Homework 1 Whole Numbers and Decimals S2 Level F

Do not use a calculator. Show all appropriate working.

1. How much would I receive if I changed Thailand£240 to bahts ? £1 = 65 bahts

2. Fourteen people share £8750 in a lottery win.How much does each person receive?

3. Round to the number of decimal places indicated :- (a) 18.275 (2 d.p.) (b) 0.98047 (3 d.p.) (c) 3.966 (1 d.p.)

4. How many significant figures are there in each number?(a) 7506 (b) 450 (c) 0.74 (d) 0.00805

5. Round to the number of significant figures indicated:-(a) 7.258 (3 s.f.) (b) 0.065 (1 s.f.) (c) 23.04 (2 s.f.)(d) 5071 (2 s.f.) (e) 1.0349 (3 s.f.) (f) 6 834 000 (1 s.f.)

6. Calculate:-(a) 3.29 40 (b) 8.69 30 000 (c) 0.06 0.7(d) 27 0.9 (e) 0.04 80 (f) 0.007 0.05

7. Calculate :-(a) 5 x (4 + 2 ) (b) 18 12 3 (c) 3 + 2 x 5 – 4

8. Copy the following and put brackets in the correct place(a) 8 + 3 x 2 = 22 (b) 24 4 x 2 = 3 (c) 12 – 4 x 3 + 1 = 32

Homework 2 Angles S2 Level F

1. Calculate the sizes of the angles marked a, b, c and d.

2. What is the (a) complement of 37º (b) supplement of 101° ?

3. Name an angle :-

(a) supplementary to AHT (b) vertically opposite toAHT (c) corresponding to AHT (d) alternate to AHT

4. Copy these figures and fill in the sizes of all unmarked angles.

5. Calculate the size of the interior and exterior angle of a regular decagon.

6. Calculate the size of the (a) reflex angle between the hands of a clock at two o’clock

(b) acute angle between the hands of a clock at ten past three.

Homework 3 Powers, Roots & Scientific Notation S2 Level F

Do not use a calculator. Show all appropriate working.

1. Find the values of :-(a) 9² (b) 4³ (c) 34 (d) 25 (e) √64 (f) √121

2. This square has an area of 400 m².

Calculate its perimeter.

3. What is the length of the largest square you could make if you had

200 square tiles each 30 centimetres long?

4. Find the lowest common multiple of :-(a) 6 and 9 (b) 4, 5 and 6

5. Find the highest common factor of :-(a) 16 and 24 (b) 45 and 75

6. Make a list of all the prime numbers which are less than 30.

7. Express each of the following numbers as a product of its prime factors :-(a) 140 (b) 360

8. Write these numbers in full(a) 314 106 (b) 9 109 (c) 22 10−3 (d) 7 10−1

9. Write these numbers in scientific notation (a) 175 000 (b) 640 000 000 (c) 0000 4 (d) 0000 000 28

Homework 4 Information Handling S2 Level F

1. Calculate the median of this set of numbers. 16, 20, 19, 13, 19, 17, 12, 19, 16

2. Alan’s 3rd year exam marks are shown below.

English – 57 Maths – 79 French – 60 Technical – 58 History – 58 Music – 74 Physics – 68 Chemistry – 66

Calculate the mean, median and mode of Alan’s marks.

3. This frequency table shows the ages of Age Frequency a group of children at a Youth Club Disco. 15 6 16 8 (a) Calculate the mean age. 17 7 18 10 (b) Write down the modal age. 19 9

4. The stem-and-leaf diagram shows Kilometres travelled the distances travelled by a 1 | 2 7 salesman over ten working days. 2 | 3 4 9

3 | 0 3 54 | 2 6

n = 10 2 | 1 represents 21 km

(a) What was the shortest distance travelled by the salesman?

(b) Calculate the range of the distances travelled by the salesman.

5. State whether each of the following variables is discrete or continuous:- (a) the time taken to run 100 metres (b) the number of matches in a box (c) shoe sizes

6. This pie chart shows how many games Newtown Wanderers won, lost and drew last season. They won 22 games, lost 10 and drew 8.

Calculate the size of the angles w, l and d.You must show your working.

7. The table below shows the marks scored by pupils in French and Italian exams.

Name Tom Ann Jim Pat Don Lee Sam SueFrench mark 15 25 50 40 35 55 70 80Italian mark 30 30 60 50 40 70 85 95

(a) Draw a scattergraph to show these marks.

