Linear equations

Greg is x years old. Greg is 5 years older than Katy.

Write down an expression, in terms of x, for Katy’s age.

Carl is twice as old as Greg.

Write down an expression, in terms of x, for Carl’s age.

Solve 4y = 12

Simplify n × n × n

Solve 5k – 4 = 26

The first three terms of a Fibonacci sequence are a 3 a 4 a The 5th term of this sequence is 286 Work out the value of a.

Factorise 6 a + 15

Solve 4(3y + 1) = 28

Solve x + x + x + x = 20

Solve y + 7 = 24

Solve 2(4 x – 5) = 18

ABCD is a quadrilateral.

All angles are measured in degrees. Show that ABCD is a trapezium.

The diagram shows two right-angled triangles.

All lengths are measured in centimetres. Given that sina = tanb work out the value of x.

x – 4, x + 2 and 3x + 1 are three consecutive terms of an arithmetic sequence.

Find the value of x.

y – 4, y + 2 and 3y + 1 are three consecutive terms of a geometric sequence.

Find the possible values of y.

P = 2g + 4h

Work out the value of P when g = 3 and h = 5

Work out the value of g when P = 38 and h = 3

V = 3r – q

Work out the value of V when r = –3 and q = 2

Mano has three shelves of books. There are x books on shelf A. There are (3 x + 1) books on shelf B. There are (2 x – 5) books on shelf C. There is a total of 44 books on the three shelves. All the books have the same mass. The books on shelf B have a total mass of 7500 g. Work out the total mass of the books on shelf A.

Solve 5 x − 14 = 52 − x

Solve 5x − 14 = 52 − x

Solve p – 2 = 3

Here is a triangle and a rectangle.

All measurements are in centimetres. The area of the triangle is 10 cm² greater than the area of the rectangle. Work out the value of x.

Here is a triangle and a rectangle.

All measurements are in centimetres. The area of the triangle is 10 cm² greater than the area of the rectangle. Work out the value of x.

Solve 4(2 x – 3) = 20

Solve m − 3 = 4

Solve 3n + n = 24

Simplify 4 c + 7 d + 3 c − d

Solve 5(2m − 6) = 40

There are x sweets in a box. There are y sweets in a packet.

Write an expression, in terms of x and y, for the total number of sweets in 3 boxes and 2 packets.

Expand 3(4 − 2 x)

Factorise 4p + 6

The profit made by a shop increases each year. The profit made by the shop in year n is £P_n Given that the profit made by the shop in the next year is £P_{n+ 1} then

The table shows the profit made by the shop in 2018 and in 2019

Work out the profit predicted to be made by the shop in 2021

Expand 2(a + d)

Factorise 6y² – 5y

Solve 4x – 7 = 37

Expand y (y + 5)

Factorise 4a – 6

Solve 2(5x – 4) = 21

Simplify 4e²f 5ef³

Expand x (x – 4)

Factorise 15y – 10

Solve 7(f – 5) = 28

Solve 3 m = 36

Solve 7 – x = 3

T = 3x + 4y

Work out the value of T when x = 5 and y = –7

Work out the value of y when T = 38 and x = 6

A hot air balloon is descending. The height of the balloon n minutes after it starts to descend is h_n metres. The height of the balloon (n +1) minutes after it starts to descend, h_{n+ 1} metres, is given by

The balloon starts to descend from a height of 1200 metres at 09 15 At 09 16 the height of the balloon is 1040 metres. Work out the height of the balloon at 09 18

Simplify 3 x + 5 y + 2 x − 4 y

Solve 5p + 7 = 22

x – 1 = 2

Work out the value of 2x²

Solve 4(x – 6) = 44

Solve t + t + t = 12

Solve x – 2 = 6

Solve 6 w + 2 = 20

You can use this rule to work out the total hire charge, in pounds (£), for hiring a 3D printer for a number of weeks.

Mia wants to hire a 3D printer for 4 weeks.

Work out the total hire charge.

Zahir hires a 3D printer. The total hire charge is £680

For how many weeks does Zahir hire the 3D printer?

Solve 3(x – 4) = 12

Factorise fully 9b – 3b²

A is the point with coordinates (5, 9) B is the point with coordinates (d, 15)

The gradient of the line AB is 3

Work out the value of d.

A is the point with coordinates (5, 9) B is the point with coordinates (d, 15)

The gradient of the line AB is 3

Work out the value of d.

The diagram shows a pentagon. The pentagon has one line of symmetry.

AE = 4 x AB = 2 x + 1 BC = x + 2

All these measurements are given in centimetres.

The perimeter of the pentagon is 18 cm.

Show that 10 x + 6 = 18

Find the value of x.

P = 4 x + 3 y

x y = – 2

Work out the value of P.

Expand 4 e (e + 2)

Solve 3(m – 4) = 21

Solve x + x + x = 51

Solve 2 f + 7 = 18

Here is a rectangle.

All measurements are in centimetres.

The area of the rectangle is 48 cm².

Show that y = 3

Here is a rectangle.

All measurements are in centimetres.

The area of the rectangle is 48 cm².

Show that y = 3

Solve 5 x − 6 = 3(x − 1)

Solve 5 x − 6 = 3(x − 1)

Simplify 7 × e × f × 8

Solve 4(x – 5) = 18

−3 t ≤ 2 t is an integer.

Write down all the possible values of t.