Linear equations: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.4 Linear equations, 2019–2025, with its mark scheme and examiner’s report.

All 174 questions on Linear equations, as a list

June 2025 (R), Paper 1 Foundation, Q5 (7 marks): (a) Simplify 4e × 7f (b) Simplify d × d × d × d × d (c) Simplify 3a + 2k + a – 7k (d) Solve x + 6 = 15 x = (e) Solve 2r – 9 = 14 r =
June 2025 (R), Paper 1 Higher, Q15 (6 marks): (a) Solve 5 a 8 2 a 5 23 3 4 Show clear algebraic working. a = 1 y (b) Express in the form cyn where c and n are numbers to be found. 3
June 2025 (R), Paper 2 Foundation, Q5 (3 marks): (a) Simplify a + a + a + a + a (b) Simplify b × c × 7 (c) Solve 5 d = 40 d =
June 2025 (R), Paper 2 Foundation, Q13 (7 marks): (a) Factorise 15 − x 5 d = 5p + 7r (b) Work out the value of p when d = 35 and r = 2 p = Sweets are sold in small packets and large packets. There are 12 sweets
June 2025 (R), Paper 2 Foundation, Q17 (5 marks): (a) Factorise fully 18 c − 45 cd (b) Solve 5 2 x x 3 4 6 Show clear algebraic working. x =
June 2025 (R), Paper 2 Higher, Q1 (5 marks): (a) Factorise fully 18 c cd − 45 (b) Solve 5 2 x 3 x 4 6 Show clear algebraic working. x =
June 2025, Paper 1 Foundation, Q4 (2 marks): (a) Simplify 4 5 × e (b) Solve f 14 29 f =
June 2025, Paper 1 Foundation, Q23 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = (b) (i) Factorise y2 – 11y + 30 (ii) Hence solve y2 – 11y + 30 = 0
June 2025, Paper 1 Foundation, Q24 (3 marks): Here is a solid cylinder. 8 cm Diagram NOT accurately drawn h cm The radius of the cylinder is 8 cm The height of the cylinder is h cm The volume of the cylinde
June 2025, Paper 1 Higher, Q6 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = 2 – 11y + 30 (b) (i) Factorise y 2 – 11y + 30 = 0 (ii) Hence solve y
June 2025, Paper 1 Higher, Q7 (3 marks): Here is a solid cylinder. 8 cm Diagram NOT accurately drawn h cm The radius of the cylinder is 8 cm The height of the cylinder is h cm The volume of the cylinde
June 2025, Paper 2 Foundation, Q3 (5 marks): (a) Simplify d + d + d + d (b) Simplify w × w × w × w × w (c) Solve 6x = 42 x = (d) Simplify 7r + 9y + 3r – 4y
November 2024, Paper 1 Foundation, Q5 (7 marks): (a) Simplify 8 d d d 4 7 (b) Simplify m × 10 p (c) Solve x 5 19 x = (d) Solve y = 6 8 y = (e) Simplify a a a a × × × k = 8 and n = 12 (f) Work out the value of
November 2024, Paper 1 Foundation, Q20 (6 marks): (a) Simplify p3 5 (b) Expand and simplify 2 n n n n 4 3 4 (c) Solve 2 x 5 x 4 3 Show clear algebraic working. x =
November 2024, Paper 1 Higher, Q3 (6 marks): (a) Simplify p3 5 (b) Expand and simplify 2 n 4 n 3 n n 4 (c) Solve 2 x 5 x 4 3 Show clear algebraic working. x =
November 2024, Paper 2 Foundation, Q8 (10 marks): (a) Simplify 7 g 3 h 4 g 5 h (b) Simplify 7 a × m 4 (c) Solve 5 x 7 12 x = (d) Expand 5 7 k 3 y + (e) Factorise 9 12 Max has c counters. Bulan has 3 times as ma
November 2024, Paper 2 Foundation, Q26 (5 marks): All the students in year 10 and all the students in year 11 named their favourite science subject from Biology, Chemistry and Physics. The pie chart shows infor
November 2024, Paper 2 Higher, Q10 (5 marks): All the students in year 10 and all the students in year 11 named their favourite science subject from Biology, Chemistry and Physics. The pie chart shows infor
November 2024, Paper 2 Higher, Q12 (7 marks): (a) Solve 3 x 2 2 x 1 x 5 3 Show clear algebraic working. x = a bc (b) Make c the subject of the formula f c d
November 2024, Paper 2 Higher, Q21 (4 marks): The Venn diagram shows information about the numbers of items in set A, set B and set C, where x is an integer. E A B x + 2 3x 4x x x + 7 2x 5x 3x + 2 C Given t
June 2024 (R), Paper 1 Foundation, Q8 (4 marks): Marie buys 3 birthday cards at $1.80 each 4 sheets of wrapping paper at $1.20 a sheet 2 identical rolls of sticky tape The total cost is $17.10 Work out the cos
June 2024 (R), Paper 1 Foundation, Q11 (8 marks): (a) Simplify c + c + c + c + c (b) Simplify 7w + 10y ‒ 9w + 2y The nth term of a sequence is given by 7n – 4 (c) Find the 1st term and the 5th term of the s
June 2024 (R), Paper 1 Foundation, Q17 (4 marks): Here is a biased spinner. 3 4 2 5 1 The table gives information about the probability that, when the spinner is spun once, it will land on each number. Number 1
June 2024 (R), Paper 1 Foundation, Q21 (4 marks): The diagram shows a solid wooden cylinder. 8 cm Diagram NOT accurately drawn h cm The cylinder has radius 8 cm and height h cm. The volume of the cylinder is 12
June 2024 (R), Paper 1 Higher, Q2 (4 marks): Here is a biased spinner. 3 4 2 5 1 The table gives information about the probability that, when the spinner is spun once, it will land on each number. Number 1
June 2024 (R), Paper 1 Higher, Q6 (4 marks): The diagram shows a solid wooden cylinder. 8 cm Diagram NOT accurately drawn h cm The cylinder has radius 8 cm and height h cm. The volume of the cylinder is 12
June 2024 (R), Paper 1 Higher, Q23 (4 marks): Here are the first three terms of an arithmetic sequence. ( 4 x 14 ) , ( x 2 ) , ( 7 x 9 ) Find, as an integer, the sum of the first 40 terms of the sequence. S
June 2024 (R), Paper 2 Foundation, Q9 (8 marks): (a) Simplify c × c × c (b) Simplify 12d × 3e (c) Solve k = 7 4 k = (d) Solve 2 g 3 6 g = (e) Expand x(x – 4) P y w 4 2 (f) Work out the value of P whe
June 2024 (R), Paper 2 Foundation, Q22 (8 marks): (a) Solve 2 f f 4 17 3 Show clear algebraic working. f = (b) Simplify (e + 12)0 where e > 0 (c) Simplify fully 12 a h 4 6 ah 4 2 (d) Factorise fully 20x5y
June 2024 (R), Paper 2 Higher, Q6 (8 marks): (a) Solve 2 f f 4 17 3 Show clear algebraic working. f = (b) Simplify (e + 12)0 where e > 0 (c) Simplify fully 12 a h 4 6 ah 4 2 (d) Factorise fully 20x5y
June 2024 (R), Paper 2 Higher, Q12 (4 marks): A Diagram NOT accurately drawn 10 cm B E C D In the diagram, ABC and AED are straight lines. BE is parallel to CD AE = 10 cm and CD = 1.5 × BE (a) Work out the
June 2024, Paper 1 Foundation, Q2 (3 marks): (a) Simplify 10p – 4p + 9p (b) Simplify 9 × 4q (c) Solve 4r = 15 r =
June 2024, Paper 1 Foundation, Q7 (4 marks): Harold works in a factory. His normal hourly rate of pay is £14 His overtime hourly rate of pay is £21 Harold is paid the normal hourly rate of pay for 35 hours
June 2024, Paper 1 Foundation, Q8 (6 marks): (a) Simplify 10x – 7y – 6x + 4y T = 4d – 6e (b) Work out the value of T when d = 13 and e = 7 T = (c) Solve 5p + 11 = 28 p =
June 2024, Paper 1 Foundation, Q21 (5 marks): (a) Expand and simplify (m + 5) (m – 8) (b) Solve 3n – 4 = 5 n + 6 3 Show clear algebraic working. n =
June 2024, Paper 1 Higher, Q6 (5 marks): (a) Expand and simplify (m + 5) (m – 8) (b) Solve 3n – 4 = 5 n + 6 3 Show clear algebraic working. n =
June 2024, Paper 2 Foundation, Q7 (4 marks): 2 jugs each contain 350 millilitres of milk. 5 bottles each contain y millilitres of milk. Peter tips all the milk from the 2 jugs and the 5 bottles into a cont
June 2024, Paper 2 Higher, Q14 (7 marks): (a) Show that 3y (2y + 5) (y + 7) can be written in the form ay 3 + by 2 + cy where a, b and c are integers. x + x − (b) Solve 2 3 + 6 5 = 163 5 4 100 Show clea
November 2023, Paper 1 Foundation, Q7 (7 marks): (a) Simplify 9d × 5c (b) Simplify 7p + 5n – 9p + 3n T = 8e − 6f (c) Work out the value of T when e = 9 and f = 5 T = (d) Solve 5m − 6 = 17 m =
November 2023, Paper 1 Foundation, Q16 (6 marks): (a) Factorise fully 12 pq − p 18 There are 56 metal bars in a box. Each metal bar is gold or silver or zinc. y metal bars are gold. (3y + 7) metal bars are silv
November 2023, Paper 1 Higher, Q2 (6 marks): (a) Factorise fully 12 pq − p 18 There are 56 metal bars in a box. Each metal bar is gold or silver or zinc. y metal bars are gold. (3y + 7) metal bars are silv
November 2023, Paper 2 Foundation, Q10 (4 marks): Here is a number machine. input × y output − 17 When the input is 7 the output is 60 (a) Work out the value of y y = Here is a different number machine. input +
November 2023, Paper 2 Foundation, Q20 (8 marks): (a) Solve 2 x 5 x 2 5 6 Show clear algebraic working. x = (b) Simplify h 15 ÷ h 3 4 (c) Simplify fully 2 g k 3 5 n (d) Given that y 5 y y 12 7 y work out the va
November 2023, Paper 2 Foundation, Q26 (5 marks): The diagram shows a hexagon ABCDEF (x + 2) cm Diagram NOT B C accurately drawn 8 cm D 25 cm E 7 cm A F (x + 6) cm AB = 25 cm BC = (x + 2) cm CD = 8 cm EF = 7 cm
