
(d) (-2,4), (0,-2), (2,-8)
2. For each of the following equations, make a table using three x-values, plot the points on a Cartesian diagram and write down the gradient of each line:
(a) y = 2x (b) y = ½x (c) y = -x (d) y = -4x
1. Plot the points on a Cartesian diagram (x and y
graph) and determine the gradient of the line passing through them: (a) (1,4), (2,7), (3,10)
(b) (-2,-3), (-2,0), (-2,3)
(c) (4,-2), (5,-2), (7,-2)
(d) (-3,7), (2,-3), (4,-7)
2. For each of the following equations, make a table using three x-values, plot the points on a Cartesian diagram and write down the gradient of each line:
(a) y = 3x + 1 (b) y = ½x + 5 (c) y = -x - 5
1. Plot the points on a Cartesian diagram (x and y graph) and determine the gradient of the line passing through them: (a) (-1,3), (0,-1), (2,-9)
(b) (1,-3), (2,-1), (3,1)
(c) (3,-3), (5,-3), (6,-3)
(d) (-3,11), (0,2), (3,-7)
2. For each of the following equations, make a table using three x-values, plot the points on a Cartesian diagram and write down the gradient of each line:
(a) y = 2x + 3 (b) y = -½x (c) y = -2x + 7
1. Plot the points on a Cartesian diagram (x and y
graph) and determine the gradient of the line passing through them: (a) (0,0), (0,4), (0,6)
(b) (-1,0), (1,0), (3,0)
(c) (6,-2), (7,-3), (8,-4)
(d) (-1,-4), (0,1), (1,6)
2. For each of the following equations, make a table using three x-values, plot the points on a Cartesian diagram and write down the gradient of each line:
(a) y = -x - 1 (b) y = -½x + 4 (c) y = -6x + 5
CfE Outcomes 4-13c, 4-13d
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
15 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line:
1. Find (i) the gradient (ii) the y-intercept
(iii) the equation of each line:
1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line:
1. Find (i) the gradient (ii) the y-intercept
(iii) the equation of each line:
CfE Outcomes 4-13b, 4-13c
(a)
(b)
(c) (d)
(a)
(b) (c)
(d)
(a)
(b)
(c)
(d)
(a) (b)
(c)
(d)
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
16 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find (i) the gradient (ii) the y-intercept (iii) the equation of each line (assume each square counts for 1 unit):
2. (a) What do you notice about the gradient? (b) What does this tell us about the lines?
1. From the following straight-line equations,
state which pair are parallel? (a) y = 4x – 3 (b) y = -2x (c) y = ⅔x (d) y = -⅔x (e) y = ¼x – 3 (f) y = -2x + 7
2. For each pair of coordinates, find (i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (-5,4), (0,12) (b) (0,4), (9,14) (c) (-3,10), (0, -5) (d) (0,0), (6,-6)
3. For each equation, state the gradient and y-intercept: (a) y = x – 5 (b) y = 3x + 22 (c) y = -x
1. From the following straight-line equations, state which pair are parallel? (a) y = 2x + 5 (b) y = -x (c) y = ¼x + 4 (d) y = ⅓x (e) y = ¼x – 3 (f) y = -2x
2. For each pair of coordinates, find
(i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (0,6), (8,12) (b) (1,4), (1,14) (c) (-4,-2), (0, -9) (d) (0,5), (4,5)
3. For each equation, state the gradient and y-intercept:
(a) y = ⅙x + 20 (b) y = 7x (c) y = -⅞x - 5
1. From the following straight-line equations,
state which pair are parallel? (a) y = 7x – 3 (b) y = 15x (c) y = -x - 8 (d) y = 9 - x (e) y = ¼x + 6 (f) y = -3x + 2
2. For each pair of coordinates, find (i) the gradient (ii) the y-intercept (iii) the equation of the line passing through them: (a) (-7,-2), (0,9) (b) (0,0), (6,-14) (c) (-2,-1), (0, -5) (d) (0,9), (6,0)
3. For each equation, state the gradient and y-intercept:
(a) y = 8 - x (b) y = 11 + 4x (c) y = 1 - ⅘x
CfE Outcomes 4-13b, 4-13c, 4-13d
(a)
(b)
(c)
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
17 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find the next three terms in each sequence (a) 8, 11, 14, 17 (b) 25, 35, 45, 55 (c) 72, 80, 88, 96 (d) 100, 98, 96, 94
2. For each of the questions above, find an
expression for the nth term. (Eg, 2n + 1)
3. Use the formula in question 2 to find the 20th
term in each sequence.
4. Find 23+15
5. Solve 7y + 2 = 4y + 20
6. Simplify: 5a + a x 2a - a
1. Find the next three terms in each sequence
(a) 5, 9, 13, 17 (b) 32, 37, 42, 47 (c) 51, 57, 63, 69 (d) 124, 121, 118, 115
2. For each of the questions above, find an
expression for the nth term. (Eg, 2n + 1)
3. Use the formula in question 2 to find the 30th
term in each sequence.
4. Find 34+13
5. Solve 12y - 2 = 6y + 40
6. Simplify: 6r + r – 3r x 2r
1. Find the next three terms in each sequence (a) 2, 11, 20, 29 (b) 15, 26, 37, 48 (c) 73, 81, 89, 97 (d) 250, 245, 240, 235
2. For each of the questions above, find an
expression for the nth term. (Eg, 2n + 1)
3. Use the formula in question 2 to find the 40th
term in each sequence.
4. Find 27+13
5. Solve 18y - 7 = 6y + 41
6. Simplify: 10p x p + p
1. Find the next three terms in each sequence
(a) 15, 19, 23, 27 (b) 400, 500, 600, 700 (c) 180, 170, 160, 150 (d) 118, 114, 110, 106
2. For each of the questions above, find an
expression for the nth term. (Eg, 2n + 1)
3. Use the formula in question 2 to find the 15th
term in each sequence.
