Name:

Exam Style Questions

Quadratic Inequalities

Equipment needed: Calculator, pen, pencil & ruler

Guidance

1. Read each question carefully before you begin answering it.

2. Check your answers seem right.
3. Always show your workings

Video Tutorial

www.corbettmaths.com/contents

Video 378

Answers and Video Solutions

© Corbettmaths 2022
13. Solve the inequality 7x² − 22x + 16 ≤ 0

............................
(4)

14. Find the set of values of x for which x² − 2x − 24 < 0 and 12 − 5x ≥ x + 9

............................
(6)

© Corbettmaths 2022
19.

(a) Write an expression for the area of the triangle.

............................
(1)

The area of the triangle is greater than 80.5cm²

(b) Show that 2x 2 − x − 171 > 0

(2)

(c) Find the possible range of values of x.

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

© Corbettmaths 2022
 Name:

Exam Style Questions

Perpendicular Lines

Equipment needed: Pencil, pen, ruler & calculator

Guidance

1. Read each question carefully before you begin answering it.

2. Check your answers seem right.
3. Always show your workings

Video Tutorial

www.corbettmaths.com/contents

Video 197

Answers and Video Solutions

© Corbettmaths 2022
10. The straight line K has equation y = 2x − 5

The straight line J is perpendicular to line K and passes through the

point (−4, 8).

Find the equation of line J

..............................
(3)

11. A straight line, L, is perpendicular to the line with equation y = 2x + 3

L passes through the point (10, 3)

Find an equation for the straight line L.

..............................
(3)

12. Line A has equation y = 3x + 2

Line B is perpendicular to Line A and passes through the point (6, 5)

Find the equation of Line B.

..............................
(3)
© Corbettmaths 2022
20. The point A has coordinates (3, 11)
The point B has coordinates (−9, 7)
The point C has coordinates (−7, 1)

Luna says that angle ABC is a right angle.

Show that Luna is correct.

(3)

21. A, B and C have coordinates (2, 9), (10, −7) and (6, k) respectively.
AB is perpendicular to AC

Find k

..............................
(3)

© Corbettmaths 2022
22.

A straight line, L, passes through the points A(−9, 3) and B(11, 8).

The point P lies on line L, such that AP : PB = 3 : 2

Find the equation of the line perpendicular to L that passes through P.

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

© Corbettmaths 2022
11. A straight line L passes through the points (0, 6) and (4, −2).
A straight line M passes through the point (0, 1) and is parallel to line L.

Find the equation of the line M

..............................
(3)

12. Write down the equation of the line that is parallel to x + 2y = 4 and passes
through the point (0, 5)

..............................
(2)
© Corbettmaths 2022
17. The line L is drawn on the grid.

(a) Find the equation of L.

..............................
(3)
The point P has coordinates (−2, 9).

(b) Find an equation of the line that is parallel to L and passes through P.

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

© Corbettmaths 2022
18. Line A and Line B are parallel.

Line A has equation y = 5x + 9

Line B passes through the point (7, 41)

Find the equation of Line B.

..............................
(3)

19. The straight line L has equation y = 3x + 2

The straight line M is parallel to line L and passes through the point (5, −1).

Find the equation of line M

..............................
(3)

20. Write down the equation of the line that is parallel to y = 8x − 4 and passes
through the point (−3, −1)

..............................
(3)
© Corbettmaths 2022
5. There are five counters in a bag.

Two counters are green, two counters are yellow and one counter is pink.
Two counters are selected without replacement

Find the probability that both counters are yellow.

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

6. A bag contains 8 marbles.

4 marbles are red

3 marbles are yellow
1 marble is black

Mahika takes two marbles from the bag at random.

Work out the probability she takes marbles that are different colour.

.........................
(3)
© Corbettmaths 2025
14. Jeremy has two bags of beads.
Bag 1 contains 7 blue beads and 3 yellow beads
Bag 2 contains 11 blue beads and 4 yellow beads

Jeremy rolls an fair six-sided dice.

