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Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 1 of 9
Embracing Diversity
GOZO COLLEGE
BOYS’ SECONDARY SCHOOL
Half Yearly Exams 2013-2014
Subject: Mathematics (Main Paper)
Form: 4 Scheme A
Time: 1 hr 40 mins
Name: _____________________________ Class: _____________________________
Instructions to Candidates
Calculators are allowed but all necessary working must be shown.
Answer all questions.
Question 1 2 3 4 5 6 7 8 9 10 11 12 13 Total
Main
Non
Calc.
Global
Mark
Mark
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 2 of 9
1. Simplify:
a) (w2)4 b) 2a
3b × 4ab
2 c) 15y
6z
2 ÷ 5yz
2
a) Ans: _____________ b) Ans: _____________ c) Ans: _____________
(5 marks)
________________________________________________________________________________
2. Find the smallest length of tape that can be cut into an exact number of either 3 m lengths or
8 m lengths or 12 m lengths.
Ans: _____________ m
(3 marks)
________________________________________________________________________________
3. If a = 4.6 × 104 and b = 2.3 × 10
5 find, in standard form, the value of:
a) 2a × b b) a + b
a) Ans: _____________ b) Ans: _____________ (4 marks)
________________________________________________________________________________
4. a) Expand and simplify:
i. 4p(q + r) – 2p(q – r) ii. (4a – 3)(3a + 7)
i) Ans: _____________ ii) Ans: _____________
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 3 of 9
b) Write and simplify an expression for the area of the triangle.
Ans: _____________
(7 marks)
________________________________________________________________________________
5. a) Factorise fully: x2
+ 4x + 4
Ans: _____________
b) Solve:
i) x2 − x − 6 = 0
Ans: _____________
ii)
+ 3 = 4
Ans: _____________
(6 marks)
________________________________________________________________________________
3t -1
4t
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 4 of 9
6. 240 boys and 180 girls sat for an examination. If 65% of the boys and 60% of the girls passed,
what percentage of the total number of candidates passed?
Give your answer correct to 1 d.p.
Ans: _____________% (4 marks)
________________________________________________________________________________
7. a) Mary invests €5500 for 3 years at 4% per annum compound interest. How much interest
does she earn?
Ans: €_____________
b) After how many years will a sum of €2000 first exceed €2800 if invested at 5% compound
interest?
Ans: _____________ years (7 marks)
________________________________________________________________________________
8. Find the equation of a straight line which passes through the points (−3, 8) and (3, −6).
Ans: __________________ (5 marks)
________________________________________________________________________________
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 5 of 9
9. The histogram below shows the height of children at a school.
a) Fill in the frequency column in the table below.
b) Calculate an estimate of the mean height of the children in the school.
Ans: _______________ cm
c) What is the modal group?
Ans: _______________
d) Which group contains the median?
Ans: _______________ (9 marks)
________________________________________________________________________________
0
20
40
60
80
100
120
140
160
180
200
130 < h ≤ 140 140 < h ≤ 150 150 < h ≤ 160 160 < h ≤ 170 170 < h ≤ 180 180 < h ≤ 190
Fre
qu
en
cy
Height, h
Height, h cm Frequency, f Mid-value interval, x fx
130 < h ≤ 140
140 < h ≤ 150
150 < h ≤ 160
160 < h ≤ 170
170 < h ≤ 180
180 < h ≤ 190
TOTAL: TOTAL:
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 6 of 9
10. A plane starts from A and flies 150 km on a bearing of 045° to B. Then it flies to C on a bearing
of 152°.
a) Find the distance BC, giving your answer correct to the nearest km.
Ans: ___________ km
b) Calculate the length of AE. Give your answer correct to the nearest km.
Ans: ___________ km
c) i) Find AD. Ans: AD = _______ km
ii) Hence, find the angle of elevation of C from A? Give your answer to 1 d.p.
(Hint: Draw triangle ADC)
Ans: ___________ ° (9 marks)
________________________________________________________________________________
25 km
B
A E
N
C
D
F 43 km 45°
N
152°
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 7 of 9
0
1
2
3
4
5
11. The travel graph shows the journey of a cyclist cycling from Mgarr to Victoria.
a) What is the average speed of the cyclist in km/h?
