Linear equations

Solve the equation 7 + p = 45.

Calculate the value of x.

You must show all your working.

Use the formula 18 x + 5 y = t to find the value of y when x = 2∙5 and t = 60.

Solve 12 x −= 3 7 x + 15.

A group of 100 pupils attended their school sports day.

13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.

Find the value of x.

One pupil is chosen at random from the group.

What is the probability that this pupil competed only in Track events?

Use the formula 18 x + 5 y = t to find the value of y when x = 2∙5 and t = 60.

The total surface area of all 6 faces of the cuboid below is 240 cm².

Find the volume of the cuboid.

You must show all your working.

A group of 100 pupils attended their school sports day.

13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.

Find the value of x.

One pupil is chosen at random from the group.

What is the probability that this pupil competed only in Track events?

The total surface area of all 6 faces of the cuboid below is 240 cm².

Find the volume of the cuboid.

You must show all your working.

Solve each of the following equations.

3y − 5 = 19

8 p + 5 = 3p − 25

Solve each of the following equations.

3y − 5 = 19

8 p + 5 = 3p − 25

Factorise w² − 6w.

The diagram shows a solid cylinder with radius 10 cm.

The total surface area of the solid cylinder is 1570·8 cm².

Find the height of the cylinder.

Simplify 5k − 8k + 6k.

Solve these equations.

15 + x = 60

20 − y = 9

6w = 54

Solve each of the following equations.

7 m 3 31

Use the formula v = u + at to find the value of t when v = 51·3, u = 2·3 and a = 9·8.

Factorise each of the following.

14a − 35

5x + x²

Solve the following equation.

The diagram below shows a shape made by joining two rectangles together.

The area of the whole shape is 89 cm².

Form and solve an equation to find the value of x.

Solve each of the following equations.

Use the formula v = u + at to find the value of t when v = 51·3, u = 2·3 and a = 9·8.

a and b are two numbers, where b > a.

The mean of the two numbers is equal to the range of the two numbers.

Show that 3a = b.

The diagram below shows a shape made by joining two rectangles together.

The area of the whole shape is 89 cm².

Form and solve an equation to find the value of x.

a and b are two numbers, where b > a.

The mean of the two numbers is equal to the range of the two numbers.

Show that 3a = b.

Solve the following equations.

52 − n = 38

How many centimetres are there in 24·8 metres?

A number machine is shown below.

Calculate the OUTPUT when the INPUT is 1·5.

Kamal worked for a total of 36 hours in one week.

On Monday, Tuesday and Wednesday, he worked the same number of hours each day. On both Thursday and Friday, he worked for half as long as he did on any of the first three days. He did not work on Saturday or Sunday.

How many hours did Kamal work for on Friday?

Kamal worked for_{…………........ ………………….} hours on Friday

A number machine is shown below.

Calculate the OUTPUT when the INPUT is 1·5.

Write down an expression for the OUTPUT when the INPUT is n.

Solve the equation 3x 10 17.

Simplify 6 f 4g 2 f 9g.

Solve the following equations.

3x 10 17

Simplify 6 f 4g 2 f 9g.

Solve the equation 7 5x 2 3x 8.

Make f the subject of the formula h 13 2 f.

Factorise 15x 35y.

Solve the equation 7 5x 2 3x 8.

Make f the subject of the formula h 13 2 f.

Factorise 15x 35y.

Solve the following equations.

11k 99

18 p 6

Solve the equation 7p 3 60.

Simplify the expression 6a 7b 2a 8b.

Express 21·76 as a percentage of 32.

Solve the equation 7p 3 60.

Simplify the expression 6a 7b 2a 8b.

Express 21·76 as a percentage of 32.

Solve 5t 3 3t 14.

The rectangle below has: • a length of 3y • a width of y + a • an area of 3y² +12y.

Find the value of a.

You must show all your working.

Another rectangle has a width of 4x 10.

Given that x is a whole number, explain why the value of x cannot be less than 3.

The perimeter of the rectangle is 14x 4.

Find the length of the rectangle in terms of x.

Simplify 12a 19a 10a.

Solve the following equations.

Solve the following equation.

Imran is 9 years older than Glyn. Glyn is twice as old as Sheila. The sum of the three ages is 49 years.

How old are Imran, Glyn and Sheila?

Imran =_........ years old. Glyn =_........ years old. Sheila =_........ years old.

Solve each of the following equations.

The solution to three of the following equations is x = 6.

For example, the solution to the equation 2x = 12 is x = 6. The solution has already been matched to this equation with an arrow.

Match the solution, x = 6, to the other two equations for which it is the correct solution.

Space for working:

AB and CD are parallel.

Calculate the value of x.

Find the value of 3f + 2g when f = 5·8 and g = −3·7.

AB and CD are parallel.

Calculate the value of x.

Solve 7 x – 3 = 11.

Find the value of 3f + 2g when f = 5·8 and g = −3·7.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

Simplify the expression 9 g – 5 g + 12 g.

Solve the equation 5y = 45.

Solve the equation w – 16 = 14.

Solve the equation 4x + 7 = 10.

Solve 5(2 x + 3) = 20.

A number machine is shown below.

Write down an expression for the OUTPUT when the INPUT is n.

Solve the equation 4 x + 7 = 10.

Simplify 8d – 6e – 3d + 4e.

Solve 5(2 x + 3) = 20.

Factorise 7a + 21.

A number machine is shown below.

Write down an expression for the OUTPUT when the INPUT is n.