If he rolls a number less than three, he takes a marble from bag 1.

If he does not roll a number less than three, he takes a marble from bag 2.

Work out the probability that Jeremy chooses a yellow marble.

.........................
(4)

15. There are 8 sweets in a bag.

Three sweets are red, three sweets are blue and two sweets are green.

Three sweets are selected at random without replacement.

Calculate the probability that the sweets are not all the same colour.

.........................
(4)
© Corbettmaths 2025
16. Thomas is playing tennis.

If it is windy the probability that he serves an ace is 0.1

If it is not windy the probability that he serves an ace is 0.25

The probability that it is windy is 0.3

Calculate the probability that Thomas serves an ace.

.........................
(4)

17. Jenny and Penny are identical twins.

They are in the same mathematics class, which has a total of twenty students.

The teacher selects two students at random to go on a trip.

Calculate the probability that at least one twin will go on the trip.

.........................
(4)
© Corbettmaths 2025
24. Keira bakes vanilla and lemon cupcakes for a party.
There are 5 more vanilla than lemon cupcakes.

Keira is going to pick two cupcakes at random.

1
The probability that she picks two cupcakes of the same flavour is
2

Work out how many cupcakes Keira baked.

.........................
(6)

© Corbettmaths 2025
1. A semi-circle has diameter 20m.

Calculate the perimeter of the semi-circle.

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

2.

Calculate the perimeter of the sector.

.........................cm
(2)
© Corbettmaths 2024
3. Shown below is a quarter circle.

(a) Work out the length of the arc.

Give your answer in terms of π

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

(b) Work out the perimeter of the quarter circle.

Give your answer in terms of π

.........................cm
(1)

4. Shown is a sector of a circle.

Calculate the length of the arc.

.........................cm
(3)
© Corbettmaths 2024
13.

The major arc length is 31.1cm.

Find the length of x, the radius of the circle.

.........................cm
(3)

© Corbettmaths 2024
3. A tree is located in the corner of a rectangular field.

The field is 10 metres long and 9 metres wide.

The tree is 4 metres tall.

Calculate the length AE

.........................m
(3)
4. Shown below is a cuboid

Calculate the length of diagonal BH.

Give your answer as a surd.

.........................cm
(3)

5.

Calculate the volume of the cone.

.........................cm³
(4)
3. The table shows information about the number of hours that 260 students spent
revising for an exam.

(a) Complete the cumulative frequency table.

(1)

(b) On the grid on the following page, draw a cumulative frequency graph for
your table.
(2)

© CORBETTMATHS 2014
6. A university surveyed 60 mathematics graduates on their starting salary.
The cumulative frequency graph shows some information about the salaries.

(a) Use the graph to find an estimate for the median salary.

£..............................
(1)

© CORBETTMATHS 2014
 The 60 mathematics graduates
had a minimum salary of £16,000
and a maximum salary of £48,000.

(b) Use this information and the cumulative frequency curve to draw a box plot
for the 60 mathematics graduates.

(3)

The university also surveyed 60 archaeology graduates.

The box plot below shows information about their salaries.

(c) Compare the distribution of the salaries of the mathematics graduates with
the distribution of the salaries of the archaeology graduates.

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

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

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

© CORBETTMATHS 2014
11. The cumulative frequency diagram below shows the distribution of marks in an
Art exam.

The lowest mark is 8.

The highest mark is 56.

(a) Draw a box plot for this data.

(b) What percentage of students scored more than the upper quartile mark?

.........................%
(1)

© CORBETTMATHS 2014
4. H varies directly to the cube of c.
When H = 40, c = 2.

(a) Express H in terms of c.

H = .......................
(3)

(b) Find the value of H when c = 5.

H = .......................
(1)

(c) Find the value of c when H = 5000.

c = .......................
(1)
5. The force, F newtons, exerted by a magnet on a metal object is inversely
proportional to the square of the distance d cm.

When d = 2 cm, F = 50 N.

(a) Express F in terms of d.