(b) Describe the correlation between the French and Italian marks.

(c) Draw a line of best fit on your graph.

(d) A pupil who scored 65 in his French exam was absent from the Italian exam.Use your line of best fit to estimate the pupil’s Italian mark.

Homework 5 Fractions S2 Level F

Do not use a calculator. Show all appropriate working.

Calculate :-

1. 2/3 + 1/4 2. 13/15 − 7/10 3. 4/5 3/8

4. 12/25 9/10 5. 15/6 + 24/9 6. 33/4 − 12/5

7. 41/2 12/3 8. 61/4 17/8

Homework 6 Straight Line Graphs S2 Level F

1. (i) Copy and complete the table for each equation. (ii) Draw the graph of each equation.

(a) y = 2x + 1 (b) y = ½x − 4

x 0 2 4 x 0 2 4y y

2. For each equation, the given points lie on the graph. Write the coordinates of the points.

(a) y = 4x A(3, ) B( −2 , ) C( , 20)

(b) y = 3x − 5 P(0, ) Q(2, ) R( , 7)

3. The height (h cm) of a candle which has been burning for h hours is given by the formula

h = 15 − 2t.

(a) Use the formula to copy and complete this table.

t (hours) 0 2 4 6h (cm)

(b) Draw the graph of the equation.

(c) How long will the candle burn for?

Homework 7 Integers S2 Level F

1. Calculate :-(a) 16 + (−20) (b) −21 + 13 (c) 2 – 25 (d) 25 – (−15) (e) −15 –25 (f) −90 – (−10)

2. Calculate :-(a) 4 × (−7) (b) −3 × 9 (c) −8 × (−6) (d) (−5)²(e) (−2)3 (f) −54 ÷ 6 (g) −56 ÷ (−8) (h) 63 ÷ (−9)

3. Calculate :- (a) 3 − 5 6 (b) (3 − 5) 6 (e) 10 − 3 (−5) (d) −36 −12 + 3 (e) −36 ( −12 + 3)

4. Solve the following equations :-

(a) x + 7 = 2 (b) x – 13 = −9 (c) x + 8 = -3

5. Simplify :-(a) 8x – 6x – x (b) 2p – (−3p) + p (c) −t – 3t – 5t(d) −h + (−h) – h (e) −3d + 2d – 4d (f) −8x + (−2x) + 10x

6. Given that p = 12, q = −3 and r = −2 calculate the values of :-(a) 10 – 2q (b) 5qr (c) p (d) pr r q

Homework 8 Expressions, Brackets & Factors S2 Level F

1. Simplify :-(a) d² + d² + d² + d² (b) a x a x a (c) 5a – 2a + 4(d) 8g – 5 + g + 7 (e) 3y x y (f) 4t x 2t(g) c x 2c x 3c (h) a x 4 + 7 (i) 20 – c x 7(j) 2a x a + 4 (k) 7 – 3v x 2v (l) 5a x 3 x 2a

2. In this question, a = 8 and b= 6. Find the values of :- (a) 2b² (b) (2b)² (c) ½(a + b) (d) 3a + c 5

3 Write out each of the following expressions without brackets :-(a) 3(2x + 5) (b) 4(3 – 2y) (c) a(b + 2)(d) b(b – 1) (e) m(7 + 4m) (f) −2(p − 5)

4. Remove the brackets, then simplify each expression(a) 10 + 2(x – 3) (b) 3(2y + 1) + 5(y – 2) (c) p(4 + p) – 3p

5. Factorise each of the following expressions :-(a) 3n + 6 (b) 12 – 8d (c) ab + 5a (d) x² - 4x

Homework 9 Probability S2 Level F

1. A die is rolled. Find the probability of getting(a) a 4 (b) an odd number (c) a square number (d) a factor of 20

2. The table below shows the hair colour of a class of S2 pupils.

Hair Colour Black Brown Blond RedNumber 6 15 3 1

(a) Find the probability (as a fraction in simplest form) that a pupil chosenat random will have brown hair.

(b) If this class is typical of a school which has 750 pupils, how many of

them would you expect to have brown hair?

3. The table shows the eye colour of all S2 pupils in a school.

Eye Colour Blue Green Grey BrownNumber 84 72 26 18

Find the probability (as a decimal) that if a pupil is chosen at random he/she will :- (a) have blue eyes (b) have brown eyes (c) not have grey eyes.