Solve these equations.

7x = 56

23 – x = 9

Sian has n boxes. Each box contains 8 pens.

How many pens does Sian have altogether?

Number of pens is_{………........ ………………}

Meic had m CDs. He gave 3 CDs to a friend.

How many CDs does Meic have now?

Number of CDs is_{………........ ………………}

Calculate the value of 3 x + 4 y when x = −6 and y = 5.

Simplify the expression 9g – 4f – 3g – 5f.

Solve the equation 3m − 7 = 8.

Expand 4(3x – 5).

Factorise x² + 4x – 21. Hence, solve x² + 4x – 21 = 0.

Factorise x² + 4x – 21. Hence, solve x² + 4x – 21 = 0.

Show that

6 x (8 x + 1) – 3(4 x + 1)(4 x – 1) ≡ 6 x + 3.

Hence, write down the value of x for which 6x(8x + 1) – 3(4x + 1)(4x – 1) = 0.

Simplify 8 p – 12 p + 9 p.

Solve the following equations.

6x = 48

32 – y = 17

Tom thinks of a number. He multiplies the number by 4. The answer is 76.

What number did Tom think of?

Solve the following equations.

13f + 2 = 6f + 5.

n is an integer.

Tick the correct statement below.

You must give an explanation for your decision.

Find the value of 5 f + 7 g when f = 3·8 and g = −2·6.

Solve the following equation.

Give your answer correct to 1 decimal place.

7 x – 4 = 12

Factorise 10 a – 15.

Solve the following equations.

13f + 2 = 6f + 5.

n is an integer.

Tick the correct statement below.

You must give an explanation for your decision.

Find the value of 5 f + 7 g when f = 3·8 and g = −2·6.

Solve the following equation.

Give your answer correct to 1 decimal place.

7 x – 4 = 12

Write down the n th term of the following sequence.

8, 11, 14, 17, ……

Make t the subject of the formula r = 3t – 8.

A rectangle has a length of (x + 5) cm and a width of (2x – 3) cm. Its perimeter is 46 cm.

Calculate the value of x.

Write down the n th term of the following sequence.

8, 11, 14, 17, ……

Make t the subject of the formula r = 3t – 8.

A rectangle has a length of (x + 5) cm and a width of (2x – 3) cm. Its perimeter is 46 cm.

Calculate the value of x.

Simplify the expression 15 x – 2 y – 7 x – 4 y.

Solve the equation 2m – 7 = 12.

Calculate the value of 5f + 3g when f = −4 and g = 7.

One of the values below is the solution to k + 3 = 6·9

Circle the correct answer.

2·3 20·7 3·9 9·9 207

Simplify the expression 12w + 15w – w.

Write down the next term in the following sequence.

Describe in words the rule for continuing the following sequence.

4, 12, 36, 108, …

Look at the sequence:

8, 16, 24, 32, …

Will any of the first 100 terms of this sequence be a prime number?

Explain how you know.

The nth term of a sequence is given by 3n – 20.

What is the value of the 6th term?

Simplify the expression 15 x – 2 y – 7 x – 4 y.

Solve the equation 2m – 7 = 12.

Calculate the value of 5f + 3g when f = −4 and g = 7.

A cuboid has sides x cm, 5 cm and 7 cm.

The total surface area of the cuboid is 142 cm².

Form an equation in terms of x.

Solve the equation to find x.

Factorise the following.

6x – 15

y² + 4y

The nth term of a sequence is given by 3n – 20.

What is the value of the 6th term?

Consider the following statement.

‘There are no odd numbers greater than 50 in this sequence.’

Show that this statement is incorrect.

A cuboid has sides x cm, 5 cm and 7 cm.

The total surface area of the cuboid is 142 cm².

Form an equation in terms of x.

Solve the equation to find x.

Solve these equations.

6x = 42

x + 9 = 28

14 – x = 8

Solve. 7

Simplify 3f + 7g + f – 4g.

Use the formula 5p + 2q = t to find the value of q when p = 4 and t = 24.6.

The diagram below shows an equilateral triangle ABC with AB = (4 x – 7) cm.

The perimeter of the triangle is 27 cm.

Calculate the value of x.

Expand and simplify the following expression.

Simplify 3f + 7g + f – 4g.

Use the formula 5p + 2q = t to find the value of q when p = 4 and t = 24.6.

The diagram below shows an equilateral triangle ABC with AB = (4 x – 7) cm.

The perimeter of the triangle is 27 cm.

Calculate the value of x.

Expand and simplify the following expression.

Write down the next two numbers in the following sequence.

Expand 5(3x – 2).

Solve 9x + 3 = 4x + 5.

ABC is an isosceles triangle with AB = AC.

Calculate the value of y.

ABC is an isosceles triangle with AB = AC.

Calculate the value of y.

Solve these equations.

7x = 56

y + 19 = 83

Simplify the expression 12k – 15k + 7k.

Team A and Team B play in a competition.

Team A has nine more points than Team B. Team A has four times as many points as Team B.

How many points does each team have?

Team A:_{……........} points Team B:_{……........} points

Team A and Team B play in a competition.

Team A has nine more points than Team B. Team A has four times as many points as Team B.

How many points does each team have?

Team A:_{……........} points Team B:_{……........} points

ABCD is a quadrilateral.

Calculate the value of x.

When ABCD is drawn to scale, would the lines AD and BC be parallel or not?

You must justify your answer without using a scale drawing.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale