Substitution into formulae

Simplify 4e × 7f

Simplify d × d × d × d × d

Simplify 3a + 2k + a – 7k

Solve x + 6 = 15

Solve 2r – 9 = 14

Lui is asked to work out the value of 30 – 4 x when x = –5

Here is his working and his answer.

Lui’s answer is wrong.

Explain what Lui has done wrong in his working.

Oni thinks of a number. She calls the number Y

Y is a positive, odd number and Y 9

Write down all the possible values of Y

Factorise 15 5x

d = 5p + 7r

Work out the value of p when d = 35 and r = 2

Sweets are sold in small packets and large packets.

There are 12 sweets in a small packet. There are 25 sweets in a large packet.

Ben buys m small packets of sweets and n large packets of sweets.

Write an expression, in terms of m and n, for the total number of packets of sweets Ben buys.

Write an expression, in terms of m and n, for the total number of sweets Ben buys.

Charlene is comparing cooking temperatures in degrees Celsius (°C) with cooking temperatures in degrees Fahrenheit (°F)

She finds this rule to change from °C to °F

Change a temperature of 175°C to a temperature in °F

Change a temperature of 482°F to a temperature in °C

A small bag of grain contains 2 kg of grain. A large sack of grain contains 7 kg of grain.

Makenna buys r small bags of grain and h large sacks of grain.

The total amount of grain Makenna buys is Fkg.

Write down a formula for F in terms of r and h

Expand x (3 – x)

Factorise fully 12a – 18b

There are 8 slices of cheese in each small pack of cheese. There are 20 slices of cheese in each large pack of cheese.

Afreen buys h small packs of cheese and j large packs of cheese. She buys a total of T slices of cheese.

Write down a formula for T in terms of h and j

Simplify 5p × 9k

Simplify 3e + 2f + 8e – 7f

Solve 2d + 7 = 16

Use Aarav’s rule to work out an estimate for the time this bus journey takes.

A different bus journey takes 55 minutes. There are 8 bus stops on the route.

Use Aarav’s rule to work out an estimate for the distance of this bus journey.

p = t – ac

t = 18 a = –3 c = 5

Work out the value of p

Make x the subject of the formula d = 3x + 10

Simplify aa×aa×a

Simplify 8b×3c

Expand 3(x + 4)

Q = 5v² – w

Work out the value of Q when v = and w =

Solve 5x = 30

Solve y – 7 = 12

Simplify h + h + h + h + h

Simplify 5a + 7f – 2a + 4f

Simplify 3c + 5d – c + 2d

Simplify 8e 5f

Solve 5r – 3 = 8

Factorise 6 x – 15

There are 200 bolts in each box of bolts. Samira buys c boxes of bolts.

Samira uses the bolts she bought to fill packets of bolts. There are 50 bolts in each packet of bolts. Samira sells d packets of bolts.

The total number of bolts Samira has left is T

Write down a formula for T in terms of c and d

Danielle is going to print some business cards.

She uses this rule to work out the total cost, in euros, of printing the business cards.

Total cost = price per card number of cards + fixed fee

price per card = 0.14 euros fixed fee = 25 euros

Danielle is going to print 350 business cards.

Work out the total cost of printing the business cards.

Solve 5 c = 15

Expand x(8 – x)

T = 5m – 6n

Work out the value of T when m = 4.2 and n = –2.5

Make g the subject of k = 2g + t

Simplify aa aa

Simplify 4b5c

Simplify 6d + 2e + d – 5e

Expand x (4 – x)

t = ab – c

a = 1.5 b = 2.4 c = –5.6

Work out the value of t.

Make d the subject of y = dx – e

Here is a number machine.

Work out the output when the input is 7

Work out the input when the output is 160

When the input is n, the output is P.

Find a formula for P in terms of n.

Simplify p + p + p + p + p + p

Simplify 5y² + 6y² – 3y²

Simplify eeeee

Simplify 5c4d

Solve x – 7 = 19

18² + 15² – 5³ = 4n

Work out the value of n.

Factorise 9t – 6

w = 5y² – y³

Work out the value of w when y = –2

Factorise fully 8p² – 2p

Expand 4t(3t – 2)

Expand and simplify (5x – 2)(x + 4)

Simplify 5c d

Solve x + 5 = 12

Solve 9y = 36

Simplify 8k + 5m – 2k + 6m

Expand 4(3g + 1)

c = 4 d = 7

Work out the value of 3c + 2d

p = −6 m = −2

Work out the value of 2p² + 3m

There are 6 eggs in a small box of eggs. There are 12 eggs in a large box of eggs.

Alex buys g small boxes of eggs and h large boxes of eggs. He buys a total of T eggs.

Write down a formula for T in terms of g and h.

Simplify h⁷h²

G = c² – 4c

Find the value of G when c = –5

Show clear algebraic working.

Simplify h⁷h²

G = c² – 4c

Find the value of G when c = –5

Show clear algebraic working.

The following rule is used to work out the total cost, in euros, of hiring a room.

Paolo hires the room for 5 hours.

Work out the total cost.

Agathe also hires the room. The total cost is 164 euros.

For how many hours does Agathe hire the room?

The total cost of hiring the room for n hours is T euros.

Write down a formula for T in terms of n.

Simplify 3r ×5t

Solve 4x+ 5 = 27

P= 7w– 5y

Find the value of P when w= 2 and y= 4

Q= 2u²− 5

Find the value of Q when u= −3

Simplify 6m− 2k+ 5m−k

P= 2a+ 3b

Work out the value of P when a= 5 and b= 8

P= 2a+ 3b

Work out the value of a when P= 16 and b= 20

The point A has coordinates (5, −4) The point B has coordinates (13, 1)

Work out the coordinates of the midpoint of AB.

Line L has equation y= 2 − 3x

Write down the gradient of line L.

Line L has equation y= 2 − 3x

Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.

The point A has coordinates (5, −4) The point B has coordinates (13, 1)

Work out the coordinates of the midpoint of AB.

Line L has equation y= 2 − 3x

Write down the gradient of line L.

Line L has equation y= 2 − 3x

Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.

Simplify 10ab

Solve n + 3 = 7

Find the value of 25 – 4 g when g = –3

Expand and simplify x (2 x + 1) + 3(x – 2) + 7

Tenzin walks in the mountains. She has a rule to estimate the temperature at different heights on a mountain.

The temperature at a height of 800 metres on a mountain is 6 C.

Use Tenzin’s rule to work out an estimate of the temperature at a height of 2000 metres on the mountain.

Tenzin also has a rule to estimate the time it will take her to complete a walk in the mountains.

She uses an average speed of 5 km / h for the distance she will walk and then adds on 1 minute for every increase of 10 metres in height.

Tenzin plans to walk 12 km in the mountains with an increase of 800 metres in height.

Use Tenzin’s rule to work out an estimate for the time it will take her to complete this walk. Give your answer in hours and minutes.