SUITABLE FOR BOTH FOUNDATION & HIGHER TIERS Summer … · Q2. P is a point on the circle, centre O. (a) Write down the mathematical name of the line OP. (1) (b) Write down the mathematical

Compiled by JustMaths – this is NOT a prediction paper and should not be used as such!

BUMPER “BETWEEN PAPERS (2 & 3)”

PRACTICE SUITABLE FOR BOTH FOUNDATION & HIGHER TIERS

Summer 2019

QUESTIONS

Not A “best” Guess paper.

Neither is it a “prediction” ... only the examiners know what is going to come up! Fact! You also need to REMEMBER that just because a topic came up on paper 1 or 2 it may still

come up on paper 3 …

We know how important it is to practise, practise, practise …. so we’ve collated a load of questions that weren’t examined in the pearson/edexcel 9-1 GCSE Maths paper 1 or 2 but we

cannot guarantee how a topic will be examined in the next paper …

Enjoy! Mel & Seager


Q1. (a) Work out the value of √7.4

9.8−2.1

Give your answer as a decimal.

Write down all the figures on your calculator display.

(2)

(b) Give your answer to part (a) correct to 2 significant figures.

(1)

Q2. P is a point on the circle, centre O.

(a) Write down the mathematical name of the line OP.

(1)

(b) Write down the mathematical name of the shaded region.

(1)

(c) Write down the fraction of the circle that is shaded.

Give your fraction in its simplest form.

(2)

Q3. (a) Write 0.8 as a percentage.

(1)

(b) Write 0.023 as a fraction.

(1)

(c) Write 5.6382 correct to 2 decimal places.

(1)

(d) Work out √42.25 + 1.32 Give your answer as a decimal.

(2)

(e) Work out 3

8 of 56.8 kg.

(2)

Q4. The diagram shows three points P, Q and R on a 1 cm grid.

(a) Write down the coordinates of P.

(1)

(b) Write down the coordinates of Q.

(1)

(c) On the grid, mark the point S so that PQRS is a rhombus.

(1)

(d) Work out the area of the rhombus PQRS.

(2)

(e) Write down the equation of the line PR.

(1)


Q5. The diagram shows a shape on a centimetre grid.

(a) Find the area of the shape.

(1)

(b) Find the perimeter of the shape.

(1)

(c) Shade 60% of the shape.

(1)

Q6. (a) (i) Work out 2.912 Write down all the figures on your calculator display.

(ii) Write your answer to part (a)(i) correct to 2 decimal places.

(2)

(b) (i) Find the cube root of 30 Write down all the figures on your calculator display.

(ii) Write your answer to part (b)(i) correct to 2 significant figures.

(2)

Q7. The diagram shows a circle inside a

rectangle.

Work out the area of the shaded region.

Give your answer correct to 3 significant

figures.

(3)

Q8. Point A has coordinates (−4, 9) Point B has coordinates (1, 5)

Find the coordinates of the midpoint of AB.

(2)

Q9. Here are 9 cards. Each card has a number on it.

(a) Write down the mode of the numbers on the cards.

(1)


(b) Work out the median of the numbers on the cards.

(2)

Sally takes at random one card.

(c)

Write down a word from the box that best describes the probability of each outcome.

(i) Sally takes a card with the number 6

(ii) Sally takes a card with the number 5

(2)

(d) Here is a probability scale.

Write down the letter of the arrow that points to the probability that Sally

(i) takes a card with the number 8

(ii) takes a card with a number greater than 0

(iii) takes a card with an even number.

(3)

Q10. Express 825 as a product of its prime factors.

(3)

Q11. A 6-sided polygon is shown on a grid.

(a) Write down the mathematical name for a 6-

sided polygon.

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

(1)

(b) On the polygon, mark with arrows (>) a pair

of parallel lines.

(1)

(c) On the polygon, mark with crosses (×) a pair

of perpendicular lines.

(1)

(d) Write down the coordinates of the point A.

(1)

(e) Find the coordinates of the midpoint of AB.. (2)


Q12. (a) Write 23 × 24 as a single power of 2

(1)

(b) 280 = 2n × 5 × 7 Find the value of n.

(2)

Q13. Here is a polygon.

(a) Write down the mathematical name for this type of polygon.

(1)

(b) Explain why this polygon is not a regular polygon.

(1)

(c) On the diagram, mark with arrows (>>) a pair of parallel lines.