F = .......................
(3)

(b) Find the force when the distance between the magnet and metal object is 10cm

F = .......................N
(1)

(c) Find the distance between the magnet and metal object when the force is 8N.

d = .......................cm
(1)

(d) Explain what happens to F when d is halved.

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

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

.....................................................................................................................................
(1)
 Name:

Exam Style Questions

Factorising Quadratics

Equipment needed: Calculator, pen

Guidance

1. Read each question carefully before you begin answering it.

2. Check your answers seem right.
3. Always show your workings

Video Tutorial

www.corbettmaths.com/contents

Videos 118, 119, 120

Answers and Video Solutions

© Corbettmaths 2023
17. Factorise y 2 − 9w 2

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

18. Factorise x 2 − 38x + 72

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

19. Factorise x 2 + 14x − 51

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

20. Factorise y 2 + 32y + 240

.....................................
(2)
© Corbettmaths 2023
21. Factorise y 2 − 12y − 64

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

22. Freddy has been asked to factorise x 2 − 11x + 30

His answer is (x + 5)(x + 6)

Explain his mistake.

……………………………………………………………………………………………

……………………………………………………………………………………………
(2)

23. A quadratic expression, x 2 + a x + 24 , can be factorised.

a is a positive integer.

How many possible values are there for a?

.....................................
(3)
© Corbettmaths 2023
42. Factorise fully (x + 4)2 + 3(x + 4)

………………………..
(2)

43. (a) Factorise 10x 2 + 9x + 2

………………………..
(2)

(b) Hence factorise 10(y − 3)2 + 9(y − 3) + 2

………………………..
(3)
© Corbettmaths 2023
 ·· 169
11. Prove algebraically that 0.512 can be written as
330

(3)

12. Convert 0.451515151... to a fraction.

Give your answer in its simplest form.

.........................
(3)
·
13. Write 1.24 as a mixed number.
Give your answer in its simplest form.

.........................
(3)
© Corbettmaths 2022
 ·· 17
14. Prove algebraically that 0.309 can be written as
55

(3)

· 13
15. Prove algebraically that 0.216 can be written as
60

(3)
··
16. Write 2.165 as a mixed number.
Give your answer in its simplest form.

.........................
(3)
© Corbettmaths 2022
3. On the grid, clearly indicate the region that satisfies all these inequalities.

y<x y≥1 x+y ≤4

(3)

4.

Tick the pair of inequalities that describe the shaded region.

x ≥ − 3 and y ≥ 4 x ≥ − 3 and y ≤ 4

x ≤ − 3 and y ≥ 4 x ≤ − 3 and y ≤ 4
(1)
© Corbettmaths 2025
9. A greengrocer sells bananas and apples.
In one day he sells
less than 80 bananas
less than 90 apples
no more than a total of 110 pieces of fruit

Let x be the number of bananas sold

Let y be the number of apples sold.

Show the region below that satisfies these inequalities

(4)

© Corbettmaths 2025
10. On the grid below, shade the region that satisfies the inequalities below.

y≥−5 y≤x 5x − 2y ≥ 1 3x + 2y ≤ 6

Label the region R.

© Corbettmaths 2025
16.

Write down the four inequalities that define the shaded region.

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

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

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

.......................................
(4)

© Corbettmaths 2025
5. Carolyn was asked to find the gradient of a straight line drawn on the below.

To find the gradient of the line, she chose two points A and B.

Carolyn says that the gradient is 2, as 6÷3=2

Is Carolyn correct?
Explain your answer.

…………………………………………………………………………………………….

…………………………………………………………………………………………….

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

© Corbettmaths 2025
6. George was asked to find the gradient of a straight line drawn on the below.

To find the gradient of the line, he chose two points A and B.

George says that the gradient is 2, as 4÷2=2

Explain why George is not correct.

…………………………………………………………………………………………….

…………………………………………………………………………………………….

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

© Corbettmaths 2025
15.

Line L is drawn on the grid.

Work out the gradient of Line L.

