Download Higher Calculator Paper Revision

Higher Calculator Paper Revision
Q1.
Calculate the value of
Write down all the figures on your calculator display.
You must give your answer as a decimal.
..............................................................................................................................................
(Total for Question is 2 marks)
Q2.
Use your calculator to work out
Write down all the figures on your calculator display.
You must give your answer as a decimal.
..............................................................................................................................................
(Total for Question is 2 marks)
Q3.
Work out
Give your answer in standard form.
..............................................................................................................................................
(Total for Question is 2 marks)
Q4.
* Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.
Talil wants to make 180 kg of concrete mix.
Talil has
15 kg of cement
85 kg of sand
100 kg of gravel
Does Talil have enough cement, sand and gravel to make the concrete mix?
(Total for Question is 4 marks)
Q5.
Here are the ingredients needed to make 16 gingerbread men.
Ingredients
to make 16 gingerbread men
180 g flour
40 g ginger
110 g butter
30 g sugar
Hamish wants to make 24 gingerbread men.
Work out how much of each of the ingredients he needs.
...........................................................g flour
...........................................................g ginger
...........................................................g butter
...........................................................g sugar
(Total for Question is 3 marks)
Q6. There are 40 people at a meeting.
Each person travelled to the meeting either by car or by train.
13 of the people are male.
10 females travelled by train.
8 males travelled by car.
Work out the total number of people who travelled by car.
......................
(Total for Question is 3 marks)
Q7.
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.
£......................
(Total for Question is 3 marks)
Q8.The diagram shows the front elevation and the side elevation of a prism.
(a) On the grid, draw a plan of this prism.
(2)
(b) In the space below, draw a sketch of this prism.
(2)
(Total for Question is 4 marks)
Q9.Helen went on 35 flights in a hot air balloon last year.
The table gives some information about the length of time, t minutes, of each flight.
On the grid below, draw a frequency polygon for this information.
(Total for Question is 2 marks)
Q10. The table gives some information about the birds Paula sees in her garden one day.
Bird
Frequency
Magpie
Thrush
Starling
Sparrow
15
10
20
27
Complete the accurate pie chart.
(Total for Question is 3 marks)
Q11.
On the grid, enlarge the shape with scale factor 3, centre A.
(Total for Question is 3 marks)
Q12.
Diagram NOT accurately drawn
Work out the total surface area of this triangular prism.
..............................................................................................................................................
(Total for Question is 4 marks)
Q13. Simon went for a cycle ride. He left home at 2 pm. The travel graph represents part of Simon's cycle
ride.
At 3 pm Simon stopped for a rest.
(a) How many minutes did he rest?
. . . . . . . . . . . . . . . . . . minutes
(1)
(b) How far was Simon from home at 5 pm?
. . . . . . . . . . . . . . . . . . km
(1)
At 5 pm Simon stopped for 30 minutes. Then he cycled home at a steady speed. It took him 1 hour 30
minutes to get home.
(c) Complete the travel graph.
Q14.
Diagram NOT accurately drawn
Quadrilaterals ABCD and LMNP are mathematically similar.
(a) Work out the length of LP.
...........................................................cm
(2)
(b) Work out the length of BC.
...........................................................cm
(2)
(Total for Question is 4 marks)
Q15. The table gives information about the time it took each of 80 children to do a jigsaw puzzle.
Work out the mean time for all 80 children.
........................................................... minutes
(Total for Question is 3 marks)
Q16. There are 15 bags of apples on a market stall.
The mean number of apples in each bag is 9
The table below shows the numbers of apples in 14 of the bags.
Number
of apples
Frequency
7
8
9
10
11
2
3
3
4
2
Calculate the number of apples in the 15th bag.
.............................................................................................................................................
(Total for Question is 3 marks)
Q17. Here is a scale drawing of a rectangular garden ABCD.
Jane wants to plant a tree in the garden
at least 5m from point C,
nearer to AB than to AD
and less than 3m from DC.
On the diagram, shade the region where Jane can plant the tree.
(Total for Question is 4 marks)
Q18.
(a) n is an integer.
–1 ≤ n < 4
List the possible values of n.
..............................................................................................................................................
(2)
(b)
Write down the inequality shown in the diagram.
..............................................................................................................................................
(2)
(c) Solve 3y – 2 > 5
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q19.