November 2023, Paper 2 Higher, Q4 (8 marks): (a) Solve 2 x 5 x 2 5 6 Show clear algebraic working. x = (b) Simplify h 15 ÷ h 3 4 (c) Simplify fully 2 g k 3 5 (d) Given that y 5 y n y 12 y 7 work out the va
November 2023, Paper 2 Higher, Q10 (5 marks): The diagram shows a hexagon ABCDEF (x + 2) cm Diagram NOT B C accurately drawn 8 cm D 25 cm E 7 cm A F (x + 6) cm AB = 25 cm BC = (x + 2) cm CD = 8 cm EF = 7 cm
June 2023 (R), Paper 1 Foundation, Q7 (5 marks): (a) Simplify 6a × 2c (b) Simplify 4d + 3e + d – 5e (c) Solve 4x – 7 = 23 x =
June 2023 (R), Paper 1 Foundation, Q28 (5 marks): Moeen has a biased 6-sided dice. The table gives information about the probability that, when the dice is thrown, it will land on each number. Number 1 2 3 4 5
June 2023 (R), Paper 1 Higher, Q12 (5 marks): Moeen has a biased 6-sided dice. The table gives information about the probability that, when the dice is thrown, it will land on each number. Number 1 2 3 4 5
June 2023 (R), Paper 1 Higher, Q24 (5 marks): Given that 2n = 2x2 × 16x × 8 and x > 0 find an expression for x in terms of n State any restrictions on n
June 2023 (R), Paper 2 Foundation, Q16 (9 marks): (a) Factorise 6y – 27 (b) Expand p( p – 2) T = 5g + 4r (c) Work out the value of r when T = 46 and g = 17 r = P = m2 – 4c (d) Work out the value of P when m = –
June 2023, Paper 1 Foundation, Q5 (6 marks): (a) Simplify p + p + p + p (b) Simplify 5e + 6f + 7e – 2f (c) Solve 13 – x = 7 x = (d) Solve 4y + 7 = 43 y =
June 2023, Paper 1 Foundation, Q8 (3 marks): Carla wraps some parcels with ribbon. She wraps 2 large parcels and 3 small parcels. For each large parcel, Carla uses 185 centimetres of ribbon. For each small
June 2023, Paper 1 Foundation, Q9 (3 marks): Here is a number machine. input × 10 + 6 output (a) Work out the output when the input is 14 Here is a different number machine. input × + 9 output When the inp
June 2023, Paper 1 Foundation, Q12 (5 marks): Pam plays netball for her school team. Here are the numbers of goals she scored in the last 8 games. The numbers of goals are written in order of size. 1 1 2 2
June 2023, Paper 2 Foundation, Q19 (4 marks): ABCD is a trapezium. B C Diagram NOT accurately drawn (3x + 46)° (3x + 10)° (4x – 27)° A D BC is parallel to AD Find the size of the largest angle inside the tr
June 2023, Paper 2 Higher, Q3 (4 marks): ABCD is a trapezium. B C Diagram NOT accurately drawn (3x + 46)° (3x + 10)° (4x – 27)° A D BC is parallel to AD Find the size of the largest angle inside the tr
June 2023, Paper 2 Higher, Q15 (7 marks): (a) Simplify fully 32 a 15 5 3 1 (b) Express in the form pxn where p and n are integers. 10 x (c) Solve 1 2 y 4 2 y 1 3 5 2 Show clear algebraic working. y
January 2023 (R), Paper 1 Foundation, Q4 (6 marks): (a) Simplify 10y – y (b) Simplify 3p× 4p (c) Solve 7x = 42 x = (d) Solve n + 6 = 5 n = (e) Simplify 8c + 5d – 2c – 3d
January 2023 (R), Paper 1 Foundation, Q12 (5 marks): Aarav uses this rule to estimate the time, in minutes, that a bus journey takes. Time = + 2.5 × length of journey in kilometres 1.5 × number of bus stops Aarav’
January 2023 (R), Paper 1 Higher, Q18 (4 marks): Solve Give your answer in the form a + b 3 where a and b are integers. Show your working clearly. x =
January 2023 (R), Paper 1 Higher, Q24 (5 marks): An arithmetic sequence has first term 8 and common difference 11 The sequence has k terms, where k > 21 The sum of the last 20 terms of the sequence is 10 170 F
January 2023 (R), Paper 2 Foundation, Q5 (4 marks): Pat has 4 parcels A, B, C and D C D A B 400 grams The weight of parcel A is 400 grams. The weight of parcel B is 350 grams more than the weight of parcel A The
January 2023 (R), Paper 2 Foundation, Q14 (7 marks): (a) Expand x(10 – x) (b) Factorise 6y + 27 (c) Make m the subject of the formula h = m 2 + 4 (d) Solve 7g + 3 = 2g – 5 Show clear algebraic working. g =
January 2023 (R), Paper 2 Foundation, Q20 (4 marks): In a bag, there are only red counters, blue counters, green counters and yellow counters. The total number of counters in the bag is 80 In the bag the number of
