Write 6324 correct to the nearest thousand.

(a) Write the following numbers in order of size. Start with the smallest number.

\(-6 \quad 6 \quad -5 \quad 0 \quad 12\)

(b) Write the following numbers in order of size. Start with the smallest number.

\(0.078 \quad 0.78 \quad 0.87 \quad 0.708\)

Write 20% as a fraction.

Here is a list of four fractions.

\[ \frac{4}{16} \quad \frac{2}{8} \quad \frac{15}{60} \quad \frac{3}{9} \]

One of these fractions is not equivalent to \(\frac{1}{4}\).

Write down this fraction.

Write down the first even multiple of 7.

(a) Simplify \(3 \times 4t\)

(b) Simplify \(8a – 3a + 2a\)

Here is a probability scale showing events A, B, C and D.

(a) Write down the letter of the event that is certain.

(b) Write down the letter of the event that is unlikely.

There are 12 counters in a bag.

• 3 of the counters are red.
• 1 of the counters is blue.
• 2 of the counters are yellow.
• The rest of the counters are green.

Caitlin takes at random a counter from the bag.

(c) Show that the probability that this counter is yellow or green is \(\frac{2}{3}\).

3 kg of meat costs £54.

Nina buys 2 kg of the meat.

Work out how much Nina pays.

The centre of this circle is marked with a cross (×).

(a) Write down the mathematical name of the straight line shown in the circle.

(b) Write down the mathematical name of the straight line that is touching the circle.

Tim and three friends go on holiday together for a week.

The 4 friends will share the costs of the holiday equally.

Here are the costs of the holiday:

• £1280 for 4 return plane tickets
• £640 for the villa
• £220 for hire of a car for the week

Work out how much Tim has to pay for his share of the costs.

Write down an example to show that each of the following two statements is not correct.

(a) The factors of an even number are always even.

(b) All the digits in odd numbers are odd.

A shop sells desktop computers, laptops and tablets.

The composite bar chart shows information about sales over the last three years.

(a) Write down the number of desktop computers sold in 2015.

(b) Work out the total number of laptops sold in the 3 years.

(c) State the item that had the greatest increase in sales over the 3 years. Give a reason for your answer.

Alex says, “In 2017, more tablets were sold than desktop computers. This means the shop makes more profit from the sale of tablets than from the sale of desktop computers.”

(d) Is Alex correct? You must justify your answer.

A piece of wire is 240 cm long.

Peter cuts two 45 cm lengths off the wire.

He then cuts the rest of the wire into as many 40 cm lengths as possible.

Work out how many 40 cm lengths of wire Peter cuts.

Gavin, Harry and Isabel each earn the same monthly salary.

Each month:

• Gavin saves 28% of his salary.
• Harry spends \(\frac{3}{4}\) of his salary and saves the rest.
• The amount Isabel saves : the amount she spends = 3 : 7.

Work out who saves the most of their salary each month.

You must show how you get your answer.

Work out 15% of 160 grams.

P = 4x + 3y

x = 5

y = -2

(a) Work out the value of P.

(b) Expand \(4e(e + 2)\)

(c) Solve \(3(m – 4) = 21\)

There are some chocolates in a box.

\(\frac{1}{4}\) of the chocolates contain nuts.

The rest of the chocolates do not contain nuts.

Write down the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts.

Give your answer in the form \(1 : n\)

\(A = \{\text{multiples of 5 between 14 and 26}\}\)

\(B = \{\text{odd numbers between 14 and 26}\}\)

(a) List the members of \(A \cup B\)

(b) Describe the members of \(A \cap B\)

(a) Work out \(2\frac{1}{7} + 1\frac{1}{4}\)

(b) Work out \(1\frac{1}{5} \div \frac{3}{4}\)

Give your answer as a mixed number in its simplest form.

In a village,

• the number of houses and the number of flats are in the ratio 7 : 4
• the number of flats and the number of bungalows are in the ratio 8 : 5

There are 50 bungalows in the village.

How many houses are there in the village?

Renee buys 5 kg of sweets to sell.

She pays £10 for the sweets.

Renee puts all the sweets into bags.

She puts 250 g of sweets into each bag.

She sells each bag of sweets for 65p.

Work out her percentage profit.

A cycle race across America is 3069.25 miles in length.

Juan knows his average speed for his previous races is 15.12 miles per hour.

For the next race across America he will cycle for 8 hours per day.

(a) Estimate how many days Juan will take to complete the race.

Juan trains for the race.

The average speed he can cycle at increases.

It is now 16.27 miles per hour.

(b) How does this affect your answer to part (a)?

Here is a solid square-based pyramid, VABCD.

The base of the pyramid is a square of side 6 cm.

The height of the pyramid is 4 cm.

\(M\) is the midpoint of \(BC\) and \(VM = 5\) cm.

(a) Draw an accurate front elevation of the pyramid from the direction of the arrow.

(b) Work out the total surface area of the pyramid.

A pattern is made from four identical squares.

The sides of the squares are parallel to the axes.

Point A has coordinates (6, 7).

Point B has coordinates (38, 36).

Point C is marked on the diagram.

Work out the coordinates of C.

On the grid below, draw the graph of \(y = 1 – 4x\) for values of \(x\) from \(-3\) to \(3\).

\(\mathbf{a} = \begin{pmatrix} 5 \\ 2 \end{pmatrix} \quad \mathbf{b} = \begin{pmatrix} -1 \\ 7 \end{pmatrix}\)

Work out \(2\mathbf{a} + \mathbf{b}\) as a column vector.