Graphs: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 3.3 Graphs, 2019–2025, with its mark scheme and examiner’s report.

All 197 questions on Graphs, as a list

June 2025 (R), Paper 1 Foundation, Q11 (3 marks): On the grid, draw the graph of y = 2x – 5 for values of x from –1 to 4 y 6 5 4 3 2 1 x O −1 4 1 2 3 −1 −2 −3 −4 −5 −6 −7 −8
June 2025 (R), Paper 1 Higher, Q21 (3 marks): The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (−6, 9) (a) Write down the coordinates of the turning point on
June 2025 (R), Paper 2 Foundation, Q10 (3 marks): This graph can be used to change between miles and kilometres. 50 45 40 35 30 kilometres 25 20 15 10 5 0 5 10 15 20 25 30 miles (a) Use the graph to change 25 m
June 2025 (R), Paper 2 Foundation, Q26 (2 marks): A straight line, L, is parallel to the line with equation y = 2 – 5x The line L passes through the point (0, 6) Find an equation of the line L
June 2025 (R), Paper 2 Higher, Q10 (2 marks): A straight line, L, is parallel to the line with equation y = 2 – 5x The line L passes through the point (0, 6) Find an equation of the line L
June 2025 (R), Paper 2 Higher, Q24 (6 marks): PQ is a straight line drawn on a square grid, with a scale of 1 cm for 1 unit on each axis. where a > 0 P has coordinates 5, a and Q has coordinates 7 3 , a The
June 2025 (R), Paper 2 Higher, Q25 (3 marks): The graph of y a x b c for 0 x is drawn on the grid below. sin( ) 360 y 5 4 3 2 1 O x 90 180 270 360 −1 −2 −3 −4 Find a suitable value for a, for b and for c a
June 2025, Paper 1 Foundation, Q8 (4 marks): (a) Complete the table of values for y x 2 1 x −2 −1 0 1 2 3 y −1 5 (b) On the grid, draw the graph of y x 1 for values of x from –2 to 3 2 y 7 6 5 4 3 2 1 O x
June 2025, Paper 1 Higher, Q10 (3 marks): (a) Complete the table of values for y = x 3 + 2x + 3 x –3 –2 –1 0 1 2 3 y –9 0 3 6 36 (b) On the grid, draw the graph of y = x 3 + 2x + 3 for –3  x  3 y 40 3
June 2025, Paper 1 Higher, Q19 (2 marks): The equation of a curve is y = f (x) There is only one minimum point on the curve. The coordinates of this minimum point are (8, –12) Write down the coordinates
June 2025, Paper 1 Higher, Q25 (5 marks): PQRS is a square. PR is a diagonal of the square. P is the point with coordinates (4, 7) R is the point with coordinates (8, –5) Find an equation of the straigh
June 2025, Paper 2 Foundation, Q5 (4 marks): The diagram shows three points, P, Q and R, marked on a grid. y 5 Q 4 P 3 2 1 x O –4 –3 –2 –1 1 2 3 4 –1 R –2 –3 (a) Write down the coordinates of point P ( , )
June 2025, Paper 2 Foundation, Q26 (5 marks): (a) Solve the inequality 7 – 3t < 2t + 15 The region R, shown shaded in the diagram, is bounded by three straight lines. y 10 9 8 7 6 5 R 4 3 2 1 x O 1 2 3 4 5
June 2025, Paper 2 Higher, Q9 (5 marks): (a) Solve the inequality 7 – 3t < 2t + 15 The region R, shown shaded in the diagram, is bounded by three straight lines. y 10 9 8 7 6 5 R 4 3 2 1 O x 1 2 3 4 5
June 2025, Paper 2 Higher, Q14 (2 marks): Here are five graphs. A C B y y y O O O x x x D E y y O x O x (a) Write down the letter of the graph that could have the equation y x 2 5 (b) Write down the let
June 2025, Paper 2 Higher, Q25 (6 marks): (a) Write 28 x x in the form a 2 − b x − c )2 where a, b and c are integers. 24 6 ( (b) On the axes below, sketch the graph of y x x 2 28 24 6 Show clearly the
November 2024, Paper 1 Foundation, Q12 (3 marks): On the grid below, draw the graph of y 1 for values of x from −2 to 3 x 2 y 2 1 O x −2 −1 1 2 3 −1 −2 −3 −4
November 2024, Paper 1 Higher, Q11 (4 marks): (a) Complete the table of values for y x 2 x x 0.5 1 2 3 4 5 6 5 6.7 12.3 y 1 for 0 5 (b) On the grid, draw the graph of y 2 x .  x  6 x y 13 12 1
November 2024, Paper 1 Higher, Q20 (4 marks): The curve with equation y x x has a minimum point. 2 4 64 Find an equation of the tangent to the curve at the minimum point. Show clear algebraic working.