January 2023 (R), Paper 2 Higher, Q6 (4 marks): In a bag, there are only red counters, blue counters, green counters and yellow counters. The total number of counters in the bag is 80 In the bag the number of
January 2023, Paper 1 Foundation, Q7 (5 marks): (a) Simplify 5p × 9k (b) Simplify 3e + 2f + 8e – 7f (c) Solve 2d + 7 = 16 d =
January 2023, Paper 1 Foundation, Q17 (3 marks): Solve 3(2 – 4x) = 5 – 8x Show clear algebraic working. x =
January 2023, Paper 1 Higher, Q2 (3 marks): Solve 3(2 – 4x) = 5 – 8x Show clear algebraic working. x =
January 2023, Paper 1 Higher, Q22 (4 marks): The first term of an arithmetic series is (2t + 1) where t > 0 The nth term of this arithmetic series is (14t – 5) The common difference of the series is 3 The
January 2023, Paper 2 Foundation, Q7 (5 marks): (a) Simplify c × c × c × c × c (b) Solve 5 + x = 12 x = (c) Solve y 6 = 3 y = (d) Expand 5(2 + 3h) (e) Factorise g2 + 7g
January 2023, Paper 2 Foundation, Q8 (5 marks): Here is a number machine. × 5 – 7 input output (a) Work out the output when the input is 9 Here is a different number machine. ÷ 5 input output When the input i
January 2023, Paper 2 Foundation, Q14 (4 marks): The diagram shows a solid prism. 8 cm Diagram NOT 6 cm accurately drawn 14 cm x cm 7.5 cm The cross section of the prism is shown shaded. The volume of the pris
January 2023, Paper 2 Foundation, Q19 (4 marks): The diagram shows rectangle ABCD 24 cm Diagram NOT A B accurately drawn (5x – 1) cm (3x + 7.4) cm D C Work out the perimeter of the rectangle. Show your working
January 2023, Paper 2 Higher, Q4 (4 marks): The diagram shows rectangle ABCD 24 cm Diagram NOT A B accurately drawn (5x – 1) cm (3x + 7.4) cm D C Work out the perimeter of the rectangle. Show your working
January 2023, Paper 2 Higher, Q13 (3 marks): Solve x + 3 7 − x − = 4 3. 4 5 Show clear algebraic working. x =
June 2022 (R), Paper 1 Foundation, Q12 (3 marks): The diagram below shows the trapezium PQRS S P Diagram NOT accurately drawn (3x – 24)° (102 – x)° Q R Angle PQR and angle QPS are right angles. Find the value o
June 2022 (R), Paper 1 Foundation, Q14 (5 marks): Jakub has bought a chicken. He is going to use this rule to work out the number of minutes it will take to cook his chicken. Cooking time (minutes) Multiply the
June 2022 (R), Paper 1 Foundation, Q19 (3 marks): Here are five cards. Each card has a number written on it. x 15 7 –2 23 The mean of the five numbers is 12 Work out the value of x x =
June 2022 (R), Paper 1 Higher, Q3 (3 marks): Here are five cards. Each card has a number written on it. x 15 7 –2 23 The mean of the five numbers is 12 Work out the value of x x =
June 2022 (R), Paper 2 Foundation, Q23 (8 marks): (a) Solve p = 3 p − 5 10 Show clear algebraic working. p = 0 where a > 0 (b) Simplify a xy 3 (c) Simplify fully 3 6 x y 2 (d) Factorise fully 10c 3d 2 + 15cd 4
June 2022 (R), Paper 2 Higher, Q6 (8 marks): (a) Solve p = 3 p − 5 10 Show clear algebraic working. p = 0 where a > 0 (b) Simplify a xy 3 (c) Simplify fully 3 6 x y 2 (d) Factorise fully 10c 3d 2 + 15cd 4
June 2022, Paper 1 Foundation, Q2 (3 marks): (a) Simplify 12a + 3a – 7a (b) Simplify 8 × 3b (c) Solve c 3 = 9 c =
June 2022, Paper 1 Foundation, Q8 (6 marks): (a) Simplify 12g − 8e − 5g + 6e A = 3b − 5c (b) Work out the value of A when b = 12 and c = 4 A = (c) Solve 4p + 9 = 24 p =
June 2022, Paper 1 Foundation, Q17 (4 marks): Here is a biased 4-sided spinner. 3 4 2 1 The table gives the probabilities that, when the spinner is spun once, it will land on 1 or it will land on 3 Number 1
June 2022, Paper 1 Foundation, Q19 (4 marks): The diagram shows parts of three regular polygons, A, B and C, meeting at a point. B 7x° Diagram NOT C 3x° accurately drawn 8x° A Polygon B has n sides. Work ou
June 2022, Paper 1 Foundation, Q20 (5 marks): (a) Expand and simplify (n − 6)(n + 4) (b) Solve 2x − 3 = 3 x − 5 4 Show clear algebraic working. x =
June 2022, Paper 1 Higher, Q2 (4 marks): Here is a biased 4-sided spinner. 3 4 2 1 The table gives the probabilities that, when the spinner is spun once, it will land on 1 or it will land on 3 Number 1