(1)

Q14. The length of a rectangle is 12 cm. The width of the rectangle is 7 cm.

Work out the area of the rectangle.

(2)

Q15. The diagram shows a fair spinner with 6 sections.

Three sections are red, two sections are yellow and one section is blue.

David spins the spinner once.

On the probability scale, mark with a cross (×) the probability that

(i) the spinner lands on red. Label this cross R.

(ii) the spinner lands on blue. Label this cross B.

(iii) the spinner lands on green. Label this cross G.

(3)


Q16. Change £50 to yen.

(2)

Q17. The diagram shows a solid prism.

The cross section of the prism is a trapezium.

The lengths of the parallel sides of the trapezium are 11 cm and 7

cm.

The perpendicular distance between the parallel sides of the

trapezium is 10 cm.

The length of the prism is 12 cm.

(a) How many faces has this prism?

(1)

(b) How many vertices has this prism?

(1)

(c) Work out the area of the trapezium.

(2)

(d) Work out the volume of the prism.

(2)

Q18.

(a) Describe fully the single transformation that

maps shape P onto shape Q.

(2)

(

b) On the grid, enlarge shape P with scale factor 3

and centre O.

(2)


(c) On the grid above, rotate shape R

90° anticlockwise with centre (0, 1)

(2)

Q19. Lisa sees a dress in a sale. The normal price of the dress is $45

The price of the dress is reduced by 12% in the sale.

(a) Work out the price of the dress in the sale.

(3)

Lisa's weekly pay increases from $525 to $546

(b) Calculate her percentage pay increase.

(3)

Q20. The cost of a litre of petrol in Hong Kong is 17.50 Hong Kong dollars ($).

Chen buys 25 litres of petrol in Hong Kong.

The only money he has to pay with are $50 notes.

(a) What is the smallest number of $50 notes he needs?

(3)

He pays with the smallest number of $50 notes.

(b) Work out how much change he should get.

(2)


Q21. Amit invests 15000 rupees.

At the end of one year, his investment has increased by 71

2%

(a) Work out the value of Amit's investment at the end of one year.

(2)

Priya invests a sum of money at an interest rate of 8% per year.

At the end of one year, the interest she receives is 1800 rupees.

(b) Work out the value of Priya's investment at the end of one year.

(3)

Q22. (a) Simplify 8d × 7d

(1)

(b) Expand 4(3e – 5)

(1)

(c) Factorise f2 – 2f

(2)

(d) H = g3 + 6g Work out the value of H when g = 2

(2)

Q23. The diagram shows a shape P, and a

shape Q.

Describe fully the single transformation

which maps shape P onto shape Q.

(3)

Q24. Ella invested $8000 for 3 years at 5% per annum compound interest. Calculate the value of her

investment at the end of 3 years.

(2)


Q25. Zara must take 5 tests. Each test is out of 100 After 4 tests, her mean score is 64%.

What score must Zara get in her 5th test to increase her mean score in all 5 tests to 70%?

(4)

Q26. Liam invests £8000 in a savings account for 4 years.

The savings account pays compound interest at a rate of

4.5% for the first year

2.75% for all subsequent years.

(a) Work out the value of Liam's investment at the end of 4 years.

(3)

Max invests some money in a savings bond.

The savings bond pays interest at a rate of 2% per year.

At the end of the first year, his savings bond is worth £5763

(b) How much money did Max invest in the savings bond?

(3)

Q27. The mean of four numbers is 2.6 One of the four numbers is 5

Find the mean of the other three numbers.

(3)

Q28. Rayna has a fair 4-sided spinner. The spinner can land on 3, 5, 7 or 9

Rayna spins the spinner 20 times. She records the score for each spin.

Here are her scores.

(a) Complete the frequency table for these results.


(2)

(b) Write down the mode of her scores.

(1)

(c) Find the range of her scores.

(1)

Rayna says that 3, 5, 7 and 9 are all prime numbers.

(d) Explain why Rayna is wrong.

(1)

Rayna now spins her spinner twice. She adds the two numbers together to get the total.

(e) Complete the table to show the total for each possible outcome. Five of the totals have been done

for you.

(2)

Rayna spins the spinner twice.

(f) (i) Write down the probability that she will get a total of 10

(ii) Write down the probability that she will get a total greater than 12

(3)

Q29. The table gives information about the number of vehicles passing a point on a road in

each of 70 intervals of equal length.


