year 9 mathematics time: 30 minutes non … the information in (a) and the pie chart ... in any...

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION

Department of Curriculum Management

Educational Assessment Unit

Annual Examinations 2017

YEAR 9 MATHEMATICS TIME: 30 minutes

Non Calculator Paper

Question 1 2 3 4 5 6 7 Total

Mark

DO NOT WRITE ABOVE THIS LINE

Name: _____________________________________ Class: _______________

Instructions to Candidates

Answer ALL questions.

This paper carries a total of 25 marks.

Calculators and protractors are NOT ALLOWED.

All necessary working must be shown.

Track 3

of 4 Mathematics – Non Calculator Paper – Year 9 – Track 3 – 2017

1. a) Tick () the numbers that are in standard form.

6.2 × 105 82.3 × 104 8.0 × 103 0.42 × 102 3.75 × 101

b) Write one of the numbers that you selected as an ordinary number.

Ans: _______________ = ___________________ Standard Form Ordinary Number

[3 marks]

2. Mark invests €5 000 for 2 years at a simple interest rate of 2.5% p.a.

Work out the interest that he receives after 2 years.

Ans: €______________

[2 marks]

3. a) John uses 300 g of ham to prepare sandwiches for a party of ten children.

How much more ham does he need if the guests are increased to 18 children?

Ans: _________ grams

b) 4 workers can paint a fence in 3 hours. If everyone works at the same rate, how long

will it take 6 workers to paint the same fence?

Ans: _________ hours

[5 marks]

Mathematics – Non Calculator Paper – Year 9 – Track 3 – 2017 of 4

4. a) Factorise completely 15x2 – 10xy2 Ans: _______________

b) Simplify 15𝑥2 – 10𝑥𝑦2

5𝑥𝑦

Ans: _______________

c) Hence or otherwise find the value of 15𝑥2 – 10𝑥𝑦2

5𝑥𝑦 when x = 2 and y = 3.

Ans: _______________

[5 marks]

5. a) Write 32 as a fraction.

Ans: _________

b) Work out 𝟏𝟑

𝟖+

𝟓

𝟏𝟐 , giving your answer as a mixed number.

Ans: _________

c) Evaluate i) 140 Ans: _________

ii) 53×55

56

Ans: _________

[6 marks]

of 4 Mathematics – Non Calculator Paper – Year 9 – Track 3 – 2017

6. a) Write down the length of AC.

Ans: AC = ___________ cm

b) If AC = 2x + 5, work out the value of x.

Ans: x = ____________

[3 marks]

7. This is the graph of y = 3x – x2.

Use your graph to solve the equation 3x – x2 = –3.

Ans: x = _________ or __________

[1 mark]

END OF NON CALCULATOR PAPER

A

B C

5 cm

12 cm

y = 3x – x2

0 x

y

Mathematics – Main Paper – Year 9 – Track 3 – 2017 Page 1 of 10

DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION

Department of Curriculum Management

Educational Assessment Unit

Annual Examinations 2017

YEAR 9 MATHEMATICS TIME: 1h 30min

Main Paper

Question 1 2 3 4 5 6 7 8 9 Total

Main

Non

Calc Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE

Name: _____________________________________ Class: _______________

1. Two dice, one 4-sided and another 6-sided, are tossed.

The numbers obtained are multiplied.

a) Fill in the possibility space to show all the products obtained.

6-sided dice

× 1 2 3 4 5 6

4-s

ided

dic

e 2 2 4 6 8 10 12

3 3 12

5 5 15 30

7 7 35

b) Work out the probability that the two dice give a square number as a product.

Ans: ______________

c) What is the probability of obtaining a product which is an even multiple of 3?

Ans: ______________

[3 marks]

Calculators are allowed but all necessary working must be shown.

Answer ALL questions.

Track 3

of 10 Mathematics – Main Paper – Year 9 – Track 3 – 2017

2. Thea uses the formula S = 180n – 360 to find the sum, S, of the interior angles of a polygon

with n sides.

a) i) Make n the subject of the formula.

Ans: n = ______________

ii) The interior angles of Thea’s regular polygon add up to 1440°.

Show that her polygon is a decagon (10 sides).

b) Thea creates a tessellation pattern around her regular decagon, using regular

pentagons. Part of her pattern is shown below.

i) Work out the value of each interior angle x.

°

Ans: x = __________

ii) Use Thea’s formula for the sum, S, of the interior angles of a

polygon, to calculate the value of angle y.

°

Ans: y = __________

iii) Explain why it was possible for Thea to create this tessellation.

___________________________________________________

___________________________________________________

[8 marks]


3. John is forming patterns with black and white circles as shown below.

Pattern 1 Pattern 2 Pattern 3 Pattern 4

a) Draw the 4th Pattern.

b) Fill in the following table.