June 2022, Paper 1 Higher, Q4 (4 marks): The diagram shows parts of three regular polygons, A, B and C, meeting at a point. B 7x° Diagram NOT C 3x° accurately drawn 8x° A Polygon B has n sides. Work ou
June 2022, Paper 1 Higher, Q5 (5 marks): (a) Expand and simplify (n − 6)(n + 4) (b) Solve 2x − 3 = 3 x − 5 4 Show clear algebraic working. x =
June 2022, Paper 1 Higher, Q23 (6 marks): A polygon has n sides, where n > 5 When arranged in order of size, starting with the largest number, the sizes of the interior angles of the polygon, in degrees
June 2022, Paper 2 Foundation, Q9 (4 marks): 3 cups each contain 200 millilitres of water. 4 jugs each contain x millilitres of water. Emma pours all the water from the 3 cups and the 4 jugs into a contain
June 2022, Paper 2 Higher, Q15 (7 marks): (a) Solve 4 5 3 2 − = 13 3 2 Show clear algebraic working. x = (b) Solve the inequality 2y2 − 7y − 30  0 Show your working clearly.
January 2022 (R), Paper 1 Foundation, Q7 (5 marks): (a) Simplify 3c + 5d – c + 2d (b) Simplify 8e × 5f (c) Solve 5r – 3 = 8 r =
January 2022 (R), Paper 2 Foundation, Q10 (3 marks): Thabisa is organising a trip to the theatre. The cost of a ticket for each adult is £11.75 The total cost of the tickets for 12 adults and 5 children is £181 Wo
January 2022 (R), Paper 2 Foundation, Q15 (6 marks): (a) Solve 5c = 15 c = (b) Expand x(8 – x) T = 5m – 6n (c) Work out the value of T when m = 4.2 and n = –2.5 T = (d) Make g the subject of k = 2g + t
January 2022 (R), Paper 2 Foundation, Q20 (5 marks): (a) Solve 4y + 5 > 12 x 4 7 (b) Solve 6 x 5 2 Show clear algebraic working. x =
January 2022 (R), Paper 2 Higher, Q3 (5 marks): (a) Solve 4y + 5 > 12 x 4 7 (b) Solve 6 x 5 2 Show clear algebraic working. x =
January 2022 (R), Paper 2 Higher, Q22 (5 marks): ABC is a triangle in which angle ABC = 90° p and q are integers such that the coordinates of A are ( p, 10 ) the coordinates of B are ( –1, –5 ) the coordinates
January 2022, Paper 1 Foundation, Q5 (4 marks): Angelina buys 3 packets of seeds at $2.45 each packet 2 bags of compost at $6.20 each bag and 4 plant pots Each plant pot costs the same amount of money. Angeli
January 2022, Paper 1 Foundation, Q7 (5 marks): (a) Solve 5x = 30 x = (b) Solve y – 7 = 12 y = (c) Simplify h + h + h + h + h (d) Simplify 5a + 7f – 2a + 4f
January 2022, Paper 2 Foundation, Q2 (6 marks): Here is a list of numbers. 3 8 9 14 23 28 30 (a) From the numbers in the list, write down (i) a cube number (ii) a factor of 70 (iii) a multiple of 6 (iv) a pri
November 2021, Paper 1 Foundation, Q7 (6 marks): (a) Solve 5x = 20 x = (b) Simplify 3a ´ 8b (c) Simplify 8w – 4y + w – 3y (d) Factorise fully 16 + 12t
November 2021, Paper 2 Foundation, Q12 (8 marks): T = 6p – 4d (a) Work out the value of T when p = 8 and d = 3 T = T = 6p – 4d (b) Work out the value of p when T = – 41 and d = 5 p = (c) Solve 4(x – 3) = 7x + 1
June 2021, Paper 1 Foundation, Q4 (4 marks): (a) Simplify 3 × 10d (b) Simplify 8e + e − 5e (c) Solve 6g = 42 g = (d) Solve 24 = 10 + h h =
June 2021, Paper 1 Foundation, Q18 (4 marks): x cm A B Diagram NOT accurately drawn 8 cm 14 cm C E D 13 cm The diagram shows the shape ABCDE. The area of the shape is 91.8 cm² Work out the value of x. x =
June 2021, Paper 1 Higher, Q3 (4 marks): x cm A B Diagram NOT accurately drawn 8 cm 14 cm C E D 13 cm The diagram shows the shape ABCDE. The area of the shape is 91.8 cm² Work out the value of x. x =
June 2021, Paper 1 Higher, Q23 (5 marks): The sum of the first N terms of an arithmetic series, S, is 292 The 2nd term of S is 8.5 The 5th term of S is 13 Find the value of N. Show clear algebraic worki
June 2021, Paper 2 Foundation, Q8 (7 marks): (a) Simplify w × w × w × w × w (b) Simplify 5a × 3c (c) Simplify 3e + 2 f − e + 5 f (d) Solve 5x – 7 = x + 12 Show clear algebraic working. x =
June 2021, Paper 2 Foundation, Q12 (6 marks): This formula can be used to work out the cost, in riyals, of hiring a bicycle in Qatar for a number of days. Cost = 65 × number of days + 44 Ghalia hired a bicy
January 2021 (R), Paper 1 Foundation, Q15 (5 marks): (a) Expand 5(3a + 4) . (b) Factorise 4c – 14 . (c) Solve 5x – 11 = x + 6 Show clear algebraic working. x = .