4. A bag contains 3 different colours of beads :- yellow, green and brown.

The probability of choosing a yellow bead is 0.2.The probability of choosing a green bead is 0.5.

(a) What is the probability of choosing a brown bead ?(b) If the bag contains 80 beads, how many of them are yellow ?

5. In a health promotion campaign, forty people were asked whether or not they took sugar in their tea. The table shows their responses. What is the probability that a person chosen at random from this group (a) is male (b) takes sugar (c) is a female who takes sugar?

Sugar No SugarFemale 9 15Male 5 11

Homework 10 Percentages S2 Level F

1. Copy and complete this table.

Percentage 50% 40% 33⅓% 8%Fraction ½ ¾ 4/5 ⅛Decimal 0.1 0.25

2. My holiday at Thomsons should cost me £380. How much will it cost me if I pay by cash ?

3. If I left £275 in the Bank of Scotia fora year, how much interest would I get ?

4. Of the 40 people asked, 16 of them said they prefer coffee to tea..(a) Express the number who prefer coffee as a fraction of the total

number of people asked. Give your answer in simplest form.(b) Express your answer as a percentage.(c) Express your answer as a decimal.

5. Steve buys a computer for £400. A year later he sells it for £260.

Calculate :-(a) his loss (in £’s) (b) his percentage loss

6. A shopkeeper bought a dozen travel bags for a total price of £45. She sold all the bags at £5 each. Calculate :-

(a) her profit (in £’s). (b) her percentage profit

7. A coat which normally costs £150 was sold for £105 in a sale .Calculate the percentage discount.

Homework 11 Enlarging & Reducing S2 Level F

1. Would each scale factor enlarge or reduce a shape? (a) 2 (b) ⅓ (c) 09 (d) 17

2. (a) Enlarge each shape by a scale factor of 3. (b) Reduce each shape by a scale factor of ½.

3. Find the scale factor used in reducing or enlarging each dark shape to the light shape.

4. For each pair of similar shapes, find the scale factor and calculate x.

Homework 12 Equations & Inequations S2 Level F

Solve these equations.

1. 9x − 25 = 29 2. 2x + 11 = 3 3. 3x − 4 = −25

4. 5x = 9x − 10 6. 8x − 2 = 3x + 18 7. 7(2 − x) − 19 = 30

8. −2(1 − 5p) = 13

9. Make an equation and solve it to find the value of x.

10. Jack and Jill have equal amounts of money. Jack buys 7 packets of fruit gums and then has 22p left. Jill buys 3 packets of fruit gums and then has £130 left. Make an equation and solve it to find the cost of one packet of fruit gums.

11. Solve these inequations.

(a) 8x + 5 < 61 (b) 5y + 10 ≥ 2y − 11

Homework 13 Area S2 Level F

Calculate the area of each of the following shapes.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. Calculate the area of this field. Give your answer in hectares.

11. How many hectares are there in 1km2. Explain your answer.

Homework 14 Distance, Speed and Time S2 Level F

1. The table shows the distances (in miles) between some cities.

(a) Find the distance between Edinburgh and Dundee.(b) How long would it take to travel from Aberdeen to Glasgow at 49

m.p.h. ?

2. Concorde flies from London to New York in 4 hours at 1380 km/h.Calculate the distance from London to New York.

3. An athlete runs 400 metres in 50 seconds.What is the athlete’s average speed ?

4. A girl cycled at a steady speed of 14 m.p.h. for 2 hours 30 minutes.How far did she travel in that time ?

5. How long (in hours and minutes) does it take for a journey of 285 kmat an average speed of 60 km/h ?

6. This is part of a train timetable.

(a) How long does the train take to travel from Carlisle to Glasgow ?

(b) How far is Glasgow from Carlisle if the train does the journey at anaverage speed of 120 km/h ?

7. On a journey of 34 miles, the average speed of a coach was 40 m.p.h.The coach started its journey at 1935.What was the time when the coach arrived at its destination ?

Homework 15 Pythagoras Theorem S2 Level F

1. Calculate the values of a and b, correct to one decimal place.

2. Calculate the length of the diagonal of this rectangle.

3. A ladder, 4 metres long, reaches 3.2 metres up a wall. How far is the foot of the ladderfrom the foot of the wall?

4. Calculate the area of this isosceles triangle.(Begin by finding its height.)

5. Calculate the perimeter of this kite.(Begin by finding the length of each side.)

6. Calculate the distance between the points A(1,2) and B(9,8).

Homework 16 Scale Drawing S2 Level F

1. On a map with representative fraction 1:50 000 the distance betweenLoch Erin and Hillend Castle is 9 centimetres.Calculate the true distance between them, in kilometres.

