Year 10 Revision Workbook

Q1. 

(a)  Show that      

(2)

(b)  Show that      

(3) 

(Total for Question is 5 marks)Q2.

A bank pays compound interest of 6% per annum on its savings accounts. Julia invests $7500 for 3 years.

Calculate the total interest gained after 3 years.

$ ...........................................................

(Total for question is 3 marks)

Q3.

Show that the recurring decimal

(Total for question is 2 marks)

Q4.There are 80 counters in a bag. The counters are either red or blue.

The ratio of the number of red counters to the number of blue counters is 3 : 1

Michael takes 15% of the red counters out of the bag.

Alison takes of the blue counters out of the bag.

How many counters are now in the bag?

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

 

(Total for question = 5 marks) 

Q5. 

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

Find the mean of the other three numbers.

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

  (Total for Question is 3 marks)

Q6. The table shows information about the heights, in metres, of 45 of the world's tallest men.

(a)  Use the information in the table to complete the histogram.

(2)(b)  Find an estimate for the number of these men with height between 2.32 metres and 2.34 metres.

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

(1) 

(Total for question = 3 marks) 

Q7. The frequency table shows information about the ages of 60 people on a train.

a)  Complete the cumulative frequency table.

(b)  On the grid, draw a cumulative frequency graph for your table.

(2)(c)  Use your graph to find an estimate for the interquartile range of the ages of the 60 people.

........................................................... years

(2)(d)  Use your graph to find an estimate for how many of the 60 people are more than 48 years of age.

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

(2) Total for question = 7 marks)

 Q8. The table gives information about the time taken by each of 600 people to reach their holiday destination.

(a)  Use the information in the table to complete the histogram.

(3)(b)  Work out an estimate for the number of people who took more than 200 minutes to reach their holiday destination.

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

(2) 

(Total for question = 5 marks) 

Q9.The table shows information about the times, in minutes, taken by 50 people to get to work.

Work out an estimate for the mean time taken to get to work.

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

(Total for Question is 4 marks)Q10. Here are the marks scored in a test by the girls in class 8C.

2     8     10     12     15     16     16     17     18     19     20

(a)  Work out the interquartile range of the girls' marks.

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

(2)

The boys in class 8C did the same test. The boys' marks had a range of 19 and an interquartile range of 11 marks.

Gareth says that the girls' marks are more spread out than the boys' marks.

(b)  Is Gareth right?

Tick ( ) the appropriate box.

Give a reason for your answer.

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

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

(1) 

(Total for question = 3 marks)

Q11. Ian plays 7 games of cricket. His mean score per game for these 7 games is 42 runs.

Ian is going to play one more game of cricket. He wants his mean score per game for the 8 games to be exactly 50 runs.

How many runs must he score in his 8th game?

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

 

(Total for question = 3 marks)Q12. The diagram shows two mathematically similar pots, A and B.

A has a volume of 264 cm3

B has a volume of 891 cm3

A has a height of 8 cm

(a)  Work out the height of pot B.

........................................................... cm

(2)B has a surface area of 459 cm2

(b)  Work out the surface area of pot A.

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

(2) (Total for question = 4 marks)

 Q13.ABCD and APQR are two similar quadrilaterals.PQ = 9 cm.BC = 6 cm.AD = 5 cm.QR = 12 cm.

(a) Find the length of DC.

........................................................... cm(2)

(b) Find the length of AR.

........................................................... cm(2)

The area of the quadrilateral ABCD is 32 cm2.

(c) Calculate the area of the shaded region.

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

(3)

(Total for question is 7 marks)Q15.

Express in the form k is a surd

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

(Total for question = 3 marks)

Q16.(a)  Show that (3 + 2√2)(4 − √2) = 8 + 5 √2

Show your working clearly.

(2)

(b)  Rationalise the denominator and simplify fully

Show your working clearly.

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

(2)(Total for question = 4 marks)

Q17. 

(a)  Find the highest common factor (HCF) of 3780 and 3240        Give your answer as a product of prime factors.

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

(2)

(b)  Find the lowest common multiple (LCM) of 3780 and 3240        Give your answer as a product of prime factors.

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

(2)

  Total for question = 4 marks)

Q18.Express 300 as a product of its prime factors.

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

(Total for question = 3 marks)

Q19. 

The diagram shows a solid cylinder.

The cylinder has radius 4√3 cm and height h cm. The total surface area of the cylinder is 56π√6 cm2

Find the exact value of h. Give your answer in the form a√2 + b√3, where a and b are integers. Show your working clearly.

h = ...........................................................

 

(Total for question = 5 marks)

 Q20.

The diagram shows a regular hexagon. The perimeter of the hexagon is 42 cm.Calculate the area of the hexagon. Give your answer correct to 3 significant figures.

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

(Total for question = 5 marks)

Q21.

 

A, B and C are points on horizontal ground. B is due North of A and AB is 14 m. C is due East of A and AC is 25 m.

A vertical flagpole, TX, has its base at the point X on BC such that the angle AXC is a right angle.

The height of the flagpole, TX, is 10 m.

Calculate the size of the angle of elevation of T from A. Give your answer correct to 1 decimal place.

(Total for question = 6 marks)

Q22.

 

Work out the value of x. Give your answer correct to 3 significant figures.

x = ...........................................................

 

(Total for question = 3 marks)

Q23. 

The diagram shows triangle KLM.

KLP is a sector of a circle with centre L and radius 10.4 cm. The region of the triangle outside the sector is shown shaded in the diagram.

Calculate the area of the shaded region. Give your answer correct to 3 significant figures.

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

 

(Total for question = 5 marks) 

Q24. 

LMNP is a quadrilateral.

Work out the size of angle MLP. Give your answer correct to 3 significant figures.

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

 

(Total for question = 6 marks) 

Q25. 

The diagram shows a sphere and a cone.

The cone has height h cm. The radius of the base of the cone is 3 times the radius of the sphere.

Given that the volume of the sphere is equal to the volume of the cone, find an expression for the radius of the sphere in terms of h. Give your expression in its simplest form.

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

 

(Total for question = 3 marks) 

Q26. 

The diagram shows a cuboid and a triangular prism.

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

Work out the value of x.

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

 

(Total for question = 4 marks) 

Q27.

Here are 8 dominoes.

The 8 dominoes are put in a bag.

Riaz takes at random a domino from the bag.

(a) Find the probability that he takes a domino with a total of 8 spots or a domino with a total of 9 spots.

...........................................................(2)

Helima takes at random 2 dominoes from the bag of 8 dominoes without replacement.

(b) Work out the probability that

(i) the total number of spots on the two dominoes is 18

...........................................................(ii) the total number of spots on the two dominoes is 17

...........................................................(5)

(Total for question is 7 marks)

Q28. Joaquim takes part in two cycle races.

The probability that he wins the first race is 0.6 The probability that he wins the second race is 0.7

(a)  Complete the probability tree diagram.

(2)(b)  Work out the probability that Joaquim wins both races.

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

(2)Joaquim takes part in a third cycle race. The probability that Joaquim wins the third race is 0.2

(c)  Work out the probability that he wins exactly one of the three races.

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

(3) 

(Total for question = 7 marks)

 Q29. Peter travels to work either by bus or by bike.

The probability that Peter will travel to work by bus on any one day is 0.7

Whenever Peter travels to work by bus, the probability that he will be late is 0.1 Whenever Peter travels to work by bike, the probability that he will be late is 0.05

Peter is going to go to work on Monday and on Tuesday.

Work out the probability that he will be late for work on at least one of these days.

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

 

(Total for question = 5 marks)