January 2021 (R), Paper 1 Foundation, Q20 (4 marks): The diagram shows a cuboid and a cylinder. Diagram NOT accurately drawn x cm 2x cm x cm 5 cm 12 cm The dimensions of the cuboid are x cm by 12 cm by 5 cm. The v
January 2021 (R), Paper 1 Higher, Q5 (4 marks): The diagram shows a cuboid and a cylinder. Diagram NOT accurately drawn x cm 2x cm x cm 5 cm 12 cm The dimensions of the cuboid are x cm by 12 cm by 5 cm. The v
January 2021 (R), Paper 2 Foundation, Q13 (3 marks): Solve 5(2x – 3) = 20 Show clear algebraic working. x =
January 2021, Paper 1 Foundation, Q7 (4 marks): (a) Simplify 10x + 4y + 3x – 6y (b) Solve 2n + 5 = 16 n =
January 2021, Paper 1 Foundation, Q21 (5 marks): (a) Factorise fully 15y 4 + 20uy 3 (b) Solve 4 – 3x = 5 − 8 x 4 Show clear algebraic working. x =
January 2021, Paper 1 Higher, Q5 (5 marks): (a) Factorise fully 15y 4 + 20uy 3 (b) Solve 4 – 3x = 5 − 8 x 4 Show clear algebraic working. x =
January 2021, Paper 1 Higher, Q24 (4 marks): An arithmetic series has first term a and common difference d. The sum of the first 2n terms of the series is four times the sum of the first n terms of the ser
January 2021, Paper 2 Foundation, Q5 (5 marks): Here is a number machine. input output + 5 ÷ 2 × 3 (a) Work out the output when the input is 7 (b) Work out the input when the output is 160 When the input is n
January 2021, Paper 2 Foundation, Q7 (8 marks): (a) Simplify p + p + p + p + p + p 2 + 6y 2 – 3y 2 (b) Simplify 5y (c) Simplify e×e×e×e×e (d) Simplify 5c× 4d (e) Solve x – 7 = 19 x = 2 + 15 2 – 5 3 = 4n 18 (f
January 2021, Paper 2 Foundation, Q10 (4 marks): The diagram shows a right-angled triangle. Diagram NOT accurately drawn (6x + 11) cm 4x cm (9x – 18) cm The perimeter of the triangle is 126 cm. Work out the ar
January 2021, Paper 2 Higher, Q14 (7 marks): (a) Solve 9 7 3 7 − = 4.55 5 4 Show clear algebraic working. a = ac + 8 (b) Make c the subject of the formula p = 3 + c
January 2021, Paper 2 Higher, Q16 (6 marks): Some students were asked the following question. “Which of the subjects Russian (R), French (F) and German (G) do you study?” Of these students 4 study all thre
November 2020 (R), Paper 1 Foundation, Q5 (8 marks): (a) Simplify w + w + w + w – w (b) Simplify 4 ×a× 2 (c) Simplify f× f ×f×f×f (d) Simplify 4c + 4h + 5c – 6h (e) Factorise 10d + 15 (f) Make t the subject of e =
November 2020 (R), Paper 1 Foundation, Q7 (4 marks): Diagram NOT accurately drawn B A A A The diagram shows four parcels. The total weight of the four parcels is 8.3 kg. The weight of the parcel labelled B is 3.2
November 2020 (R), Paper 1 Foundation, Q19 (6 marks): (a) Simplify h7×h2 G = c2 – 4c (b) Find the value of G when c = –5 G = x − (c) Solve 5 3 = 2x + 3 4 Show clear algebraic working. x =
November 2020 (R), Paper 1 Higher, Q3 (6 marks): (a) Simplify h7×h2 G = c2 – 4c (b) Find the value of G when c = –5 G = x − (c) Solve 5 3 = 2x + 3 4 Show clear algebraic working. x =
November 2020 (R), Paper 2 Foundation, Q8 (7 marks): The following rule is used to work out the total cost, in euros, of hiring a room. Total cost = 9 euros for each hour plus 20 euros Paolo hires the room for 5 h
November 2020 (R), Paper 2 Foundation, Q12 (3 marks): (a) Expand 4(m + 2) (b) Solve 2x + 5 = –19 x =
November 2020, Paper 1 Foundation, Q7 (6 marks): (a) Simplify 5c × d (b) Solve x + 5 = 12 x = (c) Solve 9y = 36 y = (d) Simplify 8k + 5m – 2k + 6m (e) Expand 4(3g + 1)
November 2020, Paper 1 Foundation, Q20 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 1 Higher, Q7 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 2 Higher, Q11 (8 marks): (a) Simplify fully (8e15) 3 − 4 y   (b) Express in the form ayn where a and n are integers.   2 x x (c) Solve 4 − 2 5 − 3 − = 6 3 4 Show clear algebraic w