4. Find 89−13
5. Solve 5y + 5 = 10y - 20
6. Simplify: y + y + y x y
CfE Outcomes 4-13a, 4-07b, 3-15a, 3-14a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
18 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Multiply out and, when necessary, collect like terms:
1. 3(a −2b)
2. m(4 − n)
3. −x (x + y )
4. 3a(5a −2b)
5. 3(x − 4) +2(5 − x )
6. 3x (2x − 1) −8x (x − 4)
Multiply out and, when necessary, collect like terms:
1. 5(x +2y )
2. t(3−u)
3. p(q − p)
4. a(5a −b)
5. 4(m − 4) −3(5 −m)
6. 3y (2z +5) +8y (y − 4z )
Multiply out and, when necessary, collect like terms:
1. 3(x +7) − 15
2. 8−2(4 − n)
3. 3x −x (x +2)
4. 12a2 −3a(5a −2)
5. 4x (x −5) −2x (3+2x )
6. 3(2x 2 − 1) −5x (1− 4x )
Multiply out and, when necessary, collect like terms:
1. 3(a −8) + 13
2. 5 − (x +2)
3. 17 − (x −5)
4. 8ab +3a(a −2b)
5. 3(x − 4) − (5 − x )
6. 3x (3x − 1) +x (4 −x )
CfE Outcomes 4-14a, 4-3b
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
19 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Factorise the following expressions:
1. 3a + 12
2. 8a +24b
3. 12a − 16ab
4. ab +a2
5. 5a2 − 15a
6. 4ab +6a2
Factorise the following expressions:
1. 4x + 12
2. 16x +24y
3. 15x − 18xy
4. 2xy − y 2
5. 7x 2 −21x
6. 12xy − 15x 2
Factorise the following expressions:
1. 3m + 15
2. 28m +36n
3. −mn − 16n
4. mn2 +m2n
5. 5m2n − 10(mn)2
6. 21m2n +28mn2
Factorise the following expressions:
1. ax +ay
2. 20px +24py
3. 12pq − 16q
4. pq + p2q
5. 5p2q2 −35p2q
6. −42p2q2 +6q2
CfE Outcomes 4-14b
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
20 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Solve the following equations:
1. 4(x +2) = 2(x +3)
2. 5(x +2) = 3(x +2)
3. 6(x +3) = 3(x +2)
4. 3(x +2) = 2(x +3)
5. 4(x −2) = 3(x +3)
6. 4(2x −2) = 3(x − 4)
Solve the following equations:
1. 5(x +2) = 3(x + 4)
2. 6(x +3) = 4(x +3)
3. 7(x +2) = 4(x +2)
4. 4(x +6) = 3(x +7)
5. 5(x −6) = 4(x +6)
6. 5(3x − 4) = 6(x −7)
Solve the following equations:
1. 7(x −3) = 4(x −5)
2. 7(x −3) = 5(x +3)
3. 8(x +2) = 5(x −2)
4. 5(x +6) = 3(x +7)
5. 6(x +7) = 3(x +6)
6. 7(4x − 4) = 5(x +7)
Solve the following equations:
1. 9(3x −3) = 7(x + 12)
2. 5(4x −3) = 7(8x −6)
3. 9(3x + 12) = 5(4x −9)
4. 3(2x −9) = 3(10x + 4)
5. 12(3x − 10) = 5(5x +3)
6. 7(2x + 12) = 10(2x +5)
CfE Outcomes 4-14a, 4-15a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
21 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 65 as a product of prime factors.
2. Solve 9(x – 2) = 3(x + 8)
3. Evaluate: 62 – 2 x (5 + 9) showing working.
4. Simplify a + a + a x a
5. Round the following to 2 significant figures:
a. 0.005999 b. 48 678
6. Find 0.00025 x 0.4
7. Find 51
43+
8. In a right-angled triangle, one of the angles is
26º, what is the unknown angle?
1. Express 96 as a product of prime factors. 2. Solve 6(x – 2) = 8(x + 8)
3. Evaluate: 52 – 2 x (5 - 7) showing working. 4. Simplify a x a – a + a + a x a 5. Round the following to 3 significant figures:
a. 0.007695 b. 785 415 6. Find 15 x 0.9
7. Find 31
72−
8. In a right-angled triangle, one of the angles is
46º, what is the unknown angle?
1. Express 42 as a product of prime factors.
2. Solve 7(x – 2) = 2(9 - 3x)
3. Evaluate: 112 – 2 x (9 - 7) showing working
4. Simplify 3a + a + a x a
5. Round the following to 3 significant figures:
a. 0.09099 b. 147 015
6. Find 0.002 x -0.8
7. Find 43
612 +
8. In a right-angled triangle, one of the angles is
22º, what is the unknown angle
1. Express 88 as a product of prime factors. 2. Solve 2(4 – 3x) = 5x + 7 3. Evaluate: 82 – 4 x (12 - 7) showing working 4. Simplify a + a x a - a 5. Round the following to 3 significant figures:
a. 0.06709 b. 999 999 6. Find 0.002 x -0.00105
7. Find 511
651 −
8. In a right-angled triangle, one of the angles is
49º, what is the unknown angle
CfE Outcomes 3-05a, 3-15a, 4-03b, 3-14a, 4-01a, 3-07a, 3-07a, 3-17a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
22 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Solve the following equations:
1. 4(x −2) = 3(x +3)
2. 5(x +2) = 2(x −2)
3. 6(x − 4) = 3(x + 1)
4. 3(x +2) + 4 = 2(x +3)
5. 4(x −2) −5 = 2+3(x +3)
6. 4(2x −2) −8 = 3(x − 4)
Solve the following equations:
1. 5(x + 4) = 3(x +5)
2. 5(2x −3) = 2(3x +2)
3. 3(2x −6) = 6(3x +2)
4. 2(2x +6) + 4 = 2(5x + 4)
5. 4(2x −6) −5 = 2−3(2x +3)
6. 6(2x −3) = 4 −5(x −5)
Solve the following equations:
1. 7(x + 4) = 5x +2
2. 5x − 10 = 8(x −2)
3. 7(x − 4) = 6(x + 1)
4. 4(2x +2) − 10 = 5(2x +3)
5. 5(x −2) −5 = 8−3(2x +7)
6. 4(8x −2) −8 = 3(7x − 4) −20
Solve the following equations:
1. 3(x +3) = 8(x + 10)
2. 6(3x −2) = 5(2x +6)
3. 9(2x − 12) = 6(6x +9)
4. 3(2x −5) − 12 = 2(8x + 4)
5. 9(3x −5) + 14 = 2−5(5x +3)
6. 7(2x + 12) = 4 − 10(x −5)
CfE Outcomes 4-14a, 4-15a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
23 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Solve the following equations:
1. 12(x − 12) = 4(x −8)
2. 14(x −3) = 1
2(x −2)
3. 13(2x −3) = 1
6(x −2)
4. 14(x −5) = 1
8(x −2)
5. 13(x + 12) = 1
4(x −2)
6. 34(x +5) = 1
5(x − 4)
Solve the following equations:
1. 13(x −9) = 5(x −3)
2. 14(x +2) = 1
2(x − 4)
3. 13(4x − 4) = 1
6(x −3)
4. 14(x −5) = 1
12(2x − 12)
5. 13(2x +3) = 1
4(3x −6)
6. 34(x −6) = 2
5(x −5)
Solve the following equations:
1. 15(2x − 12) = 1
5(x −5)
2. 15(2x + 4) = 1
6(x −2)
3. 13(2x −3) = 2
7(2x −5)
4. 34(x −2) = 1
3(x −2)
5. (x + 12)3
=(x −2)
4
6. (x −3)5
=(x −2)
4
Solve the following equations:
1. 18(x − 13) = 4(x −8)
2. 14(x −5) = 1
5(x −3)
3. 34(5x −3) = 5
6(x −2)
4. 34(x − 4) = 5
8(x −2)
5. (x +9)3
=(x +5)
7
6. (x + 10)4
=(x +8)
9
CfE Outcomes 4-14a, 4-15a
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
= =
=
=
=
=
=
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
24 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x = 2 and y = -3 find:
