Linear Equations – Forming & Solving – Foundation – GCSE Questions These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers. The worksheets are provided in a variety of sizes.

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GCSE GCSE GCSE GCSE Edexcel Foundation: June 2017 Paper 2, Q9 4𝑥° 4𝑥° 5𝑥° 5𝑥° Find the value of 𝑥. Find the value of 𝑥. (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks) GCSE GCSE Edexcel Foundation: June 2017 Paper 2, Q9 Edexcel Foundation: June 2017 Paper 2, Q9 1 1 4𝑥° 4𝑥° 5𝑥° 5𝑥° Find the value of 𝑥. Find the value of 𝑥. (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

GCSE GCSE Edexcel Foundation: November 2017 Paper 1, Q28 Here is a rectangle. 1 Here is a rectangle. 3x + 5 3x + 5 y y 6x - 7 6x - 7 All measurements are in centimetres. The area of the rectangle is 51cm2. Show that y = 3 All measurements are in centimetres. The area of the rectangle is 51cm2. Show that y = 3 (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

GCSE GCSE Edexcel Foundation: June 2017 Paper 3, Q13 The size of the largest angle in a triangle is 5 times the size of the smallest angle. The other angle is 84° less than the largest angle. Work out, in degree, the size of each angle in the triangle. You must show your working. 1 The size of the largest angle in a triangle is 5 times the size of the smallest angle. The other angle is 84° less than the largest angle. Work out, in degree, the size of each angle in the triangle. You must show your working. °, °, °, °, °, °, (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE GCSE GCSE GCSE Edexcel Foundation: June 2017 Paper 3, Q10 ABC is a straight line. 1 ABC is a straight line. 𝐴 𝐵 𝐶 𝐴 𝐵 𝐶 The length of AB is 6 times the length of BC. AC = 63cm. Work out the length AB. The length of AB is 6 times the length of BC. AC = 63cm. Work out the length AB. cm cm (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks) GCSE GCSE Edexcel Foundation: June 2017 Paper 3, Q10 Edexcel Foundation: June 2017 Paper 3, Q10 1 ABC is a straight line. 1 ABC is a straight line. 𝐴 𝐵 𝐶 𝐴 𝐵 𝐶 The length of AB is 6 times the length of BC. AC = 63cm. Work out the length AB. The length of AB is 6 times the length of BC. AC = 63cm. Work out the length AB. cm cm (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

GCSE GCSE Edexcel Foundation: November 2017 Paper 3, Q24 Here is a rectangle. The length of the rectangle is 6cm longer than the width of the rectangle. 4 of these rectangles are used to make this 8-sided shape. The perimeter of the 8-sided shape is 56cm. Wok out the area of the 8-sided shape. 1 Here is a rectangle. The length of the rectangle is 6cm longer than the width of the rectangle. 4 of these rectangles are used to make this 8-sided shape. The perimeter of the 8-sided shape is 56cm. Wok out the area of the 8-sided shape. cm3 cm3 (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE GCSE GCSE GCSE Edexcel Foundation: November 2017 Paper 1, Q24 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. 1 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks) GCSE GCSE Edexcel Foundation: November 2017 Paper 1, Q24 Edexcel Foundation: November 2017 Paper 1, Q24 1 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. 1 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

GCSE GCSE GCSE GCSE Edexcel Foundation: June 2018 Paper 3, Q17 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. 1 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. P 5x cm Q P 5x cm Q 5x cm 5x cm R R x = x = (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks) GCSE GCSE Edexcel Foundation: June 2018 Paper 3, Q17 Edexcel Foundation: June 2018 Paper 3, Q17 1 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. P 5x cm 1 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. Q P 5x cm Q 5x cm 5x cm R R x = x = (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

GCSE Edexcel Foundation: November 2017 Paper 1, Q28 Here is a rectangle. 3x + 5 y 6x - 7 All measurements are in centimetres. The area of the rectangle is 51cm2. Show that y = 3 (Total for Question 1 is 4 marks)

GCSE Edexcel Foundation: June 2017 Paper 3, Q13 The size of the largest angle in a triangle is 5 times the size of the smallest angle. The other angle is 84° less than the largest angle. Work out, in degree, the size of each angle in the triangle. You must show your working. °, °, °, (Total for Question 1 is 5 marks)

GCSE Edexcel Foundation: November 2017 Paper 3, Q24 Here is a rectangle. The length of the rectangle is 6cm longer than the width of the rectangle. 4 of these rectangles are used to make this 8-sided shape. The perimeter of the 8-sided shape is 56cm. Wok out the area of the 8-sided shape. cm3 (Total for Question 1 is 5 marks)