January 2020 (R), Paper 1 Foundation, Q6 (7 marks): (a) Simplify 3r × 5t (b) Solve 4x + 5 = 27 x = P = 7w – 5y (c) Find the value of P when w = 2 and y = 4 P = Q = 2u2 − 5 (d) Find the value of Q when u = −3 Q =
January 2020 (R), Paper 1 Foundation, Q24 (5 marks): The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ. E D J Diagram NOT accurately drawn (x + 5) cm F C A B G H (x − 1) cm (2x − 3) cm Th
January 2020 (R), Paper 1 Higher, Q10 (5 marks): The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ. E D J Diagram NOT accurately drawn (x + 5) cm F C A B G H (x − 1) cm (2x − 3) cm Th
January 2020 (R), Paper 2 Foundation, Q17 (4 marks): Three tins, A, B and C, each contain buttons. Tin A contains x buttons. Tin B contains 4 times the number of buttons that tin A contains. Tin C contains 7 fewer
January 2020 (R), Paper 2 Higher, Q3 (4 marks): Three tins, A, B and C, each contain buttons. Tin A contains x buttons. Tin B contains 4 times the number of buttons that tin A contains. Tin C contains 7 fewer
January 2020 (R), Paper 2 Higher, Q19 (6 marks): (a) Solve 4 − 3 x 3 x − 5 − = − 3 5 2 Show clear algebraic working. x = (b) Solve the inequality 5y2 – 17y  40
January 2020, Paper 1 Foundation, Q8 (7 marks): (a) Simplify 6m − 2k + 5m − k P = 2a + 3b (b) Work out the value of P when a = 5 and b = 8 P = P = 2a + 3b (c) Work out the value of a when P = 16 and b = 20 a
January 2020, Paper 1 Foundation, Q16 (4 marks): The diagram shows a shape. 12 cm Diagram NOT accurately drawn 6 cm 9 cm x cm The shape has area 129 cm2 Work out the value of x. x =
January 2020, Paper 1 Foundation, Q21 (9 marks): (a) Expand and simplify (m − 8)(m + 5) (b) Factorise fully 5y + 20y2 (c) Simplify ( p2 + 3)0 − x (d) Solve 3(2x − 5) = 9 2 Show clear algebraic working. x = for
January 2020, Paper 1 Higher, Q3 (4 marks): The diagram shows a shape. 12 cm Diagram NOT accurately drawn 6 cm 9 cm x cm The shape has area 129 cm2 Work out the value of x. x =
January 2020, Paper 1 Higher, Q7 (9 marks): (a) Expand and simplify (m − 8)(m + 5) (b) Factorise fully 5y + 20y2 (c) Simplify ( p2 + 3)0 (d) Solve 3(2x − 5) = 9 − x 2 Show clear algebraic working. x =
January 2020, Paper 2 Foundation, Q5 (2 marks): (a) Simplify 10a×b (b) Solve n + 3 = 7 n =
January 2020, Paper 2 Foundation, Q7 (4 marks): (a) Complete the number machine by writing the correct output on the dotted line. input output 10 + 5 × 4 (b) Complete the number machine by writing the correct
January 2020, Paper 2 Foundation, Q20 (4 marks): The diagram shows a triangle. 30° Diagram NOT accurately drawn (4x + 10)° (x + 20)° Work out the value of x. x =
January 2020, Paper 2 Higher, Q4 (4 marks): The diagram shows a triangle. 30° Diagram NOT accurately drawn (4x + 10)° (x + 20)° Work out the value of x. x =
June 2019 (R), Paper 1 Foundation, Q8 (8 marks): (a) Simplify a + a + a + a (b) Simplify 3c × 5c (c) Simplify 3e + 7g + 5e – 4g (d) Solve x – 9 = 14 x = (e) Factorise 5y + 15 (f) Make y the subject of H = 3y –
June 2019 (R), Paper 1 Foundation, Q12 (3 marks): Three bags, A, B and C, each contain some marbles. A B C There is a total of 75 marbles in the three bags. 1 5 of the marbles are in bag A. There are 4 more mar
June 2019 (R), Paper 1 Foundation, Q24 (3 marks): 3 years ago, the ratio of Tom’s age to Clemmie’s age was 2 : 7 Tom is now 15 years old and Clemmie is now x years old. Find the value of x. x =
June 2019 (R), Paper 1 Higher, Q4 (2 marks): Solve 4xí x x =
June 2019 (R), Paper 1 Higher, Q11 (3 marks): 3 years ago, the ratio of Tom’s age to Clemmie’s age was 2 : 7 Tom is now 15 years old and Clemmie is now x years old. Find the value of x. x =
June 2019 (R), Paper 2 Foundation, Q13 (7 marks): (a) Solve 3f - 5 = 11 (b) Expand w(w + 3) y= 5e + 20 (c) Work out the value of y when e = -3 y=. (d) Factorise x2 - 5x - 36