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

© Corbettmaths 2025
21. The line passing through (4, −7) and (8, c) has a gradient of 3

Find c.

………………………..
(3)

22. The line passing through (6, −4) and (a, 10) has a gradient of 2.

Find a

………………………..
(3)

© Corbettmaths 2025
23.

A is the point (3, 1).

B is the point (a, 11).

5
The gradient of AB is
2

Work out the value of a.

.........................
(3)

© Corbettmaths 2025
4. Olivia has been asked to find the bearing of B from A.
Shown below is her method.

Olivia’s answer is 080°

Explain Olivia’s mistake.

……………………………………………………………………………………………

……………………………………………………………………………………………
(2)

5. Oliver has been asked to find the bearing of C from D.

Shown below is his method.

Oliver’s answer is 103°

Explain Oliver’s mistake.

……………………………………………………………………………………………

……………………………………………………………………………………………
(2)
© Corbettmaths 2024
11. The diagram shows the position of two airplanes, P and Q.

The bearing of Q from P is 070°

Calculate the bearing of P from Q.

............................... °
(2)

12. The bearing of C from D is 165°

Calculate the bearing of D from C.

............................... °
(2)

13. The bearing of F from G is 300°

Calculate the bearing of G from F.

............................... °
(2)
© Corbettmaths 2024
14. The diagram shows the position of two people, A and B, who are on their Duke
of Edinburgh expedition.

The bearing of person C from person A is 062°

The bearing of person C from person B is 275°

In the space above, mark the position of person C with a cross (x). Label it C.

(3)

© Corbettmaths 2024
1. Evaluate the following

(a) 3× 7

.........................
(1)

(b) 24 ÷ 6

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

(c) 2 3×3 5

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

(d) 10 8 ÷ 2 2

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

Simplify ( 3)
2
2.

.........................
(1)

© Corbettmaths 2025
11. Write each of these in the form a 3 , where a is an integer.

(a) 6× 8

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

(b) 27 + 75

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

15
12. Rationalise the denominator of
5

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

13. Simplify fully 600 + 24

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

© Corbettmaths 2025
 12
14. (a) Rationalise the denominator of
3

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

(b) Evaluate 2× 32

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

( 3+ 5)
2
(c) Expand and simplify

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

(d) Evaluate (5 + 2 )(5 − 2)

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

© Corbettmaths 2025
 10
26. Simplify 80 −
5

.........................
(3)

27. Given that

10 − 32
=a+b 2
2

where a and b are integer.

Find the values of a and b.

a = .........................

b = .........................
(4)
© Corbettmaths 2025
 6
36. Write in the form a 2
1
+ 2
2

.........................
(4)

16
37. Show that can be written in the form a + b 11
11 − 3

.........................
(4)

© Corbettmaths 2025
 6
38. Show that can be written in the form a+b 3
2− 3

.........................
(4)

4 2 6 a 2−b
39. Write + in the form
3+ 2 2 c

.........................
(4)

© Corbettmaths 2025
4. Natalie has 8 socks in a drawer.

5 of the socks are black.

3 of the socks are white.

Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer.
Then Natalie takes out a second sock, at random, and writes down its colour.

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that the two socks are the same colour.

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

© Corbettmaths 2023
9. In a small village, one bus arrives a day.

The probability of rain in the village is 0.3.

If it rains, the probability of a bus being late is 0.4.

If it does not rain, the probability of a bus being late is 0.15.

(a) Complete the tree diagram

(2)

(b) Work out the number of days the bus should be late over a period of 200
days.

..........................
(3)

© Corbettmaths 2023
10. Shown is a spinner.

The probability of a 1 is 2x
The probability of a 2 is x
The probability of a 3 is 2x

(a) Calculate the value of x.

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

The spinner is spun twice and the scores are added together.

(b) Work out the probability of the final score being 4.

You may use the tree diagram to help you.

..........................
(4)

© Corbettmaths 2023
16. Kyle takes the free kicks for his local football team.
He takes 70% of the free kicks with his right foot.