Ans: ______________ km/h
A motorist is driving from Victoria towards Mgarr along the same road as the cyclist, leaving
Victoria at 08:15. His speed is 25 km/hr.
b) i) After how many minutes does the motorist arrive at Mgarr?
Ans: _______________mins
ii) On the same pair of axes, draw a graph to show the journey of the motorist from
Victoria to Mgarr.
iii) At what time do the cyclist and the motorist pass near each other?
Ans:______________ (7 marks)
_______________________________________________________________________________
Mgarr
Distance (km)
Victoria
Time
8:00 8:10 8:20 8:30 8:40 8:50 9:00
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 8 of 9
12. A cuboid has sides such that the length is two cm
more than the breadth, and the height side is one
cm longer than the breadth.
a) If the breadth is x cm, write an expression for:
i) the length:______________cm
ii) the height: _____________ cm
b) Form an expression to find the total surface area of the cuboid. Simplify as much as
possible.
Total Surface Area: _______________________
(5 marks)
________________________________________________________________________________
13. The equation y = 4x – 3 is plotted on the graph below.
a) Fill in the table and on the same axes, plot the line y = 3x + 1.
b) From the graph, write down the solution of the two simultaneous equations y = 4x – 3 and
y = 3x + 1 as a coordinate.
Ans: _____________
x −2 0 4
3x
+1
y
x
L
H
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Main Paper Page 9 of 9
(4 marks)
________________________________________________________________________________
END OF PAPER
-2 -1 O 1 2 3 4
-10
-8
-6
-4
-2
2
4
6
8
10
12
14
y
x
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Non-Calculator Paper Page 1 of 5
Embracing Diversity
GOZO COLLEGE
BOYS’ SECONDARY SCHOOL
Half Yearly Exams 2013-2014
Subject: Mathematics (Non – Calculator Paper)
Form: 4 Scheme A
Time: 20 mins
Name: _____________________________ Class: _____________________________
Instructions to Candidates
Answer all questions.
This paper carries a total of 20 marks.
Calculators and protractors are not allowed.
MARKS
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Non-Calculator Paper Page 2 of 5
No. Question Space for working if
required
1. Simplify: (3m2)4
Ans: _____________
2. Make t the subject of the formula in .
Ans: _____________
3. Solve = 0, giving your answer as a mixed
number.
Ans: ____________
4. Factorise completely: 8r2 + 2r
3.
Ans: _____________
5. Work out the area of this parallelogram.
Ans: _____________cm2
6.
Ans: _____________
Find tan C, giving your
answer as a fraction.
6 cm
7 cm 8 cm
4 cm
5 cm
A
B C
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Non-Calculator Paper Page 3 of 5
7. Express 126 as a product of its prime factors.
Ans: _____________
8. Express 50 as a percentage of 200.
Ans: ______________
9. Simon's weekly wage is €250. He is given a pay rise of
4%. Calculate his new weekly wage.
Ans: €_____________
10. Which line, from the four listed below, is parallel to the
line but passes through the point (0, 5)?
A:
B:
C:
D:
Ans: _____________
11. Factorise fully: .
Ans: ____________
12. Expand and simplify:
( )
Ans: ____________
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Non-Calculator Paper Page 4 of 5
13. Find the value of:
(
)
Ans: ____________
14. The diagram shows a prism with a volume of 288 cm3
and a cross-sectional area of 32 cm2. Calculate the
length of the prism.
Ans: ____________
15. A group of 5 students take 36 minutes, 40 minutes, 33
minutes, 37 minutes and 34 minutes respectively to finish
their homework. Calculate the mean time taken by these
students.
Ans: ____________mins
16. Find, giving your answer in index form, the H.C.F. of :
23 × 3
2, 2 × 3
2, 2
2 × 3
3
Ans: ____________
17. Four pencils and three rulers cost €2.40. A pencil and a
ruler cost 70c. What is the cost of a pencil?
Ans: ____________
Cross-
section
Mathematics – Secondary Schools – Scheme A – Form 4 – 2013/2014 – Non-Calculator Paper Page 5 of 5
18. Work out:
4 × 4.5 + 3 × 4.5 + 2 × 4.5
Ans: ____________
19. The perimeter of a square kitchen
tile is 32 cm. Find the area of the
shaded part.
Ans: ____________cm2
20. Find the value of:
72 – 1
Ans: ____________
END OF PAPER
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