verbum dei caro factum est - stmichaelschool.edu.mt

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† Verbum Dei caro factum est

St Michael School Mock Examinations 2018

Mathematics Core Paper

Form 5 Time: 1 hr 40mins

Name and Surname: _____________________________________ Class: Form ___

Attempt all the questions.

This paper carries a total of 80 marks.

You may use a calculator

1. a) There are two types of tourist buses which leave from Pembroke;

one leaves to Zurrieq every 35 minutes

the other leaves to Birzebbugia every 45 minutes

The first trips leave together at 8.15am. At what time will they leave together

again?

(2 marks)

b) Work out the value of the missing angles 𝑥 and 𝑦. Reasons are not required.

𝒙 = _________ , 𝒚 = _________ (2 marks)

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2. The diagram shows two parallel straight-line graphs A and B.

a) Find the gradient of line A.

(2 marks)

b) Write down the co-ordinate of the 𝑦-intercept of line B.

(1 mark)

c) Find the equation of line B.

(1 mark)

d) Write down the 𝑦-coordinate of line B, when the 𝑥-coordinate is 30.

(1 mark)

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3. The diagram shows a circle with centre C.

Two tangents AT and BT meet outside the circle at point T.

a) Show that triangles ACT and BCT are congruent.

(3 marks)

b) Angle TAC is right-angled. Why?

(1 mark)

c) The radius of the circle above is 7cm and the length of AT is 24cm.

Find the length of CT.

(2 marks)

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4. The picture shows a packet of crisps sold at a special offer.

The packet of crisps is now 25% bigger than the usual size.

a) Before the special offer, the packet contained 280g of crisps.

What is the new weight of the packet of crisps?

(2 marks)

b) Since the size of the packet increased, the cost of the packet increased by 10%.

If the new price of the packet is €2.75, how much did the packet cost before the

increase?

(2 marks)

5. Simplify as much as possible:

a) 2(𝑥 − 5) + 𝑥(𝑥2 − 2) b) 3𝑥−12

6𝑥2−24𝑥

(2 marks) (2 marks)

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6.

Doreen is standing on a dock facing a vertical tower TF. Her eyes E are 4 metres above the

water level. EX is an imaginary horizontal line between her eyes and the tower.

a) The 40o angle is called the angle of ___________________ of F from E. (1 mark)

b) Work out the horizontal distance, EX, from Doreen to the tower. Give your answer

correct to 1 decimal place.

(2 marks)

c) Angle TEF is 57°. Work out the height of the tower TF, to 1 dp.

(3 marks)

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7. The diagram below shows the cross-section ABCD of a tent where AD represents

the ground. BC is an arc with centre O and radii OB and OC. O lies on the line AD.

Also, AB = BO = OC = CD = 3 metres.

a) Work out the length of arc BC, to 1 d.p.

(2 marks)

b) The fabric of the front cross-section of this tent needs to be changed. Find the

area of the front cross-section. Give your answer to the nearest m2.

(3 marks)

c) The length of this tent is 7m. Find the volume of this tent.

(1 mark)

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

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

(2 marks)

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

(1 mark)

9. Patrick sold 88 tickets for a rock concert. He sold 𝑥 tickets at €5 each and 𝑦 tickets

at €8 each. He collected €530.

a) Given this information, form two equations.

(2 marks)

b) Solve these equations simultaneously

(4 marks)

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10. A group of 6000 people were asked what type of accommodation they live in. The

following data was recorded:

Type Maisonette Flat House Bungalow Villa

Frequency 1800 3000 700 300 200

a) This data needs to be shown on a pie chart. In the table below, write down the

angle representing each sector in the pie chart.

Type Maisonette Flat House Bungalow Villa

Angle in pie

chart

(3 marks)

b) Draw a pie chart to show this data. The sectors must be clearly labelled.

(3 marks)

c) What percentage of the group live in a maisonette?

(1 mark)

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11. In the diagram below, O is the centre of the circle and ABCD are points on the

circle’s circumference. DOB and COA are the circle’s diameter. The straight lines

EAF and GBF touch the circle’s circumference at the single points A and B

respectively. The lines EAF and GBF meet at a common point F. Also, DĈA = 25o.

Find the size of the following angles, giving reasons for your answers:

a) Angle ADB

(2 marks)

b) Angle AOB

(2 marks)

c) Angle AFB

(2 marks)

Diagram not to scale

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12. Take a look at the following patterns involving black and white circles.

a) Fill in the following table

(2 marks)

b) Find the 𝑛𝑡ℎ term for the white circles.

(2 marks) c) What is the total number of circles in the 200th pattern?

(1 mark)

d) Which pattern number will have 97 black circles?

(1 mark)

13. On the graph paper provided, set up axes from −4 ≤ 𝑥 ≤ 4 and −6 ≤ 𝑦 ≤ 6. For

both axes, use a scale of 2cm as 1 unit.

a) Plot shape ABCD having co-ordinates 𝐴(1,1), 𝐵(2,1), 𝐶(3, 2) and 𝐷(2, 2). (2 marks)

b) Reflect ABCD in the line 𝑥 = 0. Label the new shape 𝐴1𝐵1𝐶1𝐷1. (2 marks)

c) Translate ABCD by column vector (03) in order to obtain shape 𝐴2𝐵2𝐶2𝐷2. (1 mark)

d) Rotate shape ABCD about the origin through an angle of 180° in order to obtain shape

𝐴3𝐵3𝐶3𝐷3. (2 marks)

e) Describe fully the single transformation that maps 𝐴3𝐵3𝐶3𝐷3 to 𝐴2𝐵2𝐶2𝐷2.

(2marks)

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14. Solve

a) 2𝑥 − 5 = 7 b) 7𝑥

5=

2

3

(1 mark) (2 marks)

c) Four children jog round the school track. Mark jogs a distance of 𝑥

2 m. His friend Clive

jogs four times as Mark. Warren jogs 60m less than Clive and Joseph jogs twice as much

as Warren.

i. Express in terms of 𝑥:

Mark: __________________________

Clive: __________________________

Warren: __________________________

Joseph: __________________________ (2 marks)

ii. Together they cover a distance of 14695m. Form an equation and solve it to figure out

the distance Clive jogged. Give your answer in km.

(3 marks)

𝑥

2

verbum dei caro factum est - stmichaelschool.edu.mt

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