Exam Question Bank. Name Class

Transcription

1 M7 Exam Question Bank Name Class 1

2 1. Lisa worked this out on her calculator This is what her calculator showed Write down a calculation Lisa could do in her head to check whether her answer is correct... =... [2] 2

3 2. Mr Cornish sold ice cream at the local park He drew these scatter diagrams Diagram A Diagram B Total takings ( ) Temperature ( o C) Number of ice cerams sold Price (p) of one ice cream Describe the relationship shown in diagram A Diagram A... [1]... State the correlation shown in diagram B Diagram B... [1] 3

4 3. Solve the equations (a) 5x 7 = x + 13 (a) x =... [3] (b) x + 4 = 7 2 (b) x =... [2] 4

5 4. Rearrange each formula to make x the subject (a) y = 2x 5 (a) x =... [2] (b) m = 4 + 3x (b) x =... [2] 5

6 5. (a) What is the highest common factor (HCF) of 24 and 36? (a)... [1] (b) Write 60 as a product of prime numbers (b)... [2] (c) What is the reciprocal of 5? (c)... [1] 6

7 6. A ladder is 10m long. It rests 8m up the wall. 10m 8m Using pythagoras find the length from the foot of the ladder to the wall....m [3] 7

8 7. Solve these inequalities (a) 4x + 3 < 13 (a)... [2] (b) 2(x + 1) > 14 (b)... [2] 8

9 8. Two cars drove up to the filling station. For 15 litres of diesel it cost (a) One car bought 27 litres of diesel. How much did it cost? (a)... [2] (b) The other car spent on diesel. How many litres was bought? (b)...litres [2] 9

10 9. This table shows the weights of thirty babies born in a hospital during one week Weight (w kg) 0 < w < 1 1 < w < 2 2 < w < 3 3 < w < 4 4 < w < 5 5 < w < 6 Frequency Calculate an estimate of the mean weight of babies... kg [4] 10

11 10. Work out (a) Show your working (a)... [3] (b) (b)... [3] 11

12 11. A ladder 3.79 metres long rests against a wall The top of the ladder is 3.15 metres above the horizontal ground 3.15m 3.79m Not to scale x Calculate the distance, x metres, of the bottom of the ladder from the wall Give your answer to a sensible degree of accuracy x =... m [4] 12

13 12. (a) The height of a table is 57cm to the nearest centimetre State the upper and lower bounds of this height (a)......[2] (b) The size of a flat screen TV is given as 76.4cm to the nearest mm (0.1cm) What is the maximum and minimum possible screen size? (b) Maximum size... Minimum size...[2] 13

14 13. (a) Show that one solution of the equation x 3 10x + 7 = 0 lies between 2 and [1] (b) Use trial and improvement to find this solution correct to one decimal place You must show all your trials and their outcomes (b)... [3] 14

15 14. Write down the formula for the nth term of each of these sequences (a) (a)... [2] (b) (b)... [2] (c) (c)... [2] 15

16 15. An 8 sided dice is thrown 1000 times. The table shows the results Score Frequency (a) What is the relative frequency of throwing a 3? (a)...[1] (b) What is the relative frequency of throwing a 6? (b)...[1] (c) Noel thinks that the spinner is fair? Do you agree? Justify your answer.... because [1] 16

17 16. (a) A shop is increasing prices by 12% What is the new price of a skirt that previously cost 30?...[2] (b) In a sale prices are reduced by 15% What is the sale price of a computer that cost 680 before the sale? (c) The price of a TV is reduced by from 600 to 390 Calculate the percentage reduction...[2]...% [2] 17

18 17. (a) Give the coordinates of the midpoint of the line AB where A: (2, 6) B: (4, 0) (...,...) [2] (b)using pythagoras find the actual length of AB...[3] 18

19 18. (a) Write down the decimal equivalent of 5 8 (a)...[1] (b) Which of these fractions are equivalent to recurring decimals? Write Yes or No under each fraction [2] (c) You are given that 0.1 = 1 9 Use this information to write 0.4 as a fraction (c)... [1] 19

20 19. (a) Write as a power of (b) Simplify (a)... [1] (c) Simplify 3y 3 5y 2 (b)...[2] (c)... [2] 20

21 20. (a) In a sports club there are 48 women and 60 men Write the ratio of women to men in its simplest terms (a)... :... [1] (b) In another sports club the ratio of men to women is 5 : 3 There are 240 members of the club How many members are women? (b)... [2] (c) The ratio of adults to children in the sports club is 7 : 3 There are 140 adults in the club How many children are there? (c)... [2] 21

