DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION

Department of Curriculum Management

Educational Assessment Unit

Annual Examinations for Secondary Schools 2015

FORM 4 MATHEMATICS TIME: 20 minutes

Non Calculator Paper

Name: _________________________________ Class: _____________

Instructions to Candidates

Answer all questions.

This paper carries a total of 20 marks.

Calculators and protractors are NOT ALLOWED.

Track 3

Mark

Page 2 of 5 Mathematics – Non Calculator – Form 4 Secondary – Track 3 – 2015

No. Question Space for working,

if required.

1 Write 210 as a product of prime factors.

Ans: 210 = ______________________

2 This is a prism with area of

cross section 2.7 cm2 and

depth 6 cm.

Work out its volume.

Ans:____________ cm3

3 Convert 300 mm3 into cm

3.

Ans: ____________cm3

4 Use this grid to draw the

translation of point P

using the vector ( 3

−4).

Label the image Q.

5 Work out the area of this triangle.

Ans: ____________cm2

6 What is the value of x in 2x

+ 3 = 19?

Ans: x =___________

6 cm

3 cm

5 cm

2

2

4

6

–2

-2

–2 – 4

P

x

y

0

Mathematics – Non Calculator – Form 4 Secondary – Track 3 – 2015 Page 3 of 5

7

This square based pyramid is

of perpendicular height

100 cm.

Find its volume in cm3.

(Volume of pyramid = 1

3 base area × perpendicular height)

Ans: ____________cm3

8 Use the two lines,

displayed on this grid, to

solve the simultaneous

equations:

3y – 6 = 2x

y = 2x – 2

Ans: x = ______; y =______.

9 What is the area of trapezium ABCD?

Ans: _______________mm2

10 Make f subject of the formula:

𝟑𝒇 = 𝟓 + 𝒂𝒇

Ans: ___________________

30 cm 30 cm

3y = 2x + 6 y = 2x – 2

2

2

4

6

–2

-2

–2

64 mm

36 mm

32 mm

A B

C D

x

y

Name: ________________________________ Class: ______________ Track 3

0

Page 4 of 5 Mathematics – Non Calculator – Form 4 Secondary – Track 3 – 2015

11 The radius of this circle is

60 cm.

Work out the length of the

minor arc AB. Give your

answer in terms of π.

Ans: _______________ cm

12 Evaluate: 6.22 – 3.8

2

Ans: ___________________

13 A and B are two points, 100 turtle steps apart. Point A is

vertically above the turtle.

In the following procedure, the turtle draws the locus of points

equidistant from A and B. Write down the missing numbers.

PU

FD ______

LT ______

PD

FD 100

14 Arrange in order, smallest first:

20, (–2)

2, 2

–2, –2

2

Ans: __________________________________

15 Jeremy’s salary is €1000. What is the overall percentage

increase when his salary first increases by 20%, then increases

again by another 20%?

Ans: _________%

A

B

120°

A B

Mathematics – Non Calculator – Form 4 Secondary – Track 3 – 2015 Page 5 of 5

16

Simplify completely: √16𝑝4

49 × 64𝑞2

Ans: ___________________

17 1 gram of lead occupies a volume of 𝟗 × 𝟏𝟎−𝟖 m3. What is

the volume of lead occupied by 𝟖 × 𝟏𝟎𝟓 grams of lead? Give

your answer in standard form.

Ans: ________________m3

18 Write down a simplified

expression, in terms of a, for

the volume of this cuboid.

Ans: ___________________

19 Make x subject of the formula, simplifying your answer

completely.

3𝑥2𝑦2 =27

16

Ans: ___________________

20 Given that 𝐓𝐚𝐧 𝟐𝟏° =𝟓

𝟏𝟑, use the diagram below to work out

the value of: 𝒙

𝒚 .

Ans: ___________________

END OF PAPER

y

x

21°

4a5

3a4

a

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 1 of 12

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department of Curriculum Management Educational Assessment Unit Annual Examinations for Secondary Schools 2015

FORM 4 MATHEMATICS TIME: 1h 40min Main Paper

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

Volume of a Pyramid/Right Circular Cone basearea perpendicularheight

Volume of a Sphere

Solutions of 0 √

Track 3

Page 2 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

1. a) Underline the correct answers: The transformation which maps triangle P to triangle Q is a (reflection, translation, enlargement, rotation) in the (line y = 2, line x = 5, x-axis, y-axis). b) On the grid above, rotate triangle P, 90° anticlockwise about O. Label it R. c) On the grid above, enlarge triangle P using scale factor 2 and centre (7, 0). Label it S.

(6 marks) 2. a) Expand 2 3 4

Ans_____________ b) Solve 2 5 12 0

Ans x =______ or x = ______

(4 marks)

2

4

6

8

y

PQ

–8 4 62–2–4 –6 – 10 8 10 12x

O

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 3 of 12

3.

A pack is made up of cards with numbers from 1 to 7. Two cards are going to be drawn, without replacing the first one.

a) Complete the probability tree for odd and even numbers to be drawn. b) What is the probability that both cards drawn show an odd number?

Ans__________ c) A third card is now going to be drawn (without replacing the first and second cards). What is the probability that the three cards show an odd number?

