YEAR 9 Mathematics TIME: 1h 30min Main Paper

Mathematics – Main Paper – Year 9 – Track 3 – 2021 Page 1 of 12

DEPARTMENT FOR CURRICULUM,

LIFELONG LEARNING AND EMPLOYABILITY

Directorate for Learning and Assessment Programmes

Educational Assessment Unit

Annual Examinations for Secondary Schools 2021

YEAR 9 Mathematics TIME: 1h 30min

Main Paper

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

Main

Non

Calc

Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE.

Name: _____________________________________ Class: _______________

Track 3

Answer all questions.

Calculators are allowed but all necessary working must be shown.

Page 2 of 12 Mathematics – Main Paper – Year 9 – Track 3 – 2021

1. (a) Round each number to the nearest whole number and find an approximate

value for:

3.822 × 1.13

20.1 − 11.97≈

Ans: ______________

(b) Work out the value for (a) using your calculator.

Give your answer correct to 2 decimal places.

Ans: ______________

(c) Round the following numbers as indicated in brackets:

(i) 393.4 (2 significant figures) Ans:______________

(ii) 0.00792 (1 significant figure) Ans: ______________

(5 marks)

2. (a) Expand and simplify: (𝑥 + 3)(𝑥 − 4)

Ans: ______________

(b) Simplify:

2𝑎2𝑏

8𝑎𝑏3

Ans: ______________

(c) Factorise completely: 4𝑥2𝑦 − 2𝑥𝑦2

Ans: ______________

(5 marks)


3. Sam and Herman go to a sweet shop. Sam has a 10c, a 20c, a 50c and a €1 coin

in his pocket, while Herman has a 5c, a 10c, a 20c and a 50c coin in his pocket.

They decide to take out one coin each at random from their pockets. They will

then buy some sweets with the sum of the two coins picked.

(a) Complete the table below which shows all the possible sums of money of the

two coins.

Sam

10c 20c 50c 100c

Herm

an

5c 15

10c 60

20c 40 120

50c 60 70

(b) What is the probability that the total sum of the two coins is less than 30

cent?

Ans: ________

(c) What is the probability that they spend more than 50 cent?

Ans: ________

(d) What is the probability that the total sum is a multiple of 10?

Ans: ________

(5 marks)


4. A retail outlet is closing down and the owner puts a 60% off sale on all the prices.

Tania went to check some offers for her new apartment.

(a) The price of the washing machine was €500 before the sale.

What is the sale price?

Ans: ______________

(b) The sale price of an oven is marked €140.

What was the price of the oven before the sale?

Ans: ______________

(c) If Tania buys all the three appliances during the sale, she will be given a

further 10% discount on the total sale price. How much will she pay?

Ans: ______________

(7 marks)


5. The diagram represents a triangle ABC.

(a) The perimeter of the triangle is 84 cm. Form an equation and solve it for 𝑥.

Ans: 𝑥 = ________

(b) Work out the length of each side of the triangle.

Ans: ______cm, ______cm, ______cm

(c) Show that triangle ABC is right-angled.

(6 marks)

6𝑥 + 2

2𝑥 + 1

A

B C

Diagram not drawn to scale


6. Simple Interest is calculated using the formula 𝐼 =𝑃𝑅𝑇

100.

(a) Make 𝑇 the subject of the formula.

Ans: ______________

(b) Mike invested €2000 in a bank at 3% simple interest. After some years he

decided to withdraw the money earning an interest of €900. For how many

years did he invest his money in the bank?

Ans: ______________

(4 marks)

7. (a) The image shows an aerial view

of a military building in America.

Given that the shape is a regular polygon,

work out the size of each interior angle.

Ans: ______________

(b) Each interior angle of another regular polygon measures 120°.

How many sides does the polygon have?

Ans: ______________

(5 marks)

°


8. (a) The difference in the price of a doughnut and that of a muffin is 20 cent,

the doughnut being more expensive than the muffin. Let 𝑥 represent the

cost of a doughnut and 𝑦 represent the cost of a muffin. Write down an

equation representing this information.

Ans: ______________

(b) The price of two doughnuts and three muffins is €2.60. Write down another

equation in terms of 𝑥 and 𝑦.

Ans: ______________

(c) Solve these two equations simultaneously to find the cost of one doughnut

and the cost of one muffin.

Ans: 𝑥 = ____________, 𝑦 = ____________

(5 marks)


9. The diagram below represents a circle centre O. Find the size of the angles

marked 𝑎, 𝑏, 𝑐 and 𝑑, giving reasons for your answers.

𝑎 = ___________ Reason: _________________________________________

𝑏 = ___________ Reason: _________________________________________

𝑐 = ___________ Reason: _________________________________________

𝑑 = ___________ Reason: _________________________________________

(8 marks)

°

°

°

°

100°

𝑏

48°

𝑎

𝑐

𝑑

O



10. The following shapes are made up of dots.

A sequence of shapes is formed by placing dots next to each other as shown above.

The first three shapes are done for you.

(a) Draw Shape 4 in the space provided above.

(b) Complete the following table:

(c) Which shape number has 103 dots?

Ans: ______________

(5 marks)

Shape Number 1 2 3 4 5 6 10 𝑛th term

Number of dots 1 4 7

Shape 1 Shape 3 Shape 2 Shape 4


11. (a) A champagne cooler is in the shape of a cylinder with height 25 cm and

diameter 20 cm.

(i) Work out the volume of the cooler. Give your answer correct to the

nearest whole number.

Ans: ______________ cm3

(ii) The waiter dropped an empty cooler on the floor and it rotated onto

its side making three full revolutions. How far, in cm, did the cooler

roll on the ground? Give your answer correct to 3 significant figures.

Ans: ______________ cm

(b) Calculate the perimeter of the following sector.

Ans: ______________ cm

(7 marks)

25 c

m

20 cm

40°

cm


12.

(a) Work out the gradient of the line shown on the grid above.

Ans: ______________

(b) Underline the correct equation of the line shown on the grid above.

𝑦 = 2𝑥 + 3 𝑦 + 1 = 2𝑥 𝑦 = 1 − 2𝑥

(c) On the same axes, plot the line 𝑦 = −𝑥 − 4.

(d) Use the two graphs to solve the simultaneous equations:

2𝑥 − 𝑦 = 1

𝑥 + 𝑦 = −4

Ans: 𝑥 =________, 𝑦 =_________

(6 marks)

𝑥

𝑦

1

2

3

4

−1

−2

−3

−4

1 2 3 4 −1 −2 −3 −4 O


13. A vertical lamp post XY is 3.2 m high. A and B are two points on the ground. The

angle of elevation of the top of the lamp post from a point B is 42°. AX = 6.4 m.

(a) Calculate the size of angle AX̂Y.

Ans: ______________

(b) Work out the length of AB.

Ans: ______________ m

(7 marks)

End of Main Paper

°

3.2 m

X

Y B A

42°

6.4 m


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YEAR 9 Mathematics TIME: 1h 30min Main Paper