June 2019, Paper 1 Foundation, Q6 (5 marks): (a) Simplify 6e × 2f (b) Simplify 5m + 7kím + k (c) Solve 5y + 3 = 14 y =
June 2019, Paper 1 Foundation, Q19 (4 marks): Becky has a biased 6-sided dice. The table gives information about the probability that, when the dice is thrown, it will land on each number. Number 1 2 3 4 5
June 2019, Paper 1 Higher, Q5 (4 marks): Becky has a biased 6-sided dice. The table gives information about the probability that, when the dice is thrown, it will land on each number. Number 1 2 3 4 5
June 2019, Paper 1 Higher, Q12 (8 marks): (a) Factorise 2x2íx + 6 (b) Solve 4 m + 9 ím 3 Show clear algebraic working. m = y 4 (c) Write in the form yb where b is a fraction. y
June 2019, Paper 1 Higher, Q21 (5 marks): A solid is made from a hemisphere and a cylinder. The plane face of the hemisphere coincides with the upper plane face of the cylinder. Diagram NOT accurately d
June 2019, Paper 2 Foundation, Q8 (6 marks): Nina buys 8 pencils and 13 identical rulers. Each pencil costs $0.58 The total cost is $23.62 (a) Work out the cost of each ruler. $. Bjorn has $15 to spend on
June 2019, Paper 2 Foundation, Q9 (8 marks): Yuen has 2 more sweets than Simon. Giulia has 3 times as many sweets as Yuen. Simon, Yuen and Giulia have a total of T sweets. (a) Write down a formula for T in
January 2019 (R), Paper 1 Foundation, Q8 (4 marks): (a) Simplify 5x + 4y – x – y (b) Solve 2t + 3 = 12 t =
January 2019 (R), Paper 1 Foundation, Q21 (4 marks): The diagram shows the triangle PQR. R Diagram NOT accurately drawn y (3x + 10) (x + 52) P Q In the diagram, all the angles are in degrees. RP = RQ Find the valu
January 2019 (R), Paper 1 Higher, Q6 (4 marks): The diagram shows the triangle PQR. R Diagram NOT accurately drawn y (3x + 10) (x + 52) P Q In the diagram, all the angles are in degrees. RP = RQ Find the valu
January 2019 (R), Paper 2 Foundation, Q7 (3 marks): Here is a number machine. input ÷ 2 + 10 output (a) Work out the output when the input is 8 (b) Work out the input when the output is 120
January 2019 (R), Paper 2 Foundation, Q13 (7 marks): (a) Solve 7x + 3 = x – 18 x = (b) Make w the subject of t = 7w + 3 Pencils cost 2 dollars each. Rulers cost 3 dollars each. Edith buys p pencils and r rulers. T
January 2019 (R), Paper 2 Higher, Q10 (7 marks): (a) Simplify fully 16 x y 8 6 2 (b) Solve 8 − 2 x 2 x − 3 4 − = 3 2 Show clear algebraic working. x = 1 (c) Make f the subject of m ef = 3
January 2019, Paper 1 Foundation, Q13 (8 marks): (a) Expand and simplify (e + 3)(e – 5) 2 y + 1 (b) Solve y = 5 Show clear algebraic working. y = (c) Solve x2 + 3x – 18 = 0 Show your working clearly.
January 2019, Paper 1 Higher, Q1 (7 marks): (a) Factorise fully 4p + 6pq (b) Expand and simplify (e + 3)(e – 5) 2 y 1 + (c) Solve y = 5 Show clear algebraic working. y =
January 2019, Paper 1 Higher, Q5 (5 marks): D Diagram NOT C accurately drawn (30x – 5)° (4x + 15)° B E (20x + 45)° F A BCD and AFE are straight lines. Show that BCD is parallel to AFE. Give reasons for yo
January 2019, Paper 2 Foundation, Q4 (4 marks): (a) Simplify 4m + 2m – m (b) Simplify 5p × 7 (c) Solve 8g = 40 g = (d) Solve 19 – k = 4 k =
January 2019, Paper 2 Foundation, Q11 (8 marks): (a) Solve 5m + 7 = 24 m = t − e (b) Make t the subject of k = 2 (c) Simplify p8 ÷ p3 (d) Simplify n0 (e) Simplify (3x2y5)3
January 2019, Paper 2 Foundation, Q19 (5 marks): Calvin has 12 identical rectangular tiles. He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below. Diagram NOT
January 2019, Paper 2 Higher, Q5 (5 marks): Calvin has 12 identical rectangular tiles. He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below. Diagram NOT

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