Kyle scores 40% of the free kicks that he takes with his right foot.
Overall, Kyle scores 32.5% of the free kicks that he takes.

Work out what percentage of the free kicks, taken with his left foot, that Kyle
scores.

..........................%
(4)

© Corbettmaths 2023
3. The diagram shows a prism.

Work out the surface area of the prism.

.........................cm²
(4)

© CORBETTMATHS 2014
 Name:

Exam Style Questions

Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser

You may use tracing paper if needed

Guidance

1. Read each question carefully before you begin answering it.

2. Donʼt spend too long on one question.
3. Attempt every question.
4. Check your answers seem right.
5. Always show your workings

Revision for this topic

© CORBETTMATHS 2014
8. Shown below is a triangular prism.

Find the volume of the triangular prism.

.........................cm³
(3)

© CORBETTMATHS 2014
 Name:

Exam Style Questions

Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser

You may use tracing paper if needed

Guidance

1. Read each question carefully before you begin answering it.

2. Donʼt spend too long on one question.
3. Attempt every question.
4. Check your answers seem right.
5. Always show your workings

Revision for this topic

© Corbettmaths 2015
1. Shown below is a rectangle.

(a) Find the area of the rectangle in m²

......................... m²
(1)
(b) Find the area of the rectangle in cm²

......................... cm²
(1)

2. Shown below is a cube.

(a) Find the volume of the cube in m³

......................... m³
(1)
(b) Find the volume of the volume in cm³

......................... cm³
(1)

© Corbettmaths 2015
22. Mrs Jones is tiling her kitchen floor.
Each kitchen tile measures 20cm by 20cm.
The floor measures 3m wide and 5m long.

The tiles are sold in boxes of 10.

Each box costs £6

Work out the total cost of the tiles needed for the kitchen floor.

£.........................
(5)

© Corbettmaths 2015
19. Convert 2 miles into yards

......................... yards
(1)

20. Convert 1 mile into feet

......................... feet
(1)

21.

Who is taller?
You must show your working

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

© Corbettmaths 2015
22. Write these measurements in order of size, smallest first.

240 inches 4 yards 15 feet

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

23.

Which town is further away?

You must show your working

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

© Corbettmaths 2015
7. A mobile phone mast has a range of 3km.

Calculate the area of the shaded region.

Give your answer to 2 decimal places.

.........................km²
(2)

8. A circular flower bed has diameter 7 metres.

Work out the area of the flower bed.

Give your answer correct to 1 decimal place.

.........................m²
(2)

© Corbettmaths 2022
15. Shown below is a semicircle with radius 6cm.

Work out the area of the semicircle.

Give your answer to 1 decimal place.

.........................cm²
(2)

16. A pizza shop sells two different size pizzas.

A small pizza has a diameter of 6 inches.

A large pizza has a diameter of 12 inches.

Jackson says that if he orders two small pizzas, he will receive the same amount
of pizza as one large pizza.

Explain why Jackson is incorrect.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………
(3)
© Corbettmaths 2022
17. Shown below is a circle inside of a square, ABCD.
The circle touches the 4 sides of the square.

The area of the circle is 105cm²

Find the area of the square, ABCD.

.........................cm²
(4)

© Corbettmaths 2022
4. Write the following numbers in standard form.

(a) 40000

..........................................
(1)

(b) 5600

..........................................
(1)

(c) 41200000

..........................................
(1)

(d) 0.00000008

..........................................
(1)

(e) 0.000345

..........................................
(1)

5. Write 37341000000 in standard form.

..........................................
(1)
© Corbettmaths 2022
 6.32 × 1013
18. Work out
1.6 × 108

Give your answer in standard form.

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

19. Mr. Holland has 2500kg of rice.

(a) Write 2500 kg in grams.

Give your answer in standard form.

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

(b) One grain of rice has a mass of 0.03g

Write the mass of one grain of rice in standard form.

..........................................g
(1)

(c) How many grains of rice are there in 2500kg of rice?

Give your answer in standard form.