a. 224 yx − b. yx 42 −
2. Solve 7(x – 4) = 3(x + 8)
3. Evaluate: 62 – 2 x (5 - 6) showing working.
4. Simplify 5(a – 3) -4a
5. Round the following to 2 significant figures:
a. 0.007594 b. 57,546
6. Find 0.025 ÷ 0.005
7. Find 51
43×
1. If x = -4 and y = -2 find:
a. 224 yx − b. yx 42 −
2. Solve 4(x – 2) = 6(x + 3)
3. Evaluate: 22 – 2 x (7 - 7) showing working. 4. Simplify 4(a + 2) – 5(2a – 5) 5. Round the following to 3 significant figures:
a. 0.00054897 b. 4,987,756 6. Find 18 ÷ 0.9
7. Find 31
72×
1. If x = -5 and y = -4 find:
a. 224 yx + b. 242 yx −
2. Solve 7(x – 5) = 2(9 - 6x)
3. Evaluate: 92 – 2 x (4 - 7) showing working
4. Simplify 6(2a – 1) – 4(4a + 4)
5. Round the following to 3 significant figures:
a. 0.0045634 b. 759,987
6. Find 0.032 ÷ (-0.008)
7. Find 43
612 ×
1. If x = -5 and y = -4 find:
a. 224 yx + b. 242 yx −
2. Solve 3(4 – 3x) = 8x + 7 3. E valuate: 72 – 4 x (5 - 7) showing working 4. Simplify 8(a + 2) – 2(5 – a) 5. Round the following to 3 significant figures:
a. 1.048795 b. 489,999 6. Find 0.002 ÷ (-0.0005)
7. Find 511
651 ×
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
25 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 54cm, find x.
2. Solve ½(x – 4) = ¼(x + 8)
3. Increase £2400 by 2.2%.
4. Find the percentage depreciation on a boat purchased for £45,000 and sold for £32,000.
5. Find how much interest was gained on an
investment of £3400 at 4% per annum for 3 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 38cm, find x.
2. Solve ½(x – 5) = ¼(x + 9)
3. Decrease £5500 by 4.3%.
4. Find the percentage depreciation on a boat purchased for £16,000 and sold for £8,000.
5. Find how much interest was gained on an
investment of £12,000 at 3.5% per annum for 3 years.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 48cm, find x.
2. Solve ½(x – 3) = ¼(x + 2)
3. Increase £6500 by 2.2%.
4. Find the percentage depreciation on a boat purchased for £45,000 and sold for £30,000.
5. Find how much interest was gained on an
investment of £140,000 at 1.2% per annum for 4 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 36cm, find x.
2. Solve ½(2x – 7) = ¼(x + 5)
3. Decrease £13500 by 7.6%.
4. Find the percentage depreciation on a boat purchased for £500,000 and sold for £400,000.
5. Find how much interest was gained on an
investment of £125,000 at 8.2% per annum for 5 years.
CfE Outcomes 3-14a, 3-15a, 4-03a
x + 2
3x - 7
x + 8
2x - 7
2x + 2
4x - 2
3x + 1
5x - 7
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
26 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
Solve the following inequations:
1. 5x + 1 < 26
2. 2x + 6 > 30
3. 4x + 3 ≤ 23
4. 8x – 2 ≥ 38
5. 4(2x + 3) < 28
6. ½x + 6 > 14
7. 5(2x – 1) ≤ 2x + 19
8. 7x + 5 > 4(5x – 2)
Solve the following inequations:
1. 6x + 2 < 32
2. 7x + 8 > 50
3. 3x + 2 ≤ 25
4. 9x – 4 ≥ 32
5. 6(5x + 3) < 48
6. ⅓x + 3 > 33
7. 6(2x – 2) ≤ 2x + 8
8. 5x + 6 > 4(3x – 2)
Solve the following inequations:
1. 3x + 9 < 27
2. 2x + 10 > 40
3. 8x + 5 ≤ 45
4. 10x – 5 ≥ 60
5. 7(2x + 3) < 63
6. ¼x + 2 > 20
7. 8(x – 2) ≤ 2x + 18
8. x + 4 > 2(x – 2)
Solve the following inequations:
1. 8x + 7 < 71
2. 16x + 2 > 34
3. 4x + 1 ≤ 17
4. 20x – 20 ≥ 100
5. 9(x + 5) < 72
6. ⅕x + 6 > 8
7. 3(2x – 2) ≤ 2x + 5
8. x + 7 > 2(x – 2)
CfE Outcomes 4-15a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
27 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find area and the perimeter of the following shape:
2. An athlete runs round a 400m running track in 54 seconds, calculate his speed in metres per second (ms-1).
1. Find area and the perimeter of the following
shape:
2. An plane flies 4500 miles at an average speed of 550mph, how long does the journey take (give your answer in hours and minutes)?
