1. [4]
length (x – 1) cm and width 5 cm. The perimeter of rectangle A is equal to the perimeter of rectangle B. Calculate x.
Rectangle A has length (2x – 1) cm and width (x + 2) cm. Rectangle B has
4 friends decide to rent the cottage for 5 days when the fixed charge is £120.
The cost of renting a holiday cottage is given by the formula
How much will each pay if they share the cost equally?
Cost = Number of days x £60 + Fixed charge
Solve the inequality 5x – 4 > 18 and write down the smallest value of x, where x is an integer. x
x2 + 2x
Comment 2 3
Hannah is x years old. Joanne is 5 years older than Hannah. Laura is twice as old as Hannah. The total of their ages is 65. Work out Hannah’s age.
Complete the table
x2 + 2x = 10 has a solution between 2 and 3. Find the value of x, to 1 decimal place.
The basic monthly charge for a mobile phone contract is £35. This includes:
    Option 1:    300 free minutes of calls and 100 free texts OR
    Option 2:    100 free minutes of calls and unlimited free texts.
All other calls are 6p per min. Extra texts are 10p each. On average, each month, Matt
makes 500 minutes of calls and sends 250 texts. Which option should he choose?
The cost of hiring a concrete mixer is £12 for the first day and then £8 for each additional day. Alan paid £44 for hiring this mixer. For how many days did he hire the mixer?
A rectangle of length (2x + 5) cm and width x cm has a perimeter of 52 cm. Calculate the area.
When x = 4 cm, the perimeter of the quadrilateral is 68 cm. Find the value of y.
Algebra – Formula, Form and Solve Equations, Substitution, Solve Inequalities
Emma has x pounds, Nicola has 18 pounds less than Emma, and Sarah has
twice as many as Nicola. Together they have £180. Work out how much
money Nicola has.
The triangle has lengths (4x – 2) cm, (2x + 5) cm and (6x – 9) cm. Find the value of x that makes this triangle equilateral.
2x + 5 x

2. [4] 5x > 22 M1 x > 4.4 A2 5 A1ft 5 x 60 + 120 M1 £420 A1
3 × (their) 4 – (their) –1 = 13 A1ft
(5x) = 20 or x = 4 B1
(5 – 8) ÷ 3 or 3y = –3 M1
(y =) –1 A1
5 x M1
£420 A1
Their 420 ÷ 4 M1
£105 A1ft
length (x – 1) cm and width 5 cm. The perimeter of rectangle A is equal to the perimeter of rectangle B. Calculate x.
Rectangle A has length (2x – 1) cm and width (x + 2) cm. Rectangle B has
4 friends decide to rent the cottage for 5 days when the fixed charge is £120.
The cost of renting a holiday cottage is given by the formula
How much will each pay if they share the cost equally?
Cost = Number of days x £60 + Fixed charge
Solve the inequality 5x – 4 > 18 and write down the smallest value of x, where x is an integer.
6x + 2 = 2x + 8 oe B1
6x – 2x = 8 – 2 oe Allow one error in signs M1
4x = 6   ft Only from Their (2x + 8) A1 ft
1.5 oe B1 ft x
x2 + 2x
Comment 2 3
Hannah is x years old. Joanne is 5 years older than Hannah. Laura is twice as old as Hannah. The total of their ages is 65. Work out Hannah’s age.
Complete the table
Hannah is x Joanne is x Laura is 2x M1
4x + 5 = 65 M1
4x = 60 M1
15 years old A1
x2 + 2x = 10 has a solution between 2 and 3. Find the value of x, to 1 decimal place.
Values for x = 2 and 3 calculated and trial between 2 and 3 B2
Trial between 2.3 and 2.4 inclusive that “bracket” the answer B1
Trial at 2.35 and 2.3 stated as answer A1
The basic monthly charge for a mobile phone contract is £35. This includes:
    Option 1:    300 free minutes of calls and 100 free texts OR
    Option 2:    100 free minutes of calls and unlimited free texts.
All other calls are 6p per min. Extra texts are 10p each. On average, each month, Matt
makes 500 minutes of calls and sends 250 texts. Which option should he choose?
The cost of hiring a concrete mixer is £12 for the first day and then £8 for each additional day. Alan paid £44 for hiring this mixer. For how many days did he hire the mixer?
44 – 12 M1
32 ÷ 8 M1
4 A1
Hired mixer for 5 days A1ft
Option × 6 or (£) 12 or 1200 or 150 × 10 or (£) 15 or M1 (£) 27 or 62   A1
(£) 27 and 24    or    62 and 59 Option 2 (cheaper)   B1 ft
 Option 2  400 × 6 M1
A rectangle of length (2x + 5) cm and width x cm has a perimeter of 52 cm. Calculate the area.
When x = 4 cm, the perimeter of the quadrilateral is 68 cm. Find the value of y.
Algebra – Formula, Form and Solve Equations, Substitution, Solve Inequalities
14x + 6y M1
‘Their 14’ × 4 + ‘their 6’ × y = 68 M1
‘Their 6y’ = ‘their 12’ M1
y = 2 A1
6x + 10 (= 52) oe M1
x = A1
19 x 7 M1
133 cm2 A1
Emma has x pounds, Nicola has 18 pounds less than Emma, and Sarah has
twice as many as Nicola. Together they have £180. Work out how much
money Nicola has.
Emma has x Nicola has x Sarah has 2x -36 M1
4x - 54 = 180 M1
4x = 234 M1
£40.50 A1
The triangle has lengths (4x – 2) cm, (2x + 5) cm and (6x – 9) cm. Find the value of x that makes this triangle equilateral.
4x – 2 = 2x + 5 or 4x – 2 = 6x – 9 or 6x – 9 = 2x + 5 oe M1
x = 3.5 oe Solve two of the equations and obtain 3.5 for each M1A1
Must show all sides = 12 A1
2x + 5 x