..........................................
(2)
© Corbettmaths 2022
20. (a) Write five million in standard form.

..........................................
(1)

(b) Write three hundred thousand in standard form.

..........................................
(1)

(c) Work out five million multiplied by three hundred thousand.

Give your answer in standard form.

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

21. A calculator displays a number in standard form.

Write the number as an ordinary number.

..........................................
(1)
© Corbettmaths 2022
29. The population of England is 5.604 × 107
The number of people who live in London is 8.982 × 106

What percentage of the population of England live in London?

Give your answer to 2 decimal places.

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

30. Work out (2.19 × 108) × (3.52 × 103)

Give your answer in standard form.

..........................................
(2)
31. Work out (4.5 × 107) ÷ (5 × 10−2)
Give your answer in standard form.

..........................................
(2)
© Corbettmaths 2022
3. Solve the simultaneous equations

x + 7y = 64
x + 3y = 28

x = ......................... y = ..........................
(3)

4. Solve the simultaneous equations

4x − 4y = 24
x − 4y = 3

x = ......................... y = ..........................
(3)

© Corbettmaths 2022
5. Solve the simultaneous equations

2x + 4y = 14
4x − 4y = 4

x = ......................... y = ..........................
(3)

6. David buys 2 scones and 2 coffees in a shop and the cost is £18.
Ellie buys 3 scones and 2 coffees in the same shop and they cost £22.

Form two equations and solve to find the cost of each scone and each coffee.

Scone = £......................... Coffee = £..........................

(4)
© Corbettmaths 2022
17. A museum sells adult tickets or child tickets.

Fozia buys 4 adult tickets and 1 child ticket for £120

Sami buys 5 adult tickets and 3 child tickets for £171

Work out the cost of each type of ticket.

Adult ticket £ ..........................

Child ticket £ ..........................

(4)

18. Solve the simultaneous equations

4x + 3y = 7.5
3x − 5y = 10.7

x = ......................... y = ..........................
(3)

© Corbettmaths 2022
27. Albie is training for a marathon.
He jogs either route A or route B.

During April, he jogs route A nine times and route B five times.
Route B is 8 miles longer than route A.
In total, he jogs 89 miles in April.

In May, he will start jogging route C.

Route C is 20% longer than route B.

Work out the length of route C.

..........................miles
(6)

© Corbettmaths 2022
28. Solve the simultaneous equations

6x + 2y = 13c
x + 2y = − 2c

where c is a constant

Give your answers in terms of c.

x = ......................... y = ..........................
(4)

© Corbettmaths 2022
 (c) Use your graph to find an estimate for the median number of hours spent
revising.

.........................hours
(1)

(d) Use your graph to find an estimate for the number of students who spent
less than 3 hours revising.

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

© CORBETTMATHS 2014
 The 60 mathematics graduates
had a minimum salary of £16,000
and a maximum salary of £48,000.

(b) Use this information and the cumulative frequency curve to draw a box plot
for the 60 mathematics graduates.

(3)

The university also surveyed 60 archaeology graduates.

The box plot below shows information about their salaries.

(c) Compare the distribution of the salaries of the mathematics graduates with
the distribution of the salaries of the archaeology graduates.

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

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

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

© CORBETTMATHS 2014
7. The length of time, in minutes, that 80 customers spend in a shop was recorded.
A cumulative frequency diagram of this data is below.

(a) Find an estimate of the median.

.........................minutes
(1)
(b) Find an estimate of the inter-quartile range.

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

© CORBETTMATHS 2014
12. Mrs Davis sets her class a quiz, which has a maximum score of 50.
The distribution of the scores are shown in a box plot below.

(a) Write down the median score.

.........................
(1)
(b) Write down the highest score.

.........................
(1)
(c) Find the interquartile range.

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

Martin scored 35 marks.

(d) What percentage of the class scored a lower mark than Martin?

.........................%
(1)

The interquartile range is a better measure of the spread of a distribution than

the range.

Explain why.

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

................................................................................................................................
(1)

© CORBETTMATHS 2014
3. The heights of 7 footballers are measured.