1. Find area and the perimeter of the following shape:
2. An athlete runs round a 400m running track in 51 seconds, calculate his speed in metres per second (ms-1).
1. Find area and the perimeter of the following
shape:
2. An plane flies 6800 miles at an average speed of 540mph, how long does the journey take (give your answer in hours and minutes)?
CfE Outcomes 4-16b, 4-10b
30cm
24cm
20cm
15cm
30cm
10cm
50cm
20cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
28 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x = -1 and y = -5 find:
a. 3x +2y 2 b. −x −2y
2. Solve 5(x – 2) = 2(x - 7)
3. Evaluate: 32 – 3 x (7 - 6) showing working.
4. Simplify 6(a + 3) - 5a
5. Round the following to 2 significant figures:
b. 0.007814 b. 97 346
6. Find 0.035 ÷ 0.005
7. Find 23×26
1. If x = -6 and y = -1 find:
a. x − y 2 b. 3x + 4y
2. Solve 7(x – 1) = 5(x + 8)
3. Evaluate: 32 – 3 x (9 - 7) showing working. 4. Simplify 8(a + 3) – (a – 5) 5. Round the following to 3 significant figures:
a. 0.0005897 b. 7 985 756 6. Find 18 ÷ 0.2
7. Find 26×17
1. If x = -8 and y = 4 find:
a. 3x +6y b. −2x + 4y 2
2. Solve 10(x – 2) = 2(6 - x)
3. Evaluate: 42 – 1 x (8 - 7) showing working
4. Simplify 4(2a – 3) – 2(4a + 1)
5. Round the following to 3 significant figures:
a. 0.004569 b. 109 987
6. Find 0.04 ÷ (-0.008)
7. Find 1 14×23
1. If x = -3 and y = -6 find:
a. 4x + y 2 b. 2x + y 2
2. Solve 7(2 – x) = 6x + 9 3. E valuate: 32 – 2 x (-2 - 7) showing working 4. Simplify 6(a + 1) – 3(5 – a) 5. Round the following to 3 significant figures:
a. 1.098795 b. 89 999 6. Find 0.004 ÷ (-0.0005)
7. Find 1 12×1 3
4
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
29 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 36 as a product of prime factors.
2. Solve 2(x – 1) = 5(x + 4)
3. Evaluate: 32 – 2 x (5 + 5) showing working.
4. Simplify: a + a – a + 2a –a + a x a
5. Round the following to 2 significant figures:
a. 0.005160 b. 48 632
6. Find 0.0020 x 0.4
7. Find 34+23
8. In a right-angled triangle, one of the angles is
16º, what is the unknown angle?
1. Express 28 as a product of prime factors. 2. Solve 3(x – 7) = 2(x + 5)
3. Evaluate: 52 – 3 x (4 - 7) showing working. 4. Simplify: a x a + a + a + a - a 5. Round the following to 3 significant figures:
a. 0.007632 b. 776 432 6. Find 0.002 x 0.9
7. Find 27−12
8. In a right-angled triangle, one of the angles is
42º, what is the unknown angle?
1. Express 80 as a product of prime factors.
2. Solve 6(x – 2) = 2(2 + 2x)
3. Evaluate: 72 – 3 x (3 - 7) showing working
4. Simplify: 3a + a + a + a x a
5. Round the following to 3 significant figures:
a. 0.09093 b. 144 123
6. Find 0.003 x -0.6
7. Find 2 16+22
6
8. In a right-angled triangle, one of the angles is
82º, what is the unknown angle?
1. Express 86 as a product of prime factors. 2. Solve 2(3 + 3x) = 5x + 7 3. Evaluate: 92 – 3 x (11 - 6) showing working 4. Simplify: a x a x a x a 5. Round the following to 3 significant figures:
a. 0.06707 b. 999 898 6. Find 0.003 x -0.00106
7. Find 156− 1 3
4
8. In a right-angled triangle, one of the angles is
41º, what is the unknown angle?
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
30 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find the perimeter of the shape:
2. Solve ½(3x – 5) = ¼(x + 8)
3. A plane flies from Glasgow to New York in 5 hours 42 minutes, the distance is 3200miles, calculate the speed.
4. How long in hours and minutes does it take to
travel 400miles at a speed of 70mph?
5. Find how much interest was gained on an investment of £4500 at 4% per annum for 3 years.
1. Find the perimeter of the shape:
2. Solve ½(x + 3) = ¼(8x + 6)
3. A plane flies from Glasgow to New York in 6 hours 24 minutes, the distance is 3200miles, calculate the speed.
4. How long in hours and minutes does it take to
travel 500miles at a speed of 60mph?
5. Find how much interest was gained on an investment of £1100 at 4.2% per annum for 3 years.
1. Find the perimeter of the shape:
2. Solve ½(5x + 6) = ¼(3x + 9)
3. A plane flies from Glasgow to New York in 6 hours 48 minutes, the distance is 3200miles, calculate the speed.
4. How long in hours and minutes does it take to
travel 600miles at a speed of 65mph?
5. Find how much interest was gained on an investment of £12,800 at 6.5% per annum for 4 years.
1. Find the perimeter of the shape:
2. Solve ½(4x – 10) = ¼(2x + 8)
3. A plane flies from Glasgow to New York in 7 hours 36 minutes, the distance is 3200miles, calculate the speed.
4. How long in hours and minutes does it take to
travel 300miles at a speed of 70mph?
5. Find how much interest was gained on an investment of £112,000 at 4.2% per annum for 5 years.
CfE Outcomes 3-14a, 3-15a, 4-15a, 4-03a, 4-10b
120m
60m
110m
70m
115m
56m
118m
66m
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
31 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 48cm, find x.
2. Solve ½(x – 2) = ¼(x + 10)
3. Increase £4800 by 2%.
4. Find the percentage depreciation on a car purchased for £24,000 and sold for £16,000.
5. Find how much interest was gained on an
investment of £2200 at 4% per annum for 3 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 70cm, find x.
