Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 1 of 12

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION

Department of Curriculum Management

Educational Assessment Unit

Annual Examinations for Secondary Schools 2016

FORM 4 MATHEMATICS TIME: 1h 40min

Main Paper

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total

Main Non Calc

Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE.

Name: _________________________________ Class: _____________

CALCULATORS ARE ALLOWED BUT ALL NECESSARY WORKING MUST BE SHOWN.

ANSWER ALL QUESTIONS.

Table of Formulae

Curved Surface Area of Right Circular Cone πrl

Surface Area of a Sphere 4𝜋𝑟2

Volume of a Pyramid/Right Circular Cone 1

3 base area × perpendicular height

Volume of a Sphere 4

3𝜋𝑟3

Solutions of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 𝑥 = −𝑏±√𝑏2−4𝑎𝑐

2𝑎

Track 3

Page 2 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

1. Write the following in order, starting from the smallest.

(1

16)

−5

, 8−2, 311, 216.

Ans:____________________________________

(3 marks)

2. Express 𝑡 in terms of 𝑟.

𝑟 =𝑡

3− 4

Ans:________________________

(2 marks)

3. The figure shows a rectangle of length 3x drawn on

a square grid. The perimeter of the rectangle is

30 cm. Calculate the value of x.

Ans: x = __________ cm

(4 marks)

3x

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 3 of 12

4. a) A pyramid has a square base of side 9 cm and

perpendicular height 8 cm. Work out its volume.

Ans:______________ cm3

b) The pyramid above is perfectly joined from its

base to the face of a cube.

What is the total volume of the shape formed?

Ans:____________ cm3

(4 marks)

5.

a) Draw the image of shape ABC after a 90° anticlockwise rotation with centre (0, 0).

Label it A`B`C`.

b) Using ruler and compasses only, construct the locus of points which are equidistant

from the lines AB and BC.

(4 marks)

Name: ________________________________ Class: ______________

9 cm 9 cm

–8 4 6 2 –2 –4 –6

2

4

6

y

0

A B

C

x

Track 3

Page 4 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

6.

The above diagram shows the curve 𝑦 = 2𝑥2 + 2𝑥.

a) The minimum value of 2𝑥2 + 2𝑥 is ______________.

b) By using the above graph, solve the equation 2𝑥2 + 2𝑥 = 3.

Ans:____________or_____________

c) The straight line 𝑦 =1

2𝑥 + 1 passes through the points (–2, 0) and (0, 1). By drawing

this straight line, solve the equation 2𝑥2 + 2𝑥 =1

2𝑥 + 1.

Ans:____________or _____________

(4 marks)

–2 –1 1

–1

1

2

3

x

4

y

0

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 5 of 12

7. The diagram shows a side view of a panoramic

platform. The supporting structure ABC is in the

shape of a right-angled triangle, where AB is

horizontal. AB = 12.34 m and AC = 15.2 m.

a) Work out the length of BC, giving your

answer correct to 1 decimal place.

Ans: ____________ m

b) Calculate the angle of depression of C from B, correct to the nearest degree.

Ans:___________ °

(5 marks)

8. a) Expand 5𝑥(3 − 𝑥) .

Ans: ___________________

b) Factorise 9𝑥2 − 100 .

Ans: _______________________

c) Solve: 4𝑥2 − 17𝑥 = 15 .

Ans: _______________________

(7 marks)

A B

C

Name: ________________________________ Class: ______________ Track 3

Page 6 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

9. a) Prove that in a circle, the angles in the same

segment are equal.

b)

i) p = _________°; Reason: ____________________________________________

ii) Calculate the value of angle q, giving reasons for every step.

(6 marks)

A

B

C

D

p

q

45°

65°

80°

Diagram NOT to scale

O

B A

Q P

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 7 of 12

10.

This is a symmetrical design of a crab. It consists of two identical sectors, a trapezium and

several identical rectangles. The sectors are of radius 6 cm and their angle at the centre is

240°. Each rectangle is 10 cm long and 1.7 cm wide.

a) Calculate the area of one of the sectors, correct to 1 decimal place.

Ans:_______________ cm2

b) Calculate the area of the trapezium.

Ans: _______________ cm2

c) Calculate the total area of the crab.