180cm 179cm 185cm 177cm 172cm 190cm 188cm

Work out the upper quartile of the heights.

.........................
(1)

4. 11 people solve a puzzle.

The times taken, in minutes, by each person to solve the puzzle are shown
below.

8 3 7 8 9 13 4 9 9 10 9

(a) Work out the lower quartile.

.........................minutes
(1)

(b) Work out the upper quartile.

.........................minutes
(1)

© Corbettmaths 2023
5. Here are the ages of 15 people.

24 26 29 30 31 36 36 37 39 40 43 48 50 51 55

Work out the interquartile range of the ages.

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

6. 11 students guess the number of jelly beans in a jar.

Here are their guesses.

400 673 850 900 1001 1200 1222 1280 1350 1371 2600

(a) Work out the range of the guesses.

.........................
(1)

(b) Work out the interquartile range of the guesses.

.........................
(1)

© Corbettmaths 2023
5. A sequence of numbers is shown.

2 9 16 23 30 ... ...

(a) Find an expression for the nth term of the sequence.

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

(b) Find the 100th term in the sequence.

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

6. The nth term of a number sequence is n² + 3.

(a) Find the first three terms of this sequence.

1st term ..............., 2nd term ..............., 3rd term ...............

(2)

(b) Work out the difference between the 5th and 10th terms in the sequence.

.........................
(3)
13. Find the nth term of the sequences

(a) 1, 4, 9, 16, 25, ...

....................
(1)

(b) 3, 6, 11, 18, 27, ...

....................
(1)

(c) −3, 0, 5, 12, 21, ...

....................
(1)

(d) 2, 8, 18, 32, 50, ...

....................
(1)

14. The first 5 terms in a number sequence are

30 25 20 15 10 ... ...

Work out the nth term of the sequence.

.........................
(2)
15. The first 5 terms in a number sequence are

2 2.5 3 3.5 4 ... ...

(a) Work out the nth term of the sequence.

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

(b) Work out the 20th term of the sequence.

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

16. Martin has written the first 50 terms of the sequence with nth term 150 − 4n.

Work out which term is the first negative term.

.........................
(3)
!
Ratio: Problem Solving
Video 271e on www.corbettmaths.com

Question 25: A cone has radius 4cm and perpendicular height of 9cm.
A sphere has a radius of 6cm

Calculate the ratio of the volume of the cone to the volume of the sphere.

Question 26: On 1st March 2001, the ratio of Freddie’s age to his mother’s age was 1:11
On 1st March 2018, the ratio of Freddie’s age to his mother’s age was 2:5
Write the ratio of Freddie’s age to his mother’s age on 1st March 2030

Question 27: The ratio 25 000 000 000 : 500 can be written in the form n : 1
Work out the value of n
Give your answer in standard form

Question 28: The distance of Mercury from the Sun is 5.7 × 107 km
The distance of Neptune from the Sun is 4.3 × 109 km

Work out the ratio of the distance of Mercury from the Sun to the distance
of Neptune from the Sun.

Question 29: Class 10D make some cakes using milk chocolate, dark chocolate or white
chocolate.
Some of the cakes contain nuts and the rest do not.

The ratio of the number of milk chocolate cakes to dark chocolate cakes is 10:3
The ratio of the number of white chocolate cakes to milk chocolate cakes is 1:6
Of the milk chocolate cakes, the ratio of the number of cakes containing nuts to
not containing nuts is 1:8
Of the dark chocolate cakes, the ratio of the number of cakes containing nuts to
not containing nuts is 3:2
Of the white chocolate cakes, the ratio of the number of cakes containing nuts to
not containing nuts is 2:5
What percentage of the cakes contain nuts?
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© CORBETTMATHS 2018
10. Simplify

w w
×
2 4

.........................
(1)

11. Simplify fully.

3a 4
×
2 5a

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

12. Simplify fully.

5a 3 4a 2y
×
6y 2ay

.........................
(2)
© Corbettmaths 2024