Which of these numbers is **one more** than a multiple of 6 ?

Which of these numbers has **exactly three** factors?

Which of these numbers is **6 less** than −5.7?

Which shape is congruent to shape **X** ?

The map shows the positions of two ships, A and B.

The two ships are 12 cm apart on the map.

Work out the actual distance between the ships.

A gym has 375 members.

40% have bronze membership.

28% have silver membership.

The rest have gold membership.

Work out the number with gold membership.

Alan is looking at number machines.

He says,

“If I know *y* then I can work out *x*.

I subtract 4 and then I add 6.”

Does this method work?

Alan says,

“If I know *d* then I can work out *c*.

I divide by 2 and then subtract 3.”

Does this method work?

Solve 7*w* − 4 = 24

*w*=

Write an expression for the total cost, in pounds, of

*x* shirts at £15 each

and

*y* belts at £8 each.

Simplify *a* + *b* × *b* + *a* + *a*

^{2}so rearranging gives 𝑎 + 𝑎 + 𝑎 + 𝑏

^{2}= 3𝑎 + 𝑏

^{2}

Lucy says,

“3 is odd and 5 is odd,

so when you add a multiple of 3 to a multiple of 5 the answer is always even.”

Is she correct?

Tom earns £8.80 per hour.

He works for

22 hours each week

48 weeks each year.

He pays tax if he earns more then £10 000 per year.

How much does Tom earn in a year?

£Does Tom pay tax?

Three boxes contain counters.

There are 72 counters in total.

The total number of counters in box A and box B is 33 and A contains more counters.

The difference between the number of counters in box A and box B is 9.

How many counters are in each box?

Box A:

Box B:

Box C:

The pie chart shows information about the sales of 1000 tickets.

There were four times as many adult ticket sales as senior ticket sales.

How many senior ticket sales were there?

Alice makes cards.

Each card used 32 cm of ribbon.

She has 1000 cm of ribbon.

Work out the **maximum** number of cards she can make.

How much ribbon will be left over?

Luke saves 1p coins and 2p coins.

He has

five times as many 1p coins as 2p coins a total of £14

How many 1p coins does he have?

*x*= no. of 1p coins and

*y*= no. of 2p coins, then

*x*= 5

*y*and 14000 =

*x*+ 2

*y*= 7

*y*and hence 7

*y*= 14000 and

*y*= 200 and

*x*= 5

*y*= 5 × 200 = 1000

A company has bikes for hire.

The cost, £*C*, to hire a bike for *n* days is given by the formula

*C* = 15 + *n* − 1)

Write down the cost to hire a bike for 1 day.

£**Special offer!**

How much does it cost to hire a bike for 7 days with this special offer.

£How much does it cost using the first formula?

£Which is cheaper?

The graph shows the cost to hire a bike for one to five days at a different company.

The cost, £*C*, to hire a bike for *n* days from this company is given by the formula

𝐶 = 𝑎 + 𝑏(𝑛 − 1)

Work out the values of *a* and *b*.

*a*=

*b*=

*x*+

*c*, m is the gradient and

*c*is the intercept on the

*y*-axis; so here,

𝐶 = 𝑎 + 𝑏(𝑛 − 1) = (𝑎 − 𝑏) + 𝑏𝑛 and the gradient,

*b*= 5 and the intercept, (𝑎 − 𝑏) = 12; hence 𝑏 = 5 and 𝑎 = 17

Here is the outline of a company’s logo.

How many lines of symmetry does this have?

What is the name of this shape?

Mr Jones works for five days each week.

If he uses his car to travel to work, each day he drives a total distance of 27 miles his car travels 32 miles per gallon of petrol petrol costs £1.31 per litre.

If he uses the bus to travel to work, he can buy a weekly ticket for £22.00.

Use 1 gallon ≈ 4.5 litres.

What is the weekly cost if he uses car?

£Is it cheaper if he uses his car or the bus to travel to work?

Here are two number machines, **A** and **B**.

Both machines have the same input.

Work out the input that makes the output of **A** two times the output
of **B**.

*x*the output of A = 4𝑥 + 4 and for B is 6𝑥 − 2 ; hence 4𝑥 + 4 = 2(6𝑥 − 2) = 12𝑥 − 4 This gives 8 = 8𝑥 so that 𝑥 = 1

Josef runs 400 metres in 1 minute.

He says,

“I would run 20 000 metres in 50 minutes.”

Choose a box to show whether his time to run 20 000 metres is likely to be accurate.

Which sequence is a geometric progression?

This pyramid has a square base.

Volume of a pyramid =

Work out the volume of the pyramid.

^{3}(to the nearest cm

^{3})

^{3}to one decimal place, giving 741 as nearest cm

^{3}

ξ = {15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}

S = square numbers

E = even numbers

Complete a Venn diagram, as shown below.

What numbers are in S ?

{What numbers are in E ?

{What numbers are in S ∩ E ?

{^{2}and 25 = 5

^{2};

E is the set of EVEN numbers, that is 16, 18, 20, 22, 24 and the intersection of S and E gives only one member, that is 16

One of the numbers is chosen at random.

Write down *P*(S ∩ E)

A coin is rolled onto a grid of squares.

It lands randomly on the grid.

To win, the coin must land completely within one of the squares.

Meera and John each roll the coin a number of times and record their results.

Number of wins | Number of losses | |

Meera | 7 | 45 |

John | 27 | 73 |

What is Meera’s estimate of the probability that she will win? Give your answer correct to 2 d.p.

What is John’s estimate of the probability that he will win? Give your answer correct to 2 d.p.

Combine the data to give an improved estimate of winning.

What is your estimate? Give your answer correct to 2 d.p.

In a sale, the original price of a pair of shoes was reduced by

The sale price of the shoes is £21.00.

What was the original price?

Which of these is **not** used to prove that triangles are congruent?

*E* is the centre of rectangle *ABCD*.

Work out the length *DE*.

^{2}= 15

^{2}+ 25

^{2}= 225 + 625 = 850 giving DB ≈ 29.155 and DE =

Which of these is the equation of a line parallel to *y* = 3*x* + 2?

At a school

number of boys : number of girls = 8 : 7

There are 96 more boys than girls.

Work out the total number of students at the school.

Which of these equations has roots 2 and −3?

A pattern is made from two **similar** trapeziums.

Find the area of the shaded part.

^{2}

^{2}and area of smaller trapezium is

^{2}so area of shaded part = 260 – 65 = 195 cm

^{2}