A group of 55 pupils were asked if they owned a phone or a tablet.

11 said they owned both

18 said they only owned a tablet

34 said they owned a phone

a) Draw a Venn diagram to show the information.

b) A student is chosen at random from the group.

What is the probability that the student doesn't have a phone or tablet

Matt had 3 piles of coins, A, B and C.

Altogether there was 72p.

Pile B had twice as much as pile A.

Pile C had three times as much as pile B.

How long was each pile of coins

ANSWork out

a) 3 ½ – 2 ⅓

Give your answer as a mixed number in its simplest form

b) 2 ½ + 3 ½ × 4 ½

Give your answer as a fraction

Find the equation of the line on the graph above

ANSLaura is going to play one game of chess and one game of draughts.

The probability that she will win the game of chess is ⅗

The probability that she will win the game of draughts is ⅜

(a) Complete the probability tree diagram.

(b) Work out the probability that Laura will win exactly one game.

ANS

A spherical ball has a diameter of 10.4cm.

Volume of sphere = 4/3 πr^{3}

a) Estimate the volume of the ball.

b) Is your answer to part a an underestimate or an overestimate.

Explain why.

ANS

In a test out of 25 marks David got 32%

In another test out of 32 marks Jane got 75%

What was the difference between their marks

ANS

A survey of 100 adults was made to see how many hours they spent watching TV each week.

The table below shows how long in hours the adults spent.

Complete the cumulative frequency table

Time | Freq | Time | Cum Freq |

0<t≤5 | 8 | 0<t≤5 | |

5<t≤10 | 18 | 0<t≤10 | |

10<t≤15 | 26 | 0<t≤15 | |

15<t≤20 | 28 | 0<t≤20 | |

20<t≤25 | 14 | 0<t≤25 | |

25<t≤30 | 6 | 0<t≤30 |

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

c) Use your graph to find the median time spent watching TV

d) Estimate how many adults watched more than 17 hours TV per week.

ANSExpress this recurring decimal as a fraction

Make y the subject of the formula.

Prove algebraically that

(3n + 1)^{2} – (3n + 1)

is an even number for all positive integer values of n.

ANSACDE is a rectangle with = 4b, = 5a and = 8b

M is the midpoint of AC

ABC is a right angled triangle

Write each of the following vectors in terms of a and b

a)

b)

c) Show that M is the midpoint of the line BE

ANSA and B are points on the circumference of a circle, centre O.

CB is a tangent to the circle.

COA is a straight line.

Angle OCB = 34°.

Work out the size of the angle marked x.

Give reasons for your answer.

ANS

Functions f and g are such that f(x) = x^{2} and g(x) = x – 3

Solve the equation gf(x) = g^{–1}(x).

ANS