Rearranging formulae

A straight line has equation y = 5 x + 2.

Write down the gradient of the line.

Find the value of y when x = 7.

Make x the subject of y = 5 x + 2.

The diagram shows a sphere with radius r cm.

The sphere has a circumference of 50 cm.

Work out the surface area of the sphere.

[The surface area, A, of a sphere with radius r is A = 4πr².]

Rearrange this formula to make a the subject.

The diagram shows a sphere with radius 3 cm and a cube with side length x cm.

The surface area of the sphere is equal to the surface area of the cube.

Work out the side length, x cm, of the cube. You must show your working.

[The surface area, A, of a sphere with radius r is A = 4πr².]

Rearrange this formula to make x the subject.

y = x + 3

Rearrange this formula to make w the subject.

p = 3 w

A sphere has radius x cm. A cone has radius R cm and height 2 R cm.

The volume of the sphere is equal to the volume of the cone.

Write R in terms of x.

The diagram shows a regular pentagon made using ten congruent right-angled triangles. The length of one side of the pentagon is 12 cm.

Show that the area of the pentagon is 247.75 cm², correct to 2 decimal places.

The regular pentagon is the base of a pyramid.

The pyramid has volume 450 cm³. The perpendicular height of the pyramid is h cm.

Calculate the value of h. [The volume of a pyramid is × area of base × perpendicular height.]

Work out.

3⁴

Simplify. 5x² x

Rearrange this formula to make x the subject.

Show that the formula v = u + at can be rearranged to a =

Use the formula

to find the acceleration, am/s², when a particle takes 4 seconds to increase from an initial velocity of 3 m/s to a final velocity of 9 m/s.

Finley is asked to solve the equation 5 x + 4 = 19.

Finley’s working is shown below.

Write down the error that Finley has made.

Charlie is asked to use the formula

v = u + at

to find the initial velocity, when

• the acceleration is 5 m/s²

• the final velocity is 29 m/s

• the time is 3 seconds.

Charlie’s working is shown below.

Write down the error that Charlie has made.

Rearrange this formula to make u the subject.

A rocket accelerates at 90 m / s² and travels 270 km. The rocket’s final velocity is 8000 m / s.

Using part (a), or otherwise, calculate the rocket’s initial velocity in m / s.

The diagram shows a quadrilateral, PQRS.

PS = 10 cm. Angle QPS = Angle PSR = 90°.

SR is 6 cm longer than PQ. The area of quadrilateral PQRS is A cm².

Write a simplified expression for the length PQ in terms of A. You must show your working.

Rearrange this formula to make d the subject.

f = 5 d + 4

Use the formula

v = u + at

to find the final velocity, when

• the initial velocity is 5 m/s

• the acceleration is 7.5 m/s²

• the time is 6 seconds.

Here are two pieces of work.

For each one, describe the error in the method and give the correct answer.

The diagram shows a sphere and a cone.

The sphere has radius 4 cm. The cone has radius 15 cm and height 30 cm.

The sphere is completely filled with water. The same amount of water is poured into the cone.

Work out the depth, d cm, of the water in the cone. You must show your working. [The volume V of a sphere with radius r is V = r³. The volume V of a cone with radius r and height h is V = r²h.]

Here is a function.

When the input is 6, the output is 18.

Find the value of t.

Here is another function. When the input is x, the output is y.

Write an algebraic expression for x in terms of y.

Multiply out.

5 (x + 2)

Rearrange this formula to make r the subject.

p = 3 r - 5

A car accelerates at 4.06 m/s² for 10.1 seconds from an initial velocity of 2.93 m/s.

Harper rounds each value to 1 significant figure. Harper uses the rounded values and the formula

to estimate the distance travelled in the 10.1 seconds. Harper’s answer is 430 metres.

Using Harper’s method, show that their answer is wrong.

Rearrange this formula to make t the subject.

Rearrange this formula to make w the subject.

P = 2 w + 2 h

x² - 2y = 5 and 4y + z = 7.

Write z in terms of x. Give your answer in its simplest form.

Rearrange this formula to make y the subject.

A train is travelling with a velocity of 15 m / s. It then accelerates at 0.5 m / s² for 6 seconds.

Use the formula v = u + at to calculate the velocity of the train after the 6 seconds.

Rearrange the formula v = u + at to make a the subject.

Simplify fully.

3 t + 5 u - 2 t + 3 u

6a × 2a²

Make x the subject of the formula y = x² - 1.

Rearrange this formula to make x the subject.

y = x - 2

Rearrange this formula to make d the subject.

C = π d

Rearrange this formula to make y the subject.

You are given that 5 y = 4 x.

Find the value of y when x = 10.

Write y in terms of x.

Simplify.

2 p + 5 p - 3 p

6 j + 3 k - j - 5 k

Find the value of 10 h + 6 t when h = 12 and t = 4.

Rearrange this formula to make d the subject.

e = f - 7 d

Calculate s when u = 5, t = 10 and a = 3.

Make a the subject of the formula.

Rearrange the equation to make x the subject.

y = 7 x - 3

Factorise.

x² - xy

x² + 8x + 12

Find the value of 3 a + 2 b when a = 16 and b = 7.

Use the formula

v = u + at

to find the final velocity, when

• the initial velocity is 2 m/s

• the acceleration is 1.5 m/s²

• the time is 6 seconds.

Make d the subject of this formula.

c = 7 d

Rearrange the equation to make x the subject.

y = 7 x - 3

Factorise.

x² - xy

x² + 8x + 12