1. The base of a rectangular tank is 1.2 metres by 0.9 metres.

The water in the tank is 53 centimetres deep.

Calculate the number of litres of water in the tank.

Answer ....................................... litres [2]

2. Factorise 14 p2 +21 pq .

Answer ................................................ [2]

3.

The diagram shows a circle, centre O.

Find the value of x.

Answer x = ................................................ [2]

4. Ahmed, Batuk and Chand share $1000 in the ratio 8 : 7 : 5.

Calculate the amount each receives.

Answer :Ahmed $ ................................................

Batuk $ ................................................

Chand $ ................................................ [3]

5. Pavan saves $x each month.

His two brothers each save $4 more than Pavan each month.

Altogether the three boys save $26 each month.

(a) Write down an equation in x.

Answer(a) ..........................................................................[1]

(b)Solve your equation to find the amount Pavan saves each month.

Answer(b) $ ................................................. [2]

6. Solve the simultaneous equations. You must show all your working.

1
x−8 y=1
2
1
x+ 2 y =6
2

Answer x = ................................................

y = ................................................ [3]

7. The population of Olton is decreasing at a rate of 3% per year.

In 2013, the population was 50 000.

Calculate the population after 4 years.

Give your answer correct to the nearest hundred.

Answer ................................................ [3]

 7 5
8. Without using your calculator, work out 2 ÷
9 6

Give your answer as a fraction in its lowest terms.

You must show each step of your working.

Answer ................................................ [3]

9. Fritz drives a distance of 381 km in 2 hours and 18 minutes.

He then drives 75 km at a constant speed of 30 km/h.

Calculate his average speed for the whole journey.

Answer ....................................... km/h [3]

10. Jaideep builds a house and sells it for $450 000.

(a) He pays a tax of 1.5% of the selling price of the house.

Show that he pays $6750 in tax.

Answer(a)

[1]
(b)$6750 is 12.5% more than the tax Jaideep paid on the first house he built.

Calculate the tax Jaideep paid on the first house he built.

Answer(b) $ .................................................[2]

(c)The house is built on a rectangular plot of land, 21 m by 17 m, both correct to the nearest metre.

Calculate the upper bound for the area of the plot.

Answer(c) ........................................... m2 [2]

(d)On a plan of the house, the area of the kitchen is 5.6 cm2 .

The scale of the plan is 1: 200.

Calculate the actual area of the kitchen in square metres.

Answer(d) ........................................... m2 [2]

(e)The house was built using cuboid blocks each measuring 12 cm by 16 cm by 27 cm.

Calculate the volume of one block.

Answer(e) ......................................... cm 3 [2]

 (f)Jaideep changes $12 000 into euros (€) to buy land in another country.

The exchange rate is €1 = $1.33 . Calculate the number of euros Jaideep receives.

Give your answer correct to the nearest euro.

Answer(f) € ................................................. [2]

11. In this question, all lengths are in centimetres.

ABCD is a trapezium with area 15 cm2.

(i) Show that 2 x 2 +5 x – 12=0 .

Answer(i)

[3]
 (ii) Solve the equation 2 x 2 +5 x – 12=0 .

Answer(ii) x = .................... or x = .................... [3]

(iii) Write down the length of AB.

Answer(d)(iii) AB = .......................................... cm [1]

12. (a)The diagram shows a sector of a circle

with centre O and radius 24 cm.

(i)The total perimeter of the sector is 68 cm.

Calculate the value of x.

Answer(a)(i) x = ................................................ [3]

(ii)The points A and B of the sector are joined together to

make a hollow cone.

The arc AB becomes the circumference of the base of the cone.

Calculate the volume of the cone.

1 2
[The volume, V, of a cone with radius r and height h is V = π r h ]
3

Answer(a)(ii) ......................................... cm3 [6]

(b)

The diagram shows a shape made from a square, a quarter circle and a semi-circle.

OPXY is a square of side 8 cm.

OPQ is a quarter circle, centre O.

The line OMQ is the diameter of the semi-circle.

