If you want to give an answer like `x^2` then type x^2.

If you want to give an answer as a fraction e.g. `\frac{1}{4}` then type 1/4.

Any problems contact ross@mathsgrader.com

Given that `\frac{x^(5)}{x^(a)} = x^(1)`

Work out the value of `a`

Simplify `\frac{8b^(7) \times 4b^(2)}{2b^(3)}`

Simplfy `(2x^(4))^3`

Write the number 2100 in standard form.

Work out the value of $$(7.6\times 10^8)\div(2\times 10^4)$$ Giving your answer as a normal number.

Harvey invests £930 into an account with an interest rate of 7% per annum. How much will be in the account after 2 years?

A football team sells home shirts and away shirts in their club shop in the ratio 7:4.

The home shirts come in both adult size or child size and the club sells these sizes in ratio 6:1.

What fraction of the total number of shirts sold are child size home shirts?

The average house price in Manchester in 2017 was £193,436. In 2018 the average price went up to £201,174. Calculate the percentage change in house prices in Manchester between 2017 and 2018, giving your answer to the nearest whole number.

In London 1lb of tomatoes cost £1.89. In Paris 1kg of tomatoes cost €3.18. $$1kg = 2.2 lb$$ $$£1 = €1.15$$

Work out in pounds how much cheaper it is to buy 1kg of tomatoes in Paris than London.

Andy and Bernadette share some sweets in ratio 2:8. Andy gets A sweets and Bernadette gets B sweets

Chris and Donald share the same number of sweets in ratio 4:3. Chris gets C sweets and Donald gets D sweets

Work out A:B:C:D.

Here is a Venn diagram.

A number is chosen at random from `\varepsilon`. Find P(B`\cup`C)

Adam is measuring the heights of plants in his garden. The results are in the table below.

Estimate the mean height of Adam's plants giving your answer to 1 decimal place.

200`ml` of liquid A and 400`ml` of liquid B are mixed together to create liquid C.

Work out the density of liquid C to 2 decimal places.

Turn 120`cm^3` to `m^3`

Shape A is a regular triangle. Shape B is a regular octagon

Shape P is a regular polygon. How many sides does P have?

On the grid shade the region that satisfies all these inequalities

$$y \ge x-1$$ $$x \le 6-2y$$ $$x\ge -3$$

Convert `0.4\dot9` to a fraction

Using `X_{n+1} = \frac {\sqrt{5x_{n}+1}}{3}`

Starting with `X_{0} = 1` find the values of `X_{1}`, `X_{2}` and `X_{3}`

The flight from London to Budapest takes 4 hours to the nearest 10 minutes.

The distance the plane flies is 1800 miles to the nearest 100 miles.

Work out the lower boundary for the speed of the plane to the nearest mph.

Here is a distance time graph.

Work out an estimate for the acceleration when t = 4

Use 5 equal strips to find an estimate for the distance travelled in 10 seconds.

The diagram shows cuboid ABCDEFGH.

ABCD is a square with an area of 81`cm^2`

The volume of the cuboid ABCDEFGH is 1134`cm^3`

Find the length of diagonal AH to 1 decimal place

The diagram shows a badge which is formed of a sector of a circle, centre O, and a triangle AOB.

Angle AOB equals 26^o and length AO equals 5cm

Find the total area of the badge

Work out the nth term of this sequence $$36 ,48 ,66 ,90 ,120$$

The table shows information about the speed, in mph, of 120 cars.

Fill in the missing values in the table

A, B and C are points on the circumference of a circle with radius 4 cm. AB is a diameter CD is a tangent to the circle at C

CD is a tangent to the circle at C

CD = 10cm

Find the size of angle CAB to 3 significant figures.

Solve $$y = 2x-3$$ $$x^2 + y^2 = 2$$