2. Solve ½(x – 7) = ¼(x + 20)
3. Decrease £6200 by 8%.
4. Find the percentage depreciation on a caravan purchased for £24,000 and sold for £18000.
5. Find how much interest was gained on an
investment of £10,000 at 3% per annum for 3 years.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 56cm, find x.
2. Solve ½(x – 6) = ¼(x + 4)
3. Increase £6500 by 5%.
4. Find the percentage depreciation on a boat purchased for £75,000 and sold for £50,000.
5. Find how much interest was gained on an
investment of £140,000 at 5% per annum for 2 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 70cm, find x.
2. Solve ½(2x – 2) = ¼(x + 8)
3. Decrease £12200 by 9%.
4. Find the percentage depreciation on a house purchased for £800,000 and sold for £600,000.
5. Find how much interest was gained on an
investment of £128,000 at 2% per annum for 3 years.
CfE Outcomes 3-14a, 3-15a, 4-03a
x + 6
2x - 3
x + 7
4x - 2
5x + 1
9x - 1
4x + 5
7x - 3
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
32 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. For the number series below, find the next three terms and an expression for the nth term:
12, 15, 18, 21
2. For the series above, use the formula to find the 20th term in the sequence.
3. Simplify 3(a + 4) – 2(2a – 6)
4. Find 12% of £800
5. Factorise 4ab + 8a2
6. Round the following to 2 significant figures:
b. 0.000209 b. 64 089
7. Find 3 13÷2 1
4
1. For the number series below, find the next
three terms and an expression for the nth term: 21, 29, 37, 45
2. For the series above, use the formula to find the 30th term in the sequence.
3. Simplify 5(2a + 9) – 3(a – 2)
4. Find 14% of £600 5. Factorise 12xy3 + 18xy2 6. Round the following to 2 significant figures:
a. 0.09921 b. 125 555
7. Find 825÷3 1
4
1. For the number series below, find the next three terms and an expression for the nth term:
50, 90, 130, 170
2. For the series above, use the formula to find the 40th term in the sequence.
3. Simplify 8(a + 1) – 5(3a – 7)
4. Find 17.5% of £1400
5. Factorise 14h2g3 – 21 hg2
6. Round the following to 2 significant figures:
a. 9.1362 b. 300 986
7. Find 9 47÷29
1. For the number series below, find the next
three terms and an expression for the nth term:
200, 196, 192, 188 2. For the series above, use the formula to find
the 16th term in the sequence.
3. Simplify 6(4a + 1) – 3(6a – 1) 8. Find 22.5% of £1600 4. Factorise 11p2j + 44p 5. Round the following to 2 significant figures:
a. 18.0003 b. 989 700
6. Find 356÷ 1 1
3
CfE Outcomes 4-13a, 4-14a, 4-03a, 4-01a, 4-07b
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
33 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Using Pythagoras’ Theorem, calculate the
length of each missing side in these right angled triangles (2 decimal places):
1. Using Pythagoras’ Theorem, calculate the
length of each missing side in these right angled triangles (2 significant figures):
Copy the axes and use Pythagoras’ Theorem to calculate the length of each line (1 decimal place)
Copy the axes and use Pythagoras’ Theorem to calculate the length of each line (2 decimal places):
CfE Outcomes 4-16a
A cm 11 cm
14 cm
B mm
9 mm
11 mm
C m
7 m 13 m D km 120 km
115 km
P cm 17 cm
15 cm
Q mm
3 mm
8 mm
R m
19 m 22 m S km 185 km
135 km
(a)
(b)
(a)
(b)
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
34 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Draw a Cartesian diagram and use Pythagoras’
Theorem to find the length of the line joining the points (to 2.d.p): (a) A(-2,-6) & B(1,3) (b) P(0,7) & Q(9,-1)
2. The cross section of a pipe, with centre O, is filled with water as shown.
1. Draw a Cartesian diagram and use Pythagoras’
Theorem to find the length of the line joining the points (to 2.d.p): (a) A(-5,0) & B(4,-3) (b) P(0,-3) & Q(-3,9)
2. The cross section of a pipe, with centre O, is filled with water as shown.
1. Using the converse of Pythagoras’ Theorem,
determine whether the triangle is right angled:
2.
1. Using the converse of Pythagoras’ Theorem,
determine whether the triangle is right angled:
2.
CfE Outcomes 4-16a
O
Q
P R The distance from R to P is 9cm. Calculate (a) The distance from O, to the top of the water at S. (b) The total depth of the water.
5cm
S
Q
P R The distance from R to P is 11cm. Calculate (a) The distance from O, to the top of the water at S. (b) The total depth of the water.
6cm
S
10 cm
24 cm
26 cm
P m
9 m
The cross section of a tunnel is shown. The radius is given as 5m. Use the information to calculate the height P.
6 cm
The cross section of a tunnel is shown. The radius is given as 7m. Use the information to calculate the height L.
8 cm 11 cm
11 m
L m
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
35 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. For the number series below, find the next three terms and an expression for the nth term:
25, 30, 35, 40
2. For the series above, use the formula to find the 15th term in the sequence.
3. Simplify 6(a + 1) – 2(5a – 2)
4. Find 11% of £80
5. Factorise 12b - 18
6. Round the following to 2 significant figures:
a. 0.0002331 b. 28,092
7. Find 7 15÷3 1
9
1. For the number series below, find the next
three terms and an expression for the nth term: 32, 40, 48, 56
2. For the series above, use the formula to find the 20th term in the sequence.
3. Simplify 7(7a + 2) – 5(a – 6)
4. Find 13% of £300 5. Factorise 25a2b5 + 30ab4 6. Round the following to 2 significant figures:
a. 0.08067 b. 271,682
7. Find 227÷9 1
10
1. For the number series below, find the next three terms and an expression for the nth term:
20, 110, 200, 290
2. For the series above, use the formula to find the 12th term in the sequence.
3. Simplify 5(4a + 2) – 3(2a – 9)
4. Find 17.5% of £280
5. Factorise 20abc3 – 30ac
6. Round the following to 2 significant figures:
b. 9.9999 b. 213,096
7. Find 6 411÷3 3
22
1. For the number series below, find the next
three terms and an expression for the nth term:
500, 495, 490, 485 2. For the series above, use the formula to find
the 30th term in the sequence.