Calculate an estimate for the mean.

(4)

Q30. The table shows information about the snowfall in Ottawa in January one year.

Work out an estimate for the total snowfall in January.

(3)

Q31. Here is the straight line L drawn on a grid.

Find an equation for L.

(2)


Q32 The diagram shows a quadrilateral ABCD on a

centimetre grid.

(a) Write down the coordinates of

(i) point B,

(ii) point D.

(2)

(b) Write down the equation of the line AB.

(1)

(c) Work out the area of quadrilateral ABCD.

(1)

Q33. Here are three straight lines A, B and C drawn on a grid.

Write down an equation for each of these three straight lines.

(3)

Q34. The diagram shows 7 shapes, A, B, C, D, E, F and G, on a centimetre square grid.


(a) What is the mathematical name of shape E?

(1)

(b) Write down the letters of the two shapes which are congruent.

............................. and ...............................

(1)

(c) Mark an obtuse angle on one of the shapes. Label your angle x.

(1)

(d) How many lines of symmetry has shape B?

(1)

(e) Work out the area of shape C.

(2)

Q35.

The diagram shows a pentagon ABCDE.

DC is parallel to AB.

The size of an exterior angle at A is 67°

The size of an exterior angle at B is 112°

The size of an exterior angle at C is x°

The size of an exterior angle at D is 74°

The size of an exterior angle at E is y°

(a) (i) Work out the value of x.

(ii) Work out the value of y.

(4)

(b) Work out the sum of the interior angles of the pentagon ABCDE.

(2)

Q36. The diagram shows two congruent regular pentagons drawn inside a regular octagon.


One side of each pentagon lies along a side of the octagon.

AB is a side of the octagon.

AC is a side of one of the pentagons.

BC is a side of the other pentagon.

Work out the size of angle y.

Show your working clearly.

(5)

Q37. The accurate scale drawing shows the positions of two ships, L and M.


(a) Find the bearing of ship M from ship L.

(1)

The scale of the drawing is 1 cm to 5 km.

Ship P is 40 km from L and on a bearing of 240° from M.

(b) On the diagram, mark with a cross the position of ship P.

(3)

Q38.

Work out the value of x.

Give your answer correct to 3 significant figures.

(3)

Q39.



Give your answer correct to 1 decimal place.

(3)

Q40. Work out the size of each exterior angle of a regular polygon with 15 sides.

(2)

Q41. The diagram shows a circle with centre O and radius 6.5cm

(a) Work out the area of the circle. Give your answer correct to 3

significant figures.

(2)

PQ is the tangent to the circle at P OQ = 10.5cm

(b) Work out the length of PQ Give your answer correct to 3 significant figures.

(3)

Q42. The pie chart shows information about the use of water

by people in a village in Zambia on one day.

(a) (i) Calculate the size of angle x.

(ii) Explain how you found your answer.

(2)

(b) 90 litres of water were used for cooking.

How many litres were used for watering crops?

(3)

Q43. (a) Expand and simplify 3(2x − 5) − 4(x + 3)


(2)

(b) Expand and simplify (y + 7)(y + 2)

(2)

Q44. A circle has a diameter of 7.6 cm. Work out the circumference of the circle.

Give your answer correct to 3 significant figures.

(2)

Q45. The diagram shows triangle ADC.

E is a point on AD and B is a point on AC so that EB is parallel to DC.

AB = 14 cm. EB = 16 cm. DC = 20 cm.

Calculate the length of BC.

(3)

Q46. The pie chart gives information about the amounts spent by a gas

company in one year.

The amount spent on materials was 225.5 million euros.

The amount spent on services was the same as the amount spent on

wages.

Work out the amount spent on services.

(3)

Q47. Work out the size of an exterior angle of a regular polygon with 8 sides.


(2)

Q48.

The diagram shows a prism.

The cross-section of the prism is an isosceles triangle.

The lengths of the sides of the triangle are 13 cm, 13 cm and 10 cm.

The perpendicular height of the triangle is 12 cm.

The length of the prism is 8 cm.

Work out the total surface area of the prism.

(3)

Q49. Here are two cuboids, A and B.

Cuboid A has a width of 8 cm, a length of 50 cm and a height of 5 cm.

(a) Calculate the volume of cuboid A.

(2)

Cuboid B has a width of 12.5 cm and a length of 25 cm. Cuboid B has the same volume as cuboid A.