22 21. D 72 0 y E AC is parallel to DE Not to Scale A x 46 0 B (a) Find angle x Give a reason for your answer x =... o because [2] (b) Find angle y Give a reason for your answer y =... o because [2] C 22

23 22. Solve (a) 5x = 7 (a) x =... [2] (b) 4(2x 3) = 5(x + 3) (b) x =... [3] 23

24 23. The diagram shows a triangle ABC Use a ruler and compasses to construct (a) The bisector of angle A (b) The perpendicular bisector of side AC Leave in your arcs [3] [2] B A C 24

25 24. E D Not to Scale A In the diagram, AC is parallel to ED (a) Find angle x Give a reason for your answer y x =... o because [2] (b) Find angle y Give a reason for your answer y =... o because... B x C (c)... [2] The exterior angle of a regular polygon is 30 o How many sides does the polygon have?...[2] 25

26 25. (a) The temperature (F) in o F is 32 plus 1.8 times the temperature(c) in o C Write the formula for F in terms of C (b) The temperature (T) in a greenhouse is given by the formula T = p where p is the outdoor temperature. (i) Calculate T when p = 5 (a)... [2] (i)... [2] (ii) Calculate p when T = 34 (ii)... [2] 26

27 26. (a) A car travels 180km in 2 hours 30 minutes. Calculate its average speed? (a)... mph [2] (b) A train travels 390km at a speed of 120kmh. How long did the journey take? (b)...hours and...minutes [2] (c) A metal block has mass 200g and volume 8cm 3 Calculate its density. (c)... g/cm 3 [2] 27

28 27. (a) Multiply out and simplify (x + 3)(x + 5) (a)... [2] (b) Multiply out and simplify (x + 5)(x 2) (b)... [2] (c) Multiply out and simplify (x 4)(x 3) (c)... [2] 28

29 28. (a) XZ and YZ are tangents to the circle, centre O ^ Angle XZO = 27 o X Not to scale Z 27 o O Y Calculate angle XOY ^ Give a reason for each step of your calculation... o [3] (b) A circle has radius 3cm. Find an expression for the area of the circle in terms of... 29

30 29. (a) Complete the table of values for the equation y = x 2 + 2x 1 x y [2] (b) Draw the graph of y = x 2 + 2x 1 from x = 3 to x = 3 (c) Use your graph to solve the equation x 2 + 2x 1 = 0 [2] (c) x =... x =...[2] 30

31 y x

32 30. (a) Find the volume of this triangular prism 7cm 6cm 5cm 10cm (a)...cm 3 [3] (b) Find the total surface area of this triangular prism (b)...cm 2 [3] 32

33 31. (a) The Allelectric company calculates its bills on the basis of the number of units of electricity a customer uses. The cost is directly proportional to the number of units. Complete the table below Number of Units Cost ( ) [2] (b) Jim and Marie both drove up to a petrol station. Jim bought 28 litres of diesel. It cost Marie bought 42 litres of diesel. How much did it cost?... [2] 33

34 32. The frequency table below shows the time taken by the 32 students in 10T to travel to school Time (x minutes) 0 < x < 5 5 < x < < x < < x < < x < < x < 30 Frequency Calculate an estimate of the mean time to travel to school... minutes [4] 34

35 33. (a) Write 36 as a product of prime factors (a)... [2] (b) What is the lowest common multiple (LCM) of 36 and 54? (b)... [1] (c) What is the reciprocal of 0.25? (c)... [1] 35

36 34. (a)the diagram shows an irregular pentagon. 120 o x 98 o Not to scale 108 o 102 o Calculate angle x Show your working (b) Calculate the interior angle of a regular pentagon x =... o [3]... o [2] 36

37 35. (a) Round to one significant figure [1] (a)... (b) Estimate the answer to this calculation (b)... [2] (c) Estimate the answer to this calculation [2] (c)... 37

38 36. In a childrens ball pit there are green, yellow, orange and blue balls Amy picks up a ball at random This table shows the probabilities of obtaining each colour (a) Complete the table Colour Green Yellow Orange Blue Probability [1] (b) There are 1000 balls in the ball pool How many of them are yellow? (b)... [1] (c) How many of them are NOT blue? (c)... [1] 38

39 37. This scatter diagram shows the weight and waist measurements for a group of 20 men Weight (kg) Waist measurement (cm) 39

40 (a) State the correlation... [1] (b) Describe the relationship [1] (c) Dave's weight is 66kg Draw a line of best fit on the scatter diagram and use it to estimate his waist measurement (c)... [2] 40