Ans__________

(6 marks)

1st card 2nd card

1 2 3 4 5 6 7

Name: ________________________________ Class: ______________

Track 3

Page 4 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

4. a) In the space below, use compasses only to construct a regular hexagon of side 5 cm. Label it ABCDEF. b) Shade the region consisting of all the points inside the hexagon which are less than

or equal to 3 cm away from point F.

(4 marks) 5. a) Fill in: 12 5 0 is the same as 12 36 . b) Factorise 12 36

Ans__________________

c) Use the method of completing the square to solve the equation 12 5 0. Give your answers correct to 2 decimal places.

Ans x =________ or x = ________

(6 marks)

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 5 of 12

6. The diagram shows part of a scaffolding. X, A and B are points on the scaffolding and

angle XAB is 90°. The length from X to A is 4.2 m. A worker ties a rope from X to B. a) Use the above information to decide whether the rope’s length is greater, smaller or

equal to 4.2 m long. Explain.

_____________________________________________________________________

_____________________________________________________________________

b) The angle of elevation of X from B is 52°. Mark this angle on the diagram. c) Work out the length of AB, giving your answer correct to 2 decimal places.

Ans____________m d) Use Pythagoras’ Theorem to work out the length of XB. Give your answer

correct to 1 decimal place.

Ans__________m

(8 marks)

X

B

4.2 m

A

Track 3

Name: ________________________________ Class: ______________

Page 6 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

7.

a) Complete the table:

Design 1 2 3 4 5

Number of squares 4 7 10

Number of circles 2 2 2

TOTAL number of shapes 6 9 12 b) Work out an expression for the total number of shapes in design n.

Ans___________

c) What is the total number of shapes in design 100?

Ans___________

d) From design 2 onwards, there are 3 horizontal layers of squares. Explain why design 1 has only 2 horizontal layers.

_________________________________________________________________________

_________________________________________________________________________

(7 marks) 8. In 2014, the tribe population of Brazil was . . To calculate the population in

2015, this figure is multiplied by 0.96. a) What is the calculated population in 2015? Give your answer in standard form, correct to 2 decimal places.

Ans_________________people

b) What is the calculated percentage decrease in population between 2014 and 2015?

Ans___________%

c) If the population continues to decrease at the same rate each year, what is the calculated population in 2024? Give your answer in standard form, correct to 1 decimal place.

Ans__________________ people

(6 marks)

Design 1 Design 2 Design 3 Design 4

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 7 of 12

9. This graph represents the journey of the Gozo ferry from Mġarr to Ċirkewwa. a) What is the distance between Mġarr and Ċirkewwa?

Ans__________km

b) What was the speed of the ferry in the first 7 minutes? Give your answer in km/min, correct to 2 significant figures.

Ans____________km/min

c) For how long did the ferry stop moving?

Ans_________min

d) A boat departed from Mġarr at 08:34 and reached Ċirkewwa at 09:00. It travelled at constant speed without stopping.

i) On the grid above, draw a graph representing the boat’s journey. ii) At 08:36, was the boat moving faster, slower or at the same speed as the ferry? Explain.

______________________________________________________________

______________________________________________________________

(7 marks)

Time

Distance (km)

08:30 08:40 08:50 09:00

1

2

3

4

0 Mġarr

Ċirkewwa

Page 8 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

10. In a photo competition on internet, 61 photos were submitted. The one getting the greatest number of Likes is the winner.

Below is a summary of the results.

Number of Likes 0 – 49 50 – 99 100 – 149 150 – 199 200 – 249 Frequency

(number of photos) 7 12 17 18 7

a) Which is the modal class?

Ans_______________ b) In which class interval does the median lie? Show your working.

Ans_______________ c) Louisanne says, “There are 7 winners in this competition”. Do you agree with her? Explain.

____________________________________________________________________ ____________________________________________________________________

(4 marks)

11. A rectangle is cm long and cm

wide. The rectangle is divided into smaller identical rectangles as shown.

a) Fill in:

Each of the smaller rectangles is

cm long and cm wide.

b) If the perimeter of each of the smaller rectangles is 15 cm, show that

15.

c) Solve the equation 15.

Ans x = ______

(6 marks)

x

(x + 9)

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 9 of 12

12. In the diagram below, O is the centre of the circle and PQ is a tangent to the circle at A. Find the value of angles a, b, c and d. Give reasons for all your workings.

a =______ Reason: ___________________________________________________________ b =______ Reason:____________________________________________________________ c =_______ Reason:____________________________________________________________ d =______ Reason:____________________________________________________________

(8 marks)

P

A

Q

B

C

D

110°

60° a b

c

d

E

O

Diagram NOT to scale

°

°

°

°

Page 10 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

13. Kurt uses a canon to fire a ball vertically upwards. The height of the ball above the ground is given by .

h is the height in metres and t is the time in seconds from the release of the ball. a) Complete the table.

t 0 1 2 3 4 5 6 7

35t 0 35 105 140 175 245

–5t 2 0 –5 –45 –80 –125 –245

h 0 30 60 60 50 0 b) Using the grid on the opposite page, draw the graph of . c) What is the maximum height reached by the ball?

Ans__________metres d) On the same axes, draw a suitable line to solve the equation:

e) Write down the times at which the ball reaches a point which is 47 metres above the ground.

Ans__________seconds and ___________seconds

(8 marks)

Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015 Page 11 of 12

END OF PAPER

Page 12 of 12 Mathematics – Main Paper – Form 4 Secondary – Track 3 – 2015

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