3. Simplify 8(a + 1) – 7(2a – 10) 4. Find 22.5% of £320 5. Factorise 15pr2d + 20pd2 6. Round the following to 2 significant figures:
a. 19.9999 b. 201,199
7. Find 4 716
÷3 132
CfE Outcomes 4-13a, 4-14a, 4-03a, 4-01a, 4-07b
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
36 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Using the tan ratio, calculate the length of
each missing side in these right angled triangles (2 decimal places):
1. Using the sine ratio, calculate the length of
each missing side in these right angled triangles (2 decimal places):
1. Using the cosine ratio, calculate the length
of each missing side in these right angled triangles (2 decimal places):
1. Using the tan ratio, calculate the size of the
angle in these right angled triangles (nearest whole number):
CfE Outcomes 4-16a
Acm
34° 14cm Bmm
29°
11mm
Cm
7m 20°
115km
57° Dkm
Acm
36°
16cm
Bm
25° 17m
Cmm
7mm 18°
215km
62°
Dkm
Acm 44° 27cm Bmm 18° 37mm
Cm 53m
24° 98km
67° Dkm
12cm
u° 14cm 9mm
x° 11mm
4 m
7m
y°
95 km
z°
85km
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
37 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 85 as a product of prime factors.
2. Solve 7(a – 5) = 5(a + 5)
3. Evaluate: 72 – 2 x (5 + 9) showing working.
4. Simplify a - a + a x a + a2
5. Round the following to 3 significant figures:
b. 9.005003 b. 48 078
6. Find 0.00025 x 0.05
7. Find 31
94+
8. In a right-angled triangle, one of the angles is
54º, what is the unknown angle?
1. Express 98 as a product of prime factors. 2. Solve 3(a – 2) = 8(a + 7)
3. Evaluate: 42 – 2 x (5 - 3) showing working. 4. Simplify a x a – a + a x a + b x b – b2 5. Round the following to 3 significant figures:
a. 0.100695 b. 765 425 6. Find 15 x 0.003
7. Find 311
432 −
8. In an equilateral triangle, what is the size of
one of the angles?
1. Express 28 as a product of prime factors.
2. Solve 4(a – 2) = 2(9 – 6a)
3. Evaluate: 92 – 2 x (2 - 7) showing working
4. Simplify 9a + a2 + a x a
5. Round the following to 1 significant figure:
a. 0.0895 b. 184 715
6. Find 0.33 x 0.05
7. Find 32
95+
8. In a right-angled triangle, one of the angles is
45º, what is the unknown angle?
1. Express 148 as a product of prime factors. 2. Solve 4(4 – 3a) = 2a + 7 3. E valuate: 82 – 4 x (12 - 7) showing working 4. Simplify a + a x a – b + b2 5. Round the following to 4 significant figures:
a. 0.06801702 b. 819 909 6. Find 0.2 x 0.75
7. Find 542
321 −
8. In a right-angled triangle, one of the angles is
39º, what is the unknown angle?
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
38 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Using the sine ratio in A and B, and cosine in C
and D to calculate the size of each angle in these right angled triangles (to the nearest whole number):
1. Using SOHCAHTOA, calculate the length of
each missing side in these right angled triangles (2 decimal places):
1. Using SOHCAHTOA, calculate the size of
each missing angle in these right angled triangles (1 decimal place):
1. Using SOHCAHTOA, calculate the length of
each missing side or angle in these right angled triangles (2 significant figures):
CfE Outcomes 4-16a
15 cm
A°
19 cm 21 mm
B°
11 mm
13 m
7 m C°
176 km D°
184 km
A cm 38° 12 cm
B m
23° 19 m
C mm
79 mm 17°
D km
62°
215 km
30cm u°
38 cm
37 mm
v°
47 mm
14 m
9 m w°
144 km x°
155 km
A cm
33°
17 cm B mm 38°
53 mm
64 m
45 m
C°
D°
2100 km
3023 km
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
39 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
?
12cm
1. These two rectangles below are similar. Find
the length of the missing side.
2. The two trapeziums are similar. Calculate the area of the larger one.
3. Change these times to hours and minutes (a) 6.3 hours (b) 4.7 hours
4. Solve: 2(2x – 4) = 12
5. Find 34÷25
1. These two rectangles below are similar. Find
the length of the missing side.
2. The two trapeziums are similar. Calculate the
area of the larger one.
3. Change these times to hours and minutes (a) 2.1 hours (b) 3.5 hours 4. Solve: 3(5x – 2) = 39
5. Find 23÷17
1. These two rectangles below are similar. Find
the length of the missing side.
2. The two trapeziums are similar. Calculate the area of the larger one
3. Change these times to hours and minutes
(a) 9.6 hours (b) 2.8 hours 4. Solve: 4(6x – 1) = 20
5. Find 29÷14
1. These two rectangles below are similar. Find
the length of the missing side.
2. The two trapeziums are similar. Calculate
the area of the larger one
3. Change these times to hours and minutes (a) 10.25 hours (b) 6.75 hours
4. Solve: 3(7x + 2) = 48
5. Find 35÷16
CfE Outcomes 4-17b, 4-15a, 4-10b, 4-07b
32cm 8cm 3cm ?
5cm 15cm
18cm 12cm
?
72cm 48cm ?
6cm
2cm
6cm 12cm
Area = 20cm2
3cm 9cm
Area = 10cm2
4cm 8cm
Area = 22cm2
16cm 32cm
Area = 120cm2
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
40 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Find all the missing angles:
2. The diagram represents a tunnel. If the
diameter of the tunnel is 16m, find the height of the tunnel.
1. Find all the missing angles:
2. The diagram represents a water pipe. If the
diameter of the tunnel is 40mm and the surface of the water is 34mm across, find the depth of the water.
1. Find all the missing angles:
2. The diagram represents a tunnel. If the
diameter of the tunnel is 24m, find the height of the tunnel.
1. Find all the missing angles:
2. The diagram represents a water pipe. If the
diameter of the tunnel is 200mm and the surface of the water is 80mm across, find the depth of the water.
