[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

[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 60 + 120 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 + 5 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 1 200 × 6 or (£) 12 or 1200 or 150 × 10 or (£) 15 or 1500 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 = 7 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 - 18 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

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 = 4 B1 (5 – 8) ÷ 3 or 3y = –3 M1 (y =) –1 A1 3 × (their) 4 – (their) –1 = 13 A1ft -1 13

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 60 + 120 M1 £420 A1 Their 420 ÷ 4 M1 £105 A1ft

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

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

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 = 7 A1 19 x 7 M1 133 cm2 A1

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 = 12 A1

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 - 18 Sarah has 2x -36 M1 4x - 54 = 180 M1 4x = 234 M1 £40.50 A1

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 = 2 A1

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 (£) 15 M1 (£) 27 or 62   A1 Option 2  400 × 6 M1 (£) 27 and 24   or   62 and 59 Option 2 (cheaper)  B1 ft

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 22 + 2 x 2 = 8 Too low 3 32 + 2 x 3 = 15 Too high 2.5 2.52 + 2 x 2.5 = 11.25 2.3 2.32 + 2 x 2.3 = 9.89 2.4 2.42 + 2 x 2.4 = 10.56 2.35 2.352 + 2 x 2.35 = 10.2225 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

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

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 > 22 M1 x > 4.4 A2 5 A1ft