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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

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Page 1: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 2: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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: _____________

Page 3: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 4: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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)

________________________________________________________________________________

Page 5: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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:

Page 6: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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°

Page 7: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 8: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 9: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 10: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 11: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 12: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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: ____________

Page 13: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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

Page 14: Half Yearly Exams 2013-2014 - Education 4 2013-14 Maths... · Half Yearly Exams 2013-2014 Subject: Mathematics (Main ... leaving Victoria at 08:15 ... plot the line y = 3x + 1. b)

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