3. 1 o’clock (5x) = 20 or x = 4 B1 (5 – 8) ÷ 3 or 3y = –3 M1 (y =) –1 A1
Complete the table 20
(5x) = 20 or x = B1
(5 – 8) ÷ 3 or 3y = –3 M1
(y =) – A1
3 × (their) 4 – (their) –1 = 13 A1ft -1 13

4. 2 o’clock 5 x 60 + 120 M1 £420 A1 Their 420 ÷ 4 M1 £105 A1ft
The cost of renting a holiday cottage is given by the formula
Cost = Number of days x £60 + Fixed charge
4 friends decide to rent the cottage for 5 days when the fixed charge is £120.
How much will each pay if they share the cost equally?
5 x M1
£420 A1
Their 420 ÷ 4 M1
£105 A1ft

5. 3 o’clock Hannah x Joanne x + 5 Laura 2x M1 4x + 5 = 65 M1 4x = 60 M1
Hannah is x years old. Joanne is 5 years older than Hannah. Laura is twice as old as Hannah. The total of their ages is 65.
Work out Hannah’s age.
Hannah x
Joanne x + 5
Laura 2x M1
4x + 5 = 65 M1
4x = 60 M1
15 years old A1

6. 4 o’clock 44 – 12 M1 32 ÷ 8 M1 4 A1 Hired mixer for 5 days A1ft
The cost of hiring a concrete mixer is £12 for the first day and then £8 for each additional day. Alan paid £44 for hiring this mixer.
For how many days did he hire the mixer?
44 – 12 M1
32 ÷ 8 M1
4 A1
Hired mixer for 5 days A1ft

7. 5 o’clock 6x + 10 (= 52) oe M1 x = 7 A1 19 x 7 M1 133 cm2 A1 2x + 5
A rectangle of length (2x + 5) cm and width x cm has a perimeter of 52 cm. Calculate the area.
6x + 10 (= 52) oe M1
x = A1
19 x M1
133 cm A1

8. 6 o’clock 4x – 2 = 2x + 5 or 4x – 2 = 6x – 9 or 6x – 9 = 2x + 5 oe M1
The triangle has lengths (4x – 2) cm, (2x + 5) cm and (6x – 9) cm. Find the value of x that makes this triangle equilateral.
4x – 2 = 2x + 5 or 4x – 2 = 6x – 9 or
6x – 9 = 2x + 5 oe M1
x = 3.5 oe Solve two of the equations and
obtain 3.5 for each M1A1
Must show all sides = A1

9. 7 o’clock Emma has x Nicola has x - 18 Sarah has 2x -36 M1
Emma has x pounds, Nicola has 18 pounds less than Emma, and Sarah has twice as many as Nicola. Together they have £180.
Work out how much money Nicola has.
Emma has x Nicola has x Sarah has 2x -36 M1
4x - 54 = 180 M1
4x = 234 M1
£ A1

10. 8 o’clock 14x + 6y M1 ‘Their 14’ × 4 + ‘their 6’ × y = 68 M1
When x = 4 cm, the perimeter of the quadrilateral is 68 cm. Find the value of y.
14x + 6y M1
‘Their 14’ × 4 + ‘their 6’ × y = 68 M1
‘Their 6y’ = ‘their 12’ M1
y = A1

11. 9 o’clock Option 1 200 × 6 or 1200 or (£) 12 or
The basic monthly charge for a mobile phone contract is £35. This includes:
Option 1:  300 free minutes of calls and 100 free texts OR
Option 2:  100 free minutes of calls and unlimited free texts.
All other calls are 6p per min. Extra texts are 10p each.
On average, each month, Matt makes 500 minutes of calls and sends 250 texts. Which option should he choose?
Option 1
200 × 6 or 1200 or (£) 12 or
150 × 10 or 1500 or (£) M1 (£) 27 or 62   A1
Option 2 
400 × M1
(£) 27 and 24   or   62 and 59 Option 2 (cheaper)  B1 ft

12. 10 o’clock
x2 + 2x = 10 has a solution between 2 and 3. Find the value of x, to 1 decimal place. x
x2 + 2x
Comment 2
x 2 = 8
Too low 3
x 3 = 15
Too high
2.5
x 2.5 = 11.25
2.3
x 2.3 = 9.89
2.4
x 2.4 = 10.56
2.35
x 2.35 =
Values for x = 2 and 3 calculated and trial between 2 and 3 B2
Trial between 2.3 and 2.4 inclusive that “bracket” the answer B1
Trial at 2.35 and 2.3 stated as answer A1

13. 11 o’clock
Rectangle A has length (2x – 1) cm and width (x + 2) cm.
Rectangle B has length (x – 1) cm and width 5 cm.
The perimeter of rectangle A is equal to the perimeter of rectangle B. Calculate x.
6x + 2 = 2x + 8 oe B1
6x – 2x = 8 – 2 oe Allow one error in signs M1
4x = 6   ft Only from Their (2x + 8) A1 ft
1.5 oe B1 ft

14. 12 o’clock 5x > 22 M1 x > 4.4 A2 5 A1ft
Solve the inequality 5x – 4 > 18 and write down the smallest value of x, where x is an integer.
5x > M1
x > A2
A1ft