Ans: ______________ cm2

(6 marks)

22 cm

240°

6 cm

12 cm

26 cm

Page 8 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

11. In a dog competition, the judges Kirsten, Chantelle and Danika categorise the dogs

according to their weight. Every judge uses different groupings to categorise all the dogs.

ii) There is a winner for each section. All dogs have an equal chance of winning.

Kelsey is a dog weighing 6 kg. What is the probability that Kelsey wins its section?

Ans: _________

c) Complete this histogram

displaying Chantelle’s table.

(7 marks)

Kirsten

Weight (w)

in kg

Frequency

5 < w < 7 2

7 < w < 9 1

9 < w < 11 2

11 < w < 13

13 < w < 15 1

15 < w < 17 0

17 < w < 19 0

19 < w < 21 1

21 < w < 23 4

23 < w < 25 1

25 < w < 27 1

27 < w < 29 1

29 < w < 31 3

31 < w < 33 1

33 < w < 35 0

35 < w < 37 3

37 < w < 39 0

39 < w < 41 1

41 < w < 43 1

43 < w < 45 0

Chantelle

Weight (w) in

kg

Frequency

5 < w < 10 4

10 < w < 15 3

15 < w < 20 0

20 < w < 25 6

25 < w < 30 3

30 < w < 35 3

35 < w < 40 4

40 < w < 45

Danika

Weight (w)

in kg

Frequency

5 < w < 25 13

25 < w < 45 11

frequency

0 weight (kg)

5 10 15

a) Use the information in the tables to fill in the 2 empty

boxes.

b) i) In the competition, there is the light-weight section

and the heavy-weight section. Fill in:

The table of judge _______________ best shows

the amount of dogs in these sections because

____________________________________________

____________________________________________

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 9 of 12

12. Neil wants to calculate the electrical consumption of his new A/C. He switches it on and

observes the readings on the electricity meter every minute, for the first 5 minutes.

Meter Reading (units) 1221.0 1221.4 1221.8 1222.2 1222.6 1223.0

Time (min) 0 1 2 3 4 5

a) Plot the straight line graph of meter reading against time.

b) What is the meter reading at the 7th minute?

Ans: _________ units

c) Work out the gradient of the straight line.

Ans: __________

d) If y represents the meter reading and x represents time, show that the equation of

the straight line can be written as 5𝑦 = 2𝑥 + 6105.

e) What is the meter reading at the 55th minute?

(Assume the consumption remains constant.)

Ans: _________ units

(10 marks)

time (min)

meter

reading

(units)

1

1221

1222

2 3 4 5 0

1223

Page 10 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

13. Michaela is making a design of the George Cross. The first step in the design is a cross,

symmetrical about the horizontal and vertical axes. The internal angles A, B, D, E, G, H,

J, K and the external angles C, F, I, L are all right angles. All measurements in the diagram

are in centimetres.

a) Show that the length of BC can be expressed as 10 – x .

b) Show that the area of the cross can be expressed as 𝟖𝒙𝟐 + 𝟒𝟎𝒙 .

2x

2x 20

A B

C D

E F

G H

I J

K L 2x

Diagram NOT to scale

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016 Page 11 of 12

Michaela then designs four quadrants with centres L, C, F and I.

The radius of all the quadrants is x .

c) Taking the value of 𝜋 as 3, show that the total area of the design can be

expressed as 𝟏𝟏𝒙𝟐 + 𝟒𝟎𝒙.

d) Given that the total area of the design is 178 cm2

, work out the value of x ,

correct to 2 decimal places.

Ans: x = ___________ cm

(10 marks)

2x

2x 20

A B

C D

E F

G H

I J

K L

Page 12 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2016

14. a) Janice invests a sum of money. She has two options.

i) Which option is better if she invests her money for 1 year?

Ans: Option ______. Explanation: _________________________________

________________________________________________________

ii) Which option is better if she invests her money for 10 years?

Show your working.

Ans: Option ______

b) Jeremy borrows €1000 from a bank. Interest is to be paid at the rate of 3.5% p.a.

After each year he pays back €300.

i) What is the interest after 1 year?

Ans: €______________

ii) What is the amount of money Jeremy still owes the bank after 2 years?

Ans: €______________

(8 marks)

END OF PAPER

Option A Simple Interest at 3.2% p.a.

Option B Compound Interest at 3% p.a.

p.a.