CfE Outcomes 4-06b, 4-01a, 4-03a, 3-11a, 3-11b
d
b a 45° 115° c
e
f
i
g
h
10m
d b
a 50°
c
e
34mm
d
b a 51° 121° c
e
f
i
g
h
16m
d b
a 47°
c
e
80mm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
41 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
6. Find angles ‘a’ and ‘b’:
7. The diagram represents a design for a badge. If
the radius of the circle is 12cm, find the height ‘h’ of the badge.
3. Find angles ‘a’, ‘b’ and ‘c’:
8. The diagram represents a design for a badge. If
the radius of the circle is 16cm, find the height ‘h’ of the badge.
1. Find angles ‘a’ and ‘b’:
2. The diagram represents a design for a badge. If
the bottom of the badge is 14cm across, find the height ‘h’ of the badge.
1. Find angles ‘a’, ‘b’ and ‘c’:
2. The diagram represents a design for a badge. If
the bottom of the badge is 20cm across, find the height ‘h’ of the badge.
CfE Outcomes 4-17a
b b
a
40°
c
34mm
16m 80mm
a
62°
62°
h
54°
h
b a
112°
60°
h
14cm
b a
25°
c
59°
h
20cm
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
42 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x =7 and y = -2 find:
a. 224 yx − b. yx 42 −
2. Solve 5 (a + 7) = 4 (4a - 3)
3. Evaluate: 32 – 7 x (5 + 6) showing working.
4. Simplify 8(c – 11) - 4c
5. Round the following to 3 significant figures:
a. 0.078013 b. 82 105
6. Find 0.025 ÷ 0.0005
7. Find 51
43÷
1. If x = -7 and y = 4 find:
a. 226 yx − b. yx 49 −
2. Solve 2(x – 7) = 6(x + 3)
3. Evaluate: 52 – 2 x (9 - 7) showing working. 4. Simplify 7(z + 2) – 5(8z – 6) 5. Round the following to 3 significant figures:
a. 0.4065 b. 869 201 6. Find 16 ÷ 0.08
7. Find 31
72÷
1. If x = -3 and y = 4 find:
a. 248 yx + b. 237 yx −
2. Solve 5(x – 1) = 5(7 - 2x)
3. Evaluate: 112 – 2 x (9 - 7) showing working
4. Simplify 3(3a – 7) + 4(a + 9)
5. Round the following to 3 significant figures:
a. 4.702845 b. 400 749
6. Find 0.040 ÷ (-0.008)
7. Find 43
65÷
1. If x = -5 and y = -4 find:
a. 224 yx + b. 242 yx −
2. Solve 3(4 – 3x) = 8x + 7 3. Evaluate: 52 – 4 x (9 - 7) showing working 4. Simplify 8(a + 2) – 2(5 – a) 5. Round the following to 3 significant figures:
a. 12.00004 b. 100 900 000 6. Find 0.002 ÷ (-0.0005)
7. Find 156÷ 1 1
5
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
43 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. Express 76 as a product of prime factors.
2. Solve 4(x – 3) = 2(x -7)
3. Evaluate: 62 – 2 x (5 + 9) showing working.
4. Simplify a + a + a ÷ a
5. Round the following to 2 significant figures:
a. 0.008943 b. 35 596
6. Find 0.00075 x 0.5
7. Find 13+56
8. In a right-angled triangle, one of the angles is
65º, what is the unknown angle?
1. Express 78 as a product of prime factors. 2. Solve 5(x – 4) = 7(x + 3)
3. Evaluate: 42 – 5 x (3 - 6) showing working. 4. Simplify a x a – 2a ÷ a + a + 3a 5. Round the following to 3 significant figures:
a. 0.004856 b. 394 412 6. Find 12 x 0.7
7. Find 34−16
8. In a right-angled triangle, one of the angles is
56º, what is the unknown angle?
1. Express 99 as a product of prime factors.
2. Solve 3(x – 3) = 4(4 - 4x)
3. Evaluate: 122 – 3 x (10 - 6) showing working
4. Simplify 4a + a + a x a ÷ a2
5. Round the following to 3 significant figures:
a. 0.06065 b. 468 286
6. Find 0.052 x (-0.7)
7. Find 227+58
8. In a right angled triangle, one of the angles is
88º, what is the unknown angle
1. Express 55 as a product of prime factors. 2. Solve 4(4 – 7x) = 7x + 7 3. Evaluate: 92 – 8 x (16 - 8) showing working 4. Simplify a + a ÷ a – a2 5. Round the following to 3 significant figures:
a. 0.07765 b. 409 795 6. Find 0.072 x -0.05
7. Find 156− 1 1
5
8. In an isosceles triangle, the two equal angles
are 39º each, what is the unknown angle
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
44 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
6. Write down each of the coordinates from the
diagram below.
The coordinates (-3, 6), (-2, 1) and (2, 5) represent three vertices of a rhombus, the fourth vertex has coordinate (3, y), find y.
1. Write down each of the coordinates from the diagram below.
The coordinates (-6, -6), (2, -6) and (-3, -2) represent three vertices of a parallelogram, the fourth vertex has coordinate (x, -2), find x.
1. Write down each of the coordinates from the
diagram below.
The coordinates (1, 0), (-3, 4) and (-7, 0) represent three vertices of a square, the fourth vertex has coordinate (-3, x), find x.
1. Write down each of the coordinates from the diagram below.
The coordinates (-3, -3), (3, -3) and (0, 3) represent three vertices of a parallelogram, the fourth vertex has coordinate (x, 3), find x.
CfE Outcomes 4-18a
NON-‐
G
D
F
A
E B
C
G
D
F
A
E B
C
G
D
F
A
E
B
C
G
D
F
A E
B
C
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
45 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 52cm, find x.
2. Solve ½(6x – 6) = ¼(2x + 7)
3. Increase £1600 by 2.2%.
4. Find the percentage depreciation on a boat purchased for £125,000 and sold for £110,000.
5. Find how much interest was gained on an
investment of £600 at 4% per annum for 3 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 38cm, find x.
2. Solve ½(3x – 5) = ¼(5x + 9)
3. Decrease £5500 by 4.3%.
4. Find the percentage depreciation on a boat purchased for £165,000 and sold for £148,000.
5. Find how much interest was gained on an
investment of £3000 at 3.5% per annum for 3 years.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 54cm, find x.