2. The distance between Glentattie and Spybrae is 16 kilometres.How far apart are they on a map with representative fraction 1:200 000?

3. James has a model sports car which is 30 centimetres long.The real car is 45 metres long.Find the scale of the model, as a representative fraction.

4. Use a protractor to find the bearing of :-

(a) P from O(b) Q from P(c) O from Q

5. A plane leaves Sturrock Airport and flies for 80 km on a bearingof 035° to drop supplies at Monmouth Island.From the island, the pilot flies for 50 km on a bearing of 120° toFowler Airport.

Make a scale drawing (with a suitable scale) and use it to find thebearing and distance of Sturrock Airport from Fowler Airport.

Homework 17 Formulae & Sequences S2 Level F

1. Evaluate each formula for the given values. (a) A = ½bh when b = 75 and h = 6. (b) S = 6s² when s = 5. (c) v = u + at when u = 30, a = 98 and t = 7. (d) A = ½h(a + b) when h = 8, a = 7 and b = 11. (e) F = 9C + 32 when C = 20. 5 (f) f = uv when u =20 and v = 30. u + v

2. Write down a formula for the total areaof this shape which consists of arectangle and a triangle.

3. Andy can complete a canoe slalom in 120 seconds.For each gate he hits, 10 seconds is added to his time.(a) Find his total time if he hits 3 gates.(b) Write down a formula for the total time, t seconds, when

he hits g gates.

4. A garden centre sells bags of sand at £250 each. In addition they have a home delivery service which costs £6 per order.(a) Find the cost of having 8 bags of sand delivered.(b) Write down a formula for the total cost, £C, of having b bags of sand delivered.(c) How many bags of sand can be delivered for £56?

5. The formulae shown are used to calculate Peco

the cost, £C, of hiring two different types of C = 9h + 5dinghy, for h hours.

(a) For how long could you hire each type Mirage dinghy if the hire cost is £59? C = 7h + 10(c) Find the number of hours for which the hire

cost would be the same for both dinghies.

6. For each of the following sequences find a formula for the nth term.

(a)Term number 1 2 3 4 5 nValue of term 3 11 19 27 35

(b)Term number 1 2 3 4 5 nValue of term 40 37 34 31 28

Homework 18 Circle S2 Level F

Give all answers correct to 3 significant figures.

1. Calculate the circumference of each of the following circles :-

(a) (b)

2. Calculate the diameter of a circle with circumference 62.8 cm.

3. I want to draw a circle with circumference 40 centimetres. At what radius must I set my compasses to do this ?

4. Calculate the areas of each of the following circles :-

(a) (b)

5. Calculate the area of this quarter circle.

6. A circular hole is cut out from a square piece of cardboard. Calculate the shaded area.

7. This shape consists of a semi circle on top of a rectangle. Calculate the area of the complete shape.

8. Calculate the perimeter of this running track which consists of a rectangle and two semi circles.

Homework 19 Ratio & Proportion S2 Level F

1. Write down these ratios in their simplest form :-(a) 2 mm : 1 cm (b) 1 minute : 45 seconds (c) £2 : 75p(d) 400g : ¾ kg (e) 1½ m : 75 cm (f) 40 ml : ½ litre

2. The ratio of male : female monkeys at a zoo is 2:9.There are 72 females. How many males are there?

3. Jane and Ryan share £360 in the ratio 5:4. Work out Jane’s share?

4. To produce a particular colour of paint, an assistant at B&Q mixes blue, red and white in the ratio 2:3:5.

(a) If she uses 300 ml of blue, how much red and white does she need?(b) If she uses 800 ml of white, how much paint does she get altogether?(c) If she needs 900 ml of paint altogether, how much red does she need?

5. A 5 centimetre piece of chocolate roll weighs 70 grams.What should an 8 cm piece weigh ?

6. If I exchange £20 for francs I get 170 francs. How many francs would I receive for £24 ?

7. It takes six men 30 minutes to cut the grass at their local football pitch. How long would five men have taken working at the same rate ?

8. A cyclist travelling at 24 km/h takes 28 minutes to travel to work. If he is injured and his average speed drops to16 km/h, how long would it now take him to get to work ?

9. Which of the graphs shown below shows direct proportion. Give a reason for your answer.