Calculate the area of the shape.

Answer(b) ......................................... cm2 [5]

13. aAt noon the temperature was 4 °C.

At midnight the temperature was –5.5 °C.

Work out the difference in temperature between noon and midnight.

Answer ........................................... °C [1]

14. Rice is sold in 75 gram packs and 120 gram packs.

The masses of both packs are given correct to the nearest gram.

Calculate the lower bound for the difference in mass between the two packs.

Answer ............................................. g [2]

15. Georg invests $5000 for 14 years at a rate of 2% per year compound interest.

Calculate the interest he receives.

Give your answer correct to the nearest dollar.

Answer $ ................................................ [3]

16. (a)Write 30 as a product of its prime factors.

Answer(a) ................................................[1]

(b)Find the lowest common multiple (LCM) of 30 and 45.

Answer(b) ................................................ [2]

17.

The diagram shows a toy.

The shape of the toy is a cone, with radius 4 cm and height 9 cm, on top of a hemisphere with

radius 4 cm.

Calculate the volume of the toy. Give your answer correct to the nearest cubic centimetre.

1 2
[The volume, V, of a cone with radius r and height h is V = π r h ]
3

4 3
[The volume, V, of a sphere with radius r is V = π r ]
3
 Answer ......................................... cm3 [3]

18. 12 000 vehicles drive through a road toll on one day.

The ratio cars : trucks : motorcycles = 13 : 8 : 3.

(a) (i) Show that 6500 cars drive through the road toll on that day.

Answer(a)(i)

[1]

(ii) Calculate the number of trucks that drive through the road toll on that day.

Answer(a)(ii) ................................................. [1]

(b)The toll charges in 2014 are shown in the table.

Show that the total amount paid in tolls on that day is $34 500.

Answer(b)

[2]

(c)This total amount is a decrease of 8% on the total amount paid on the same day in 2013.

Calculate the total amount paid on that day in 2013.

(d)Answer(c) $ .................................................. [3]

2750 of the 6500 car drivers pay their toll using a credit card.

Write down, in its simplest terms, the fraction of car drivers who pay using a credit card.

(e)Answer(d) ................................................. [2]

To the nearest thousand, 90 000 cars drive through the road toll in one week.

Write down the lower bound for this number of cars.

Answer(e) ................................................. [1]

19. The diagram shows a shaded shape formed by three semi-circular arcs.

The radius of each semi-circle is shown in the diagram.

(i) Calculate the perimeter of the shaded shape.

Answer((i) ........................................... cm [2]

(ii)The shaded shape is made from metal 1.6 mm thick.

Calculate the volume of metal used to make this shape.

Give your answer in cubic millimetres.

Answer(ii) ........................................ mm3 [4]

20. On the first part of a journey, Alan drove a distance of x km and his car used 6 litres of fuel.

600
The rate of fuel used by his car was litres per 100 km.
x

(a) Alan then drove another (x + 20) km and his car used another 6 litres of fuel.

(i) Write down an expression, in terms of x, for the rate of fuel used by his car on this part

of the journey. Give your answer in litres per 100 km.

Answer(a)(i) .............................. litres per 100 km [1]

(ii)On this part of the journey the rate of fuel used by the car decreased by 1.5 litres per 100 km.

Show that x 2+20 x – 8000=0 .

Answer(a)(ii)

[4]
2
(b) Solve the equation x +20 x – 8000=0 .

Answer(b) x = ............................... or x = ............................... [3]

(c)Find the rate of fuel used by Alan’s car for the complete journey.

Give your answer in litres per 100 km.

Answer(c) .............................. litres per 100 km [2]

21. (a) Expand and simplify.

3 x( x – 2)– 2 x(3 x – 5)

Answer(a) ................................................ [2]

(b) Factorise the following completely.

(i) 6 w+ 3 wy – 4 x – 2 xy

Answer(b)(i) ................................................ [2]

(ii) 4 x 2 – 25 y 2

Answer(b)(ii) ................................................ [2]

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