Pattern number 1 2 3 4 5

Black Circles 2

White Circles 2

Total number of circles 4

c) Fill in the blanks. In the 8th Pattern John will use _______ black circles

and_______ white circles, that is a total of ______ circles in all.

d) Write down the nth terms for the following sequences.

i) The number of black circles used ____________________

ii) The number of white circles used ____________________

iii) The total number of circles used ____________________

e) John notices that the total number of circles is always even.

Explain why this happens.

____________________________________________________________________

____________________________________________________________________

[10 marks]

Name: ____________________________________ Class: _____________

Track 3


H

N

4. Ship S is sailing 75 km away from Harbour H, on a bearing of 036°.

Tanker T is 48 km away from Harbour H on a bearing of 306°.

a) Fill in all the above details in the rough sketch below to show the positions of the ship

S and the tanker T.

°

b) Fill in the blanks. The bearing of harbour H from tanker T is___________ .

c) Explain why THS = 90°.

d) Calculate HST.

°

Ans: _____________

e) Work out the distance between the tanker and the ship.

Ans: __________ km

[10 marks]


5. a) The circle below has centre O and radius 4.5 cm. Work out its circumference.

Ans: _______________ cm

b) Using ruler and compasses only, inscribe hexagon ABCDEF in the circle above.

Label all the vertices.

c) i) Join points A to C, C to E and E to A, to form ACE.

ii) Shade the area within the circle but outside ACE.

d) Take all the necessary measurements from your construction to work out the

following, giving your answers correct to the nearest cm2.

i) area of the circle ii) area of triangle ACE iii) the shaded area

Ans: __________ cm2 Ans: __________ cm2 Ans: __________ cm2

[10 marks]

Name: ____________________________________ Class: _____________

Track 3

O A


6. A magazine compared the lifetime of two different batteries, ALFA and BETA.

a) The experiment gave the following readings (in hours) for the ALFA batteries.

ALFA

Battery

lifetime

(hours)

1.5 2 2 2.5 3 3 3 3.5 4 4

4.5 5 5 5 5.5 6 6 6 6 6

6 6.5 7 7 7.2 7.5 8 8.5 9 9

i) Work out the mean lifetime for the ALFA batteries. Show all your working.

Ans: _________________ hours

ii) What is the modal lifetime? Ans: _________________ hours

b) A total of 48 BETA batteries were also tested for their lifetime, t, in hours.

The data collected is shown in the pie chart below.

BETA Battery lifetime (hours)

Use the information in (a) and the pie chart above to complete the following frequency

table.

Battery Lifetime (hours)

1 < t ≤ 3 3 < t ≤ 5 5 < t ≤ 7 7 < t ≤ 9

ALFA 7 6

BETA 4 12

3 < t ≤ 5

5 < t ≤ 7

1 < t ≤ 3

7 < t ≤ 9


c) i) Write the probability that an ALFA battery chosen at random satisfies this label.

Ans: __________

ii) You want a battery with a greater chance of lasting more than 7 hours.

Which of these batteries would you choose? Give a reason for your answer.

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

[9 marks]

7. a) Complete the following fact.

In any circle an angle at ___________ is ____________ the angle at circumference.

b) Use the fact above to show thatABC = 90°.

_____________________________________________

_____________________________________________

_____________________________________________

c) Find the value of the missing angles x, y, and z in the diagram below.

°

Ans: x = ___________ ; Reason: ___________________________

°

y = ___________ ; Reason: ___________________________

°

z = ___________ ; Reason: ___________________________

[8 marks]

Battery life

(hours) 6 7 8 9 10

B

O

C

A

B

O

C

A

D z

x

y

63°


8. Containers A and B are both cylindrical but have different sizes.

Water flows in each container at a constant rate.

The graph below shows the % height that is filled

with water in each container in t seconds.

a) The water flow stops after 40 seconds. Which container is completely full?

Ans: Container _______

b) i) Fill in. After 25 seconds container A is ______% full.

ii) After 25 seconds the height of water in container A is 16.8 cm.

Calculate the height, h, of container A.

Ans: h = ________ cm

A

B

h

0 5 10 15 20 25 30 35 40 t0

20

40

60

80

100A

B

t (seconds)

% h

eig

ht


c) Container A has a radius of 10.3 cm.

Calculate its maximum volume, giving your answer correct to 1 significant figure.

Ans: ___________ cm3

d) The ratio of the height of container A to the height of container B is 3 : 5.

Work out the height of container B.

Ans: ___________ cm

e) The radius of container B is 9.8 cm.

Work out the curved surface area of container B.

Ans: __________ cm2

[10 marks]


9. In this puzzle, each symbol stands for an unknown number.

The number at the end of each row gives the total of all the numbers in that row.

a) Using x to represent the number that ‘’ stands for and y to represent the number

that ‘’ stands for, write two equations in terms of x and y.

Ans: ___________________ and ___________________

b) Solve the two simultaneous equations found in (a).

Ans: x = ____________ and y = ____________

c) Give the total of the third row.

Ans: __________

[7 marks]

END OF EXAM

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year 9 mathematics time: 30 minutes non … the information in (a) and the pie chart ... in any...

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