date: time: total marks available: total marks achieved: · 6/6/2015 · jon has a flower garden...

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Questions 1-11 Non Calculator Questions 12-21 Calculator

Questions Q1.

Work out the area of this triangle.

...............................................................................................................................(Total for Question is 3 marks) Q2.

Triangle ABC is drawn on a centimetre grid. A is the point (2, 2). B is the point (6, 2). C is the point (5, 5).

Triangle PQR is an enlargement of triangle ABC with scale factor ½ and centre (0, 0).

Work out the area of triangle PQR.

. . . . . . . . . . . . . . . . . . . . . . cm2

(Total for Question is 3 marks)

Q3.

A water trough is in the shape of a prism.

Hamish fills the trough completely.

Water leaks from the bottom of the trough at a constant rate. 2 hours later, the level of the water has fallen by 20 cm.

Water continues to leak from the trough at the same rate.

How many more minutes will it take for the trough to empty completely?

. . . . . . . . . . . . . . . . . . . . . . minutes


Q4.

The diagram shows a triangular prism.

Diagram NOT accurately drawn

Work out the total surface area of the prism.

. . . . . . . . . . . . . . . . . . cm2


Q5.

ABCDE is a regular pentagon. BCF and EDF are straight lines.

Work out the size of angle CFD. You must show how you got your answer.

...........................................................°


Q6.

S and T are points on the circumference of a circle, centre O. PT and PS are tangents. Angle TPO = 24°.

Work out the size of angle SOT.

. . . . . . . . . . . . . . . . . . . . . .°


Q7.

Shape P is reflected in the line x = –1 to give shape Q.

Shape Q is reflected in the line y = 0 to give shape R.

Describe fully the single transformation that maps shape P onto shape R.

.............................................................................................................................................. ..............................................................................................................................................


Q8.

* Marc drives a truck. The truck pulls a container. The container is a cuboid 10 m by 4 m by 5 m.

Marc fills the container with boxes. Each box is a cuboid 50 cm by 40 cm by 20 cm.

Show that Marc can put no more than 5000 boxes into the container.


Q9.

*

ABC is parallel to DEF. EBP is a straight line. AB = EB. Angle PBC = 40°. Angle AED = x°.

Work out the value of x. Give a reason for each stage of your working.


Q10.

Richard's car uses 1 litre of petrol every 8 miles. Petrol costs £1.30 per litre.

Richard drives 240 miles.

Work out the total cost of the petrol the car uses.

..............................................................................................................................................


Q11.

∗

In a competition, a prize is won every 2014 seconds.

Work out an estimate for the number of prizes won in 24 hours. You must show your working.


Q12.

The diagram shows a swimming pool in the shape of a prism.

The swimming pool is empty.

The swimming pool is filled with water at a constant rate of 50 litres per minute.

(a) Work out how long it will take for the swimming pool to be completely full of water. Give your answer in hours. (1 m3 = 1000 litres)

........................................................... hours

(5)

Here are four graphs.

(b) Write down the letter of the graph that best shows how the depth of the water in the pool above the line MN changes with time as the pool is filled.

...........................................................

(1)

(Total for question = 6 marks)

Q13.

A small photograph has a length of 4 cm and a width of 3 cm. Shez enlarges the small photograph to make a large photograph.

The large photograph has a width of 15 cm.

Diagram NOT accurately drawn

The two photographs are similar rectangles.

Work out the length of the large photograph.

..............................................................................................................................................


Q14.

Ella is designing a glass in the shape of a cylinder.

The glass must hold a minimum of ½ litre of liquid.

The glass must have a diameter of 8 cm.

Calculate the minimum height of the glass.

..............................................................................................................................................


Q15.

Jon has a flower garden in the shape of a circle. The diameter of the garden is 5 metres.

Jon wants to put fencing around the edge of the garden. The fencing costs £1.80 per metre.

Work out the total cost of the fencing.

..............................................................................................................................................


Q16.

Jane has a flower bed in the shape of an equilateral triangle.

The perimeter of the flower bed is 15 metres.

(a) Work out the area of the flower bed.

Give your answer correct to 1 decimal place.

........................................................... m2

(3)

Jane has some containers in the shape of hemispheres with diameter 35 cm.

Jane is going to fill the containers completely with compost.

She has 80 litres of compost.

1 litre = 1000 cm3.

(b) Work out how many containers Jane can fill completely with compost.

...........................................................

(4)


Q17.

The diagram shows a trundle wheel.

Trundle wheels are used to measure distances along the ground.

The radius of the trundle wheel is 20 cm.

Jim wants to work out the distance between two junctions on a road. He rolls the trundle wheel between the two junctions.

The trundle wheel rotates exactly 34 times.

Work out the distance between the two junctions. Give your answer in metres correct to the nearest metre.

...........................................................m

(Total for question = 3 marks)

Q18.

The diagram shows the position of two boats, B and C.

Boat T is on a bearing of 060° from boat B. Boat T is on a bearing of 285° from boat C.

In the space above, draw an accurate diagram to show the position of boat T.

Mark the position of boat T with a cross (×). Label it T.


Q19.

Sue is driving home from her friend's house.

Sue drives

10 miles from her friend's house to the motorway 240 miles on the motorway 5 miles from the motorway to her home

Sue

takes 20 minutes to drive from her friend's house to the motorway drives at an average speed of 60 mph on the motorway takes 25 minutes to drive from the motorway to her home

Sue stops for a 30 minute rest on her drive home.

Sue leaves her friend's house at 9.00 am.

What time does Sue get home? You must show all your working.

...........................................................


Q20.

A, B and C are 3 service stations on a motorway.

AB = 25 miles BC = 25 miles

Aysha drives along the motorway from A to C.

Aysha drives at an average speed of 50 mph from A to B. She drives at an average speed of 60 mph from B to C.

Work out the difference in the time Aysha takes to drive from A to B and the time Aysha takes to drive from B to C. Give your answer in minutes.

..............................................................................................................................................


Q21.

Triangles ABC and DEF are mathematically similar.

The base, AB, of triangle ABC has length 2(x – 1) cm The base, DE, of triangle DEF has length (x2 – 1) cm

The area of triangle ABC is 4 cm2 The area of triangle DEF is T cm2

Prove that

T = x2 + 2x + 1


Mark Scheme Q1.

Q2.

Q3.

Question Working Answer Mark Notes

45 200 minutes 6 M1 for 120× 20×30(= 72000) M1 for "72000"÷120 A1 for 600cm3 min oe M1 for ½ × (120 + 80) × 40 × 30 (= 120000) M1 for "120000÷"600" A1 for 200 minutes or 3 hours 20 mins oe SC B1 for 4 hours

Q4.

Q6.

Q7.

Q8.

Q9.

Q11.

Q12.

Q13.

Q14.

Q15.

Q16.

Q17.

Q18.

Q19.

Q20.

date: time: total marks available: total marks achieved: · 6/6/2015 · jon has a flower garden...

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