(b) Calculate the height of cuboid B.

(3


Q50. The diagram shows three points, A, B and P, on a

centimetre grid.

The point A has coordinates (4, 5) and the point B

has coordinates (2, −1).

(a) Find the coordinates of the midpoint of AB.

(2)

AB is a diameter of a circle.

P is the point (7, 6)

C is the point on the circle such that PA = PC.

(b) On the diagram, mark with a cross (×) the point C.

Label your point C.

(2)

Q51. 2 kilograms of grapes cost £6.20 500 grams of grapes and 3 kilograms of plums cost £11.60

Work out the cost of 1 kilogram of plums.

(3)

Q52. The diagram shows a cuboid and a triangular prism.

The volume of the cuboid is equal to the volume of the triangular prism.


(4)

Q53. (a) Multiply out 6(n − 2)

(1)

(b) Factorise p2 − 5p

(2)

(c) Solve 7𝑥−3

2 = x Show clear algebraic working.

(3)


Q54. (a) Show that

(2)

(b) Show that

(3)

Q55. Solve the simultaneous equations

y − 2x = 6

y + 2x = 6

Show clear algebraic working.

(5)

Q56 The probability that it will rain on Saturday is 0.8

If it rains on Saturday, the probability that it will rain on Sunday is 0.65

If it does not rain on Saturday, the probability that it will rain on Sunday is 0.4

(a) Use this information to complete the probability tree diagram.

(2)

(b) Work out the probability that it will rain on just one of these two days.

(3)


Q57

List the members of the set

(2)

Q58. (a) Factorise 2t2 − 7t + 3

(2)

(b) Rearrange the formula y = a − bx2 to make x the subject.

(3)

Q59.

(a) List the members of

(1)

C is a set such that

The set C has 4 members.

(b) List the members of one possible set C

(2)

Q60 This graph can be used to find the cost, in US dollars ($), of cleaning a carpet with an

area of up to 50 m2.

A carpet has an area of 41m2


(a) Use the graph to find the cost of cleaning this carpet.

(1)

The cost of cleaning another carpet is $65

(b) Use the graph to find the area of this carpet.

(1)

A rectangular carpet has a length of 6.8 m and a width of 5 m.

(c) Find the cost of cleaning this carpet.

(3)

Q61. Lia left home at 1100 to drive to a shopping centre.

On her way, she stopped at a friend's house.

Here is the distance-time graph for her journey to the shopping centre.

(a) (i) For how many minutes did Lia stay at her friend's house?

(ii) How far is it from her friend's house to the shopping centre?

(2)

Lia stayed at the shopping centre for 11

2 hours.

She then drove back home.

She arrived home at 16 30

(b) Show all this information on the distance-time graph.

(2)


Q62. Carlos has a cafe in Clacton. Each day, he records the maximum temperature in degrees Celsius (°C) in

Clacton and the number of hot chocolate drinks sold.

The scatter graph shows this information.

On another day the maximum temperature was 6 °C and 35 hot chocolate drinks were sold.

(a) Show this information on the scatter graph.

(1)

(b) Describe the relationship between the maximum temperature and the number of hot chocolate drinks

sold.

(1)

(c) Draw a line of best fit on the scatter diagram.

(1)

One day the maximum temperature was 8 °C.

(d) Use your line of best fit to estimate how many hot chocolate drinks were sold.

(1)

Q63. A car company records the number of miles cars of different engine sizes, in litres, travel using one

gallon of fuel. The scatter graph shows this information.


Another car has an engine size of 1.8 litres and travels 42 miles using one gallon of fuel.

(a) Plot this information on the scatter graph.

(1)

(b) What type of correlation does this scatter graph show?

.

(1)

(c) Draw a line of best fit.

(1)

A car has an engine size of 2.8 litres.

(d) Find an estimate for the number of miles this car travels using one gallon of fuel.

(1)

Q64. 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.


(2)

Q65. The table shows some information about the ages of 60 teachers.

(a) Write down the modal class interval.

(1)

(b) Draw a frequency polygon for the information in the table.

(2)

Q66. Amzol thinks that (x + 5)2 = x2 + 25 for all values of x. Is Amzol right?

You must show how you get your answer. (2)


Documents

SUITABLE FOR BOTH FOUNDATION & HIGHER TIERS Summer … · Q2. P is a point on the circle, centre O. (a) Write down the mathematical name of the line OP. (1) (b) Write down the mathematical