2. Solve ½(5x – 2) = ¼(7x + 9)
3. Increase £12500 by 6.7%.
4. Find the percentage depreciation on a boat purchased for £540,00 and sold for £320,000.
5. Find how much interest was gained on an
investment of £67,000 at 3.3% per annum for 5 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 46cm, find x.
2. Solve ½(9x + 12) = ¼(3x + 3)
3. Decrease £80500 by 5.9%.
4. Find the percentage depreciation on a boat purchased for £880,000 and sold for £540,000.
5. Find how much interest was gained on an
investment of £45,000 at 6.2% per annum for 4 years.
CfE Outcomes 3-14a, 3-15a, 4-03a
x + 4
5x - 2
x + 8
6x - 3
x + 12
8x - 4
x + 10
2x - 12
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
46 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. For the number series below, find the next
three terms and an expression for the nth term
40, 60, 80, 100
2. For the series above, use the formula to find the 11th term in the sequence.
3. Simplify 2(y + 4) – 4(5y – 7)
4. Find 18% of £1200
5. Factorise 18tp + 20p
6. Round the following to 2 significant figures:
b. 0.15020 b. 31 028
7. Find 4 19÷2 1
3
1. For the number series below, find the next three terms and an expression for the nth term
21, 32, 43, 54
2. For the series above, use the formula to find the 100th term in the sequence.
3. Simplify 6(5y + 3) – 2(3y – 1)
4. Find 15% of £640 5. Factorise 20abc + 50ac 6. Round the following to 2 significant figures:
a. 0.00235 b. 222 298
7. Find 1 215
÷ 1 130
1. For the number series below, find the next
three terms and an expression for the nth term
10, 140, 270, 400
2. For the series above, use the formula to find the 10th term in the sequence.
3. Simplify 10(7y + 1) – 5(2y – 3)
4. Find 17.5% of £440
5. Factorise 27prt + 9p2t
6. Round the following to 2 significant figures:
a. 0.1029346 b. 629 748
7. Find 1 313
÷2 526
1. For the number series below, find the next three terms and an expression for the nth term
600, 590, 580, 570 2. For the series above, use the formula to find
the 40th term in the sequence.
3. Simplify 8(y + 2) – 6(2y – 1) 4. Find 22.5% of £680 5. Factorise 8v2g – 12vg2 6. Round the following to 2 significant figures:
a. 134 b. 8953.02
7. Find 1 714
+ 1 328
CfE Outcomes 4-13a, 4-14a, 4-03a, 4-01a, 4-07b
NON-‐ MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
47 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. If x = 9 and y = 6 find:
a. 5x 2 +2y 2 b. yx 42 −
2. Solve 4(x – 4) = 2(x + 8)
3. Evaluate: 42 – 3 x (8 + 9) showing working.
4. Simplify 5(a – 3) - 2a
5. Round the following to 2 significant figures:
a. 0.599453 b. 426 785
6. Find 0.625 ÷ 0.005
7. Find 52
43×
1. If x = -4 and y = 5 find:
a. 7x +3y 2 −x b. 6x + 4y 3
2. Solve 6(x – 2) = 9(x + 3)
3. Evaluate: 82 – 2 x (5 - 4) showing working. 4. Simplify 4(a + 3) – 5(2a – 2) 5. Round the following to 3 significant figures:
a. 0.007695 b. 785 415 6. Find 18 ÷ 0.9
7. Find 31
32×
1. If x = 5 and y = 3 find:
b. 5x +2y 2 b. 2xy −5x
2. Solve 4(x – 5) = 8(9 - 6x)
3. Evaluate: 32 – 2 x (9 - 6) showing working
4. Simplify 6(4a – 1) – 4(4a + 9)
5. Round the following to 3 significant figures:
a. 0.23455 b. 472 345
6. Find 0.072 ÷ (-0.008)
7. Find 43
652 ×
1. If x = 8 and y = 2 find:
b. 7x + 4y 2 b. 2x 2 −6y 2 2. Solve 5(4 – 3x) = 8x + 9 3. E valuate: 52 – 4 x (12 - 2) showing working 4. Simplify 8(a + 6) – 2(5 – a) 5. Round the following to 3 significant figures:
a. 0.06709 b. 999 454 6. Find 0.64 ÷ (0.0008)
7. Find 761
541 ×
CfE Outcomes 3-14a, 3-15a, 4-03b, 4-14a, 3-14a, 3-01a, 3-07a, 3-04a
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only
Exercise 1 Exercise 2
Exercise 4
48 Homework Fourth Level Homework Booklet CALCULATOR
Exercise 3
© Zeta Maths Ltd.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 42cm, find x.
2. Solve ⅓(x – 2) = ⅙(x + 8)
3. Increase £1300 by 3%.
4. Find the percentage depreciation on a watch purchased for £32,000 and sold for £16,000.
5. Find how much interest was gained on an
investment of £3800 at 5% per annum for 3 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 56cm, find x.
2. Solve ⅓(x + 12) = ⅙(x - 20)
3. Decrease £5400 by 7%.
4. Find the percentage depreciation on a boat purchased for £32,000 and sold for £24000.
5. Find how much interest was gained on an
investment of £12,000 at 4�3% per annum for 5 years.
1. (a) Find an expression for the perimeter of the rectangle.
(b) The perimeter is 108cm, find x.
2. Solve ⅓(x – 10) = ⅙(x - 4)
3. Increase £6300 by 9%.
4. Find the percentage depreciation on a boat purchased for £125,000 and sold for £75,000.
5. Find how much interest was gained on an
investment of £134,000 at 6�4% per annum for 2 years.
1. (a) Find an expression for the perimeter of the
rectangle.
(b) The perimeter is 44cm, find x.
2. Solve ⅓(2x – 3) = ⅙(x + 9)
3. Decrease £14200 by 8%.
4. Find the percentage depreciation on a car purchased for £600,000 and sold for £120,000.
5. Find how much interest was gained on an
investment of £198,000 at 2�7% per annum for 3 years.
CfE Outcomes 3-14a, 3-15a, 4-03a
2x + 3
3x - 7
x + 3
3x + 5
2x + 5
3x + 4
5x - 9
7x - 9
MEARNS CASTLE HIGH SCHOOL
Licensed to staff and pupils of Mearns Castle High School only