Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 1 of 12

DEPARTMENT FOR CURRICULUM,

RESEARCH, INNOVATION AND LIFELONG LEARNING

Directorate for Learning and Assessment Programmes

Educational Assessment Unit

Annual Examinations for Secondary Schools 2018

YEAR 10 MATHEMATICS TIME: 1h 40min

Main Paper

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

Main

Non

Calc Global

Mark

Mark

DO NOT WRITE ABOVE THIS LINE

Name: _____________________________________ Class: _______________

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 Sphere 4

3πr3

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

2𝑎

Calculators are allowed but all necessary working must be shown.

Answer all questions.

Track 3

Page 2 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

1. Light takes 8.283 minutes to travel from the surface of the Sun to the Earth.

a) Write this time in hours, giving your answer in standard form.

Ans: _________________ hours

The speed of light is 1.08 × 109 km/h.

b) Fill in the blanks, giving your answer in standard form:

The distance between the Sun and the Earth is approximately km.

(4 marks)

2. In the diagrams below, the top brick is the product of the factors in the two bricks below it.

Fill in the empty bricks.

(4 marks)

5 x + 3

3x2 + 12

3x2 – 19x – 14

Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 3 of 12

3. a) A can of tomato paste has a radius of 3.6 cm and is 11 cm high.

i) Work out the total surface area of the metal used to make the

closed cylindrical can.

Ans: Total Surface Area = _________________ cm2

ii) Each can is completely full. Calculate the volume of tomato paste in one can.

Give your answer correct to the nearest cm3.

Ans: Volume = __________________ cm3

b) The supplier is offering a bigger can at the same price.

Its new weight is 600 g instead of 480 g.

Fill in the special offer label with the percentage increase.

(7 marks)

Name: ____________________________________ Class: ___________ Track 3

Page 4 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

4. At ‘Watch It First’ cinema complex there are 210 clients watching a particular film.

The table and histogram below show the data collected about their ages.

Age Frequency

0 < age ≤ 10 10

10 < age ≤ 20 16

20 < age ≤ 30 89

30 < age ≤ 40

40 < age ≤ 50

50 < age ≤ 60 21

60 < age ≤ 70 4

a) Use the information above to complete the frequency table and the histogram.

b) What is the modal age group? Ans: ___________________

c) Estimate the mean age of the clients watching the film.

Ans: ___________________

A one-year cinema ticket is to be drawn as a prize among the clients watching this film.

d) What is the probability that the prize winner is aged over 50 years?

Ans: ___________________

(10 marks)

F

req

uen

cy

0

Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 5 of 12

5. From a piece of cardboard Alan cuts out a sector of radius 28 cm, as shown in the diagram below.

a) Work out the area of cardboard that he cuts.

Ans: _____________ cm2

b) The curved surface area of a cone is given by A = rl.

Make r the subject of this formula.

Ans: r = _____________

c) Alan uses the sector above to form a cone, without overlapping any cardboard.

Work out the radius of the base of the cone, giving your answer correct to 1 decimal

place.

Ans: r = ___________ cm

(5 marks)

235°

Name: ____________________________________ Class: ___________ Track 3

Page 6 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

6. The back door of a truck is transformed into a ramp as shown in the diagram below. The vertical height of the base of the truck from the ground is 0.9 m.

The ramp reaches a horizontal distance of 2.94 m on the ground.

a) Work out the angle that the ramp makes with the ground.

°

Ans: __________________

The ramp may be extended further.

When extended to its full length, the ramp touches the ground at an angle of 11.5°.

b) Find the extra horizontal distance (x metres) reached by the fully extended ramp.

Ans: ________________ m

c) Calculate the length of the fully extended ramp.

Ans: ________________ m

(7 marks)

0.9 m

2.94 m

x metres 2.94 m

Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 7 of 12

7. On this map, using ruler and compasses only, construct:

a) The locus of points 3 cm away from point A.

b) The locus of points equidistant from B and C.

c) The locus of points equidistant from AB and BC.

The above is a map of a treasure island with a scale of 1 cm = 1 m.

Jack finds this treasure map along with the following clues.

d) Using your constructions on the map above, shade the region where the treasure is hidden.

(6 marks)

A

B C

Page 8 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

2.4 m

x metres

8. This tent frame is in the form of a prism and is made of aluminium tubing.

DIAGRAM NOT DRAWN TO SCALE

The depth, y, is 0.4 m shorter than twice the vertical length x.

a) Express y in terms of x.

Ans: y = _______________

Jason buys a tent which uses 36 m of tubing.

b) i) Show that 14x + 8 = 36.

ii) Solve this equation to find x.

Ans: x = _____________

Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 9 of 12

The highest point of Jason’s tent is 2.5 m above the ground.

c) Work out the area of the cross-section of Jason’s tent.

Ans: _____________ m2

d) i) Find the value of y.

Ans: y = _____________

ii) Calculate the volume of air inside Jason’s tent.

Ans: _____________ m3

(11 marks)

Page 10 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

9. This table of values gives the coordinates of points on the curve y = x2 – 3x + k.

x 2 1 0 1 2 3 4 5

y 6 0 4 6 6 4 0 6

a) Use a pair of coordinates from the table to determine the value of k.

Ans: k = _____________

b) Plot the graph using the given table of values above.

c) What is the minimum value of the graph? Ans: y = _____________

d) Use your graph to solve the equation x2 – 3x – 8 = 0.

Ans: x = ___________________

(9 marks)

-2 -1 1 2 3 4 5

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

y

x 0

x

Mathematics – Main Paper – Year 10 – Track 3 – 2018 Page 11 of 12

10. a) AP is a tangent to circle centre O and ABCD is a cyclic quadrilateral.

Work out the values of angles a, b and c, giving reasons for your answers.

°

Ans: a = ________ reasons: ____________________________________________

°

b = ________ reason: _____________________________________________

°

c = ________ reason: _____________________________________________

b) AC is a tangent to circle centre O. In AOC, angles x and y are in the ratio 1 : 2.

Work out the value of angle z.

°

Ans: z = ______________

(10 marks)

O

A C

B

y

x

z

DIAGRAM NOT DRAWN TO SCALE

A

B O

b

C

72° P D

65°

c

a

DIAGRAM NOT DRAWN TO SCALE

Page 12 of 12 Mathematics – Main Paper – Year 10 – Track 3 – 2018

11.

DIAGRAM NOT DRAWN TO SCALE

a) Show that P, the perimeter of this triangle, can be simplified to P = x2 + 8x + 7

x.

b) The perimeter of this triangle is 20 cm.

Write down an equation and solve it to find the value of x, giving your answer correct

to 1 decimal place.

Ans: x = ____________

(7 marks)

END OF EXAM

9 – 2x

7

𝑥

3x 1