(a) Expand
3(x + 2)
..............................................................................................................................................
(2)
12 x3y – 18 xy2
(b) Factorise completely
..............................................................................................................................................
(2)
(c) Expand and simplify
(2x – 3)(x + 4)
..............................................................................................................................................
(2)
(d) Simplify
5x4y3 × 2x3y2
..............................................................................................................................................
(2)
(Total for Question is 8 marks)
Q20.
5 female giraffes have a mean weight of x kg.
7 male giraffes have a mean weight of y kg.
Write down an expression, in terms of x and y, for the mean weight of all 12 giraffes.
..............................................................................................................................................
(Total for Question is 2 marks)
Q21. The equation x3 + 27x = 90
has a solution between 2 and 3
Use a trial and improvement method to find this solution. Give your answer correct to one decimal place.
You must show all your working.
x = ...........................................................
(Total for question = 4 marks)
Q22. Here are the first five terms of an arithmetic sequence.
(a) Write down an expression, in terms of n, for the nth term of this sequence.
..............................................................................................................................................
(2)
2
The nth term of a different number sequence is 3n + 7
(b) Find the 10th term of this sequence.
..............................................................................................................................................
(2)
Q23. (a) Complete the table of values for y = x2 − 2x − 1
(2)
(b) On the grid, draw the graph of y = x − 2x − 1 for values of x from x = −2 = 3
2
(2)
(c) Find estimates for the solutions of the equation x2 − 2x − 1 = 0
...........................................................
(2)
(Total for Question is 6 marks)
Q24. Bill's weight decreases from 64.8 kg to 59.3 kg.
Calculate the percentage decrease in Bill's weight. Give your answer correct to 3 significant figures.
..............................................................................................................................................
(Total for Question is 3 marks)
Q25. * Viv wants to invest £2000 for 2 years in the same bank.
At the end of 2 years, Viv wants to have as much money as possible.
Which bank should she invest her £2000 in?
(Total for Question is 4 marks)
Q26. Write the following numbers in order of size.
Start with the smallest number.
0.038 × 102
3800 × 10–4
380
0.38 × 10–1
..............................................................................................................................................
(Total for Question is 2 marks)
Q27. Wendy goes to a fun fair.
She has one go at Hoopla.
She has one go on the Coconut shy.
The probability that she wins at Hoopla is 0.4
The probability that she wins on the Coconut shy is 0.3
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q28. Kelly recorded the length of time 48 teachers took to travel to school on Monday.
The table shows information about these travel times in minutes.
Least time
Greatest time
Median
Lower quartile
Upper quartile
5
47
28
18
35
(a) Work out the number of teachers with a travel time of 35 minutes or more.
......................
(2)
(b) On the grid, draw a box plot to show the information in the table.
(2)
Kelly then recorded the times the same 48 teachers took to travel to school on Tuesday.
The box plot shows some information about these times.
(c) Compare the travel times on Monday and on Tuesday.
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q29.*
A, B, C and D are points on the circumference of a circle with centre O. Angle ABC = 116°
Find the size of the angle marked x. Give reasons for your answer.
(Total for Question is 4 marks)
Q30.
The diagram shows a cuboid drawn on a 3-D grid.
Three of the vertices of the cuboid are P (3, 2, 0)
Q (3, 0, 0)
R (3, 0, 4)
(a) Label the vertex Q with a cross (×).
(1)
The vertex S is shown on the diagram.
(b) Write down the coordinates of the vertex S.
..............................................................................................................................................
(1)
(Total for Question is 2 marks)
Q31.
* Here is a map.
The position of a ship, S, is marked on the map.
Point C is on the coast.
Ships must not sail closer than 500 m to point C.
The ship sails on a bearing of 037°
Will the ship sail closer than 500 m to point C?
You must explain your answer.
(Total for Question is 3 marks)
Q32.* The diagram shows a ladder leaning against a vertical wall.
The ladder stands on horizontal ground.
The length of the ladder is 6 m.
The bottom of the ladder is 2.25 m from the bottom of the wall.
A ladder is safe to use when the angle marked y is about 75°.
Is the ladder safe to use?
You must show all your working.
(Total for Question is 3 marks)
Q33.
Solve the simultaneous equations
3x + 2y = 4
4x + 5y = 17
x ...........................................................
y ...........................................................
(Total for Question is 4 marks)
Mark Scheme
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