GCSE Edexcel Foundation: November 2017 Paper 1, Q24 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. (Total for Question 1 is 4 marks)

GCSE Edexcel Foundation: June 2018 Paper 3, Q17 1 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. P 5x cm Q 5x cm R x = (Total for Question 1 is 3 marks)

GCSE = 9𝑥° 360° - 90° = 270° 9𝑥 = 270 1𝑥 = 270 ÷ 9 = 30° 𝑥 = 30° Edexcel Foundation: June 2017 Paper 2, Q9 1 = 9𝑥° 4𝑥° 5𝑥° 360° - 90° = 270° Find the value of 𝑥. 9𝑥 = 270 1𝑥 = 270 ÷ 9 = 30° 𝑥 = 30° (Total for Question 1 is 3 marks)

6x – 7 = 3x + 5 (-3x) (-3x) 3x – 7 = 5 (+7) (+7) 3x = 12 (÷3) (÷3) GCSE Edexcel Foundation: November 2017 Paper 1, Q28 1 Here is a rectangle. 3x + 5 y 6x - 7 All measurements are in centimetres. The area of the rectangle is 51cm2. Show that y = 3 6x – 7 = 3x + 5 (-3x) (-3x) 3x – 7 = 5 (+7) (+7) 3x = 12 (÷3) (÷3) x = 4 3x + 5 = (3×4) + 5 = 17 17 × y = 51 y = 51 17 = 3 (Total for Question 1 is 4 marks)

GCSE Edexcel Foundation: June 2017 Paper 3, Q13 1 The size of the largest angle in a triangle is 5 times the size of the smallest angle. The other angle is 84° less than the largest angle. Work out, in degree, the size of each angle in the triangle. You must show your working. 5x 5x - 84 x 5x + 5x + x – 84 = 11x - 84 11x – 84 = 180° 11x = 264° x = 24° (5×24)−84 =36 5×24 =120 24 36 120 °, °, °, (Total for Question 1 is 5 marks)

GCSE Edexcel Foundation: June 2017 Paper 3, Q10 6x x 1 ABC is a straight line. 54 𝐴 𝐵 9 𝐶 The length of AB is 6 times the length of BC. AC = 63cm. Work out the length AB. 7x = 63 x = 9cm AB = 6x = 54 54 cm (Total for Question 1 is 3 marks)

x + 6 x Perimeter = 8x + 36 = 56 8x = 20 x = 2.5 8.5cm 2.5cm GCSE Edexcel Foundation: November 2017 Paper 3, Q24 x + 6 1 Here is a rectangle. The length of the rectangle is 6cm longer than the width of the rectangle. 4 of these rectangles are used to make this 8-sided shape. The perimeter of the 8-sided shape is 56cm. Wok out the area of the 8-sided shape. x x + 6 x (x + 6) – (x) = 6 x x + 6 (x + 6) – (x) = 6 x + 6 x x x + 6 Perimeter = 8x + 36 = 56 8x = 20 x = 2.5 8.5cm 2.5cm Area = 8.5 x 2.5 = 21.25 Total Area = 4 x 21.25 = 85 85 cm3 (Total for Question 1 is 5 marks)

GCSE Pete : Jo : Mary x : x + 8 : 3(x+8) = Total = 92 Edexcel Foundation: November 2017 Paper 1, Q24 1 Joseph is 8 years older than Pete. Mary is three times as old as Jo. The sum of their three ages is 92 Find the ratio of Pete’s age to Joseph's age to Mary’s age. Pete : Jo : Mary x : x + 8 : 3(x+8) = Total = 92 x + x + 8 + 3x + 24 = 92 5x + 32 = 92 5x = 60 x = 12 Pete : Jo : Mary 12 : 12 + 8 : 3(12+8) 12 : 20 : 60 3 : 5 : 15 (Total for Question 1 is 4 marks)

GCSE Edexcel Foundation: June 2018 Paper 3, Q17 1 PRQ is an isosceles triangle. The area of the triangle is 800 cm2 Work out the value of x. P 5x cm Q 5x cm ½ × 5𝑥 × 5𝑥 = 800 ½ × 25𝑥2 = 800 R 12.5𝑥2 = 800 𝑥2 = 64 𝑥 = 64 = +/- 8 cm 8 x = (Total for Question 1 is 3 marks)

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