November 2024, Paper 1 Higher, Q23 (5 marks): The curve C has equation y x x 9 2 8 The straight line L has equation y k where k is an integer. = C and L intersect at the points A and B The coordinates of po
November 2024, Paper 2 Foundation, Q23 (4 marks): (a) On the grid, draw the straight line with equation (i) x = 3 (ii) y = 1 (iii) x y 7 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8
November 2024, Paper 2 Higher, Q7 (4 marks): (a) On the grid, draw the straight line with equation (i) x = 3 (ii) y = 1 (iii) x y 7 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8
November 2024, Paper 2 Higher, Q18 (4 marks): The straight line L is perpendicular to the straight line with equation 2 x y 9 and passes through the point with coordinates (8, 11) Find an equation for L Giv
November 2024, Paper 2 Higher, Q19 (3 marks): A curve has equation y f x There is only one minimum point on the curve. The coordinates of this minimum point are (5, 4) Write down the coordinates of the mini
June 2024 (R), Paper 1 Foundation, Q9 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y B 4 3 A 2 C 1 O x −5 −4 −3 −2 −1 1 2 3 4 5 −1 −2 −3 −4 (a) Write down the coordinates of A ( ,
June 2024 (R), Paper 1 Foundation, Q24 (3 marks): Line L is drawn on the grid. y 4 3 L 2 1 O x −4 −3 −2 −1 1 2 3 4 −1 −2 Find an equation for L Give your answer in the form y = mx + c
June 2024 (R), Paper 1 Higher, Q9 (3 marks): Line L is drawn on the grid. y 4 3 L 2 1 O x −4 −3 −2 −1 1 2 3 4 −1 −2 Find an equation for L Give your answer in the form y = mx + c
June 2024 (R), Paper 1 Higher, Q20 (5 marks): (a) Express 2 x x in the form a x − b − c where a, b and c are numbers to 2 11 9 ( ) 2 be found. The curve C has equation y 2 ( x 3 ) 2 11 ( x 3 ) 9 The point
June 2024 (R), Paper 2 Foundation, Q13 (3 marks): On the grid, draw the graph of y = 5 − 2x for values of x from –2 to 3 y 11 10 9 8 7 6 5 4 3 2 1 O x −2 −1 1 2 3 −1 −2
June 2024 (R), Paper 2 Higher, Q16 (2 marks): Here are six graphs. A B C y y y O O O x x x D E F y y y O O O x x x Write down the letter of the graph that could have the equation 1 (i) y x (ii) y = sin x°
June 2024 (R), Paper 2 Higher, Q21 (4 marks): ABCD is a square. The point A has coordinates (−5, 2) The point B has coordinates (3, 5) Find an equation of the line that passes through B and C Give your answ
June 2024 (R), Paper 2 Higher, Q23 (2 marks): A curve has equation y = f(x) The coordinates of the minimum point on this curve are (6, −3) Write down the coordinates of the minimum point on the curve with e
June 2024, Paper 1 Foundation, Q13 (3 marks): On the grid, draw the graph of y = 2 x – 3 for values of x from –2 to 4 y 6 5 4 3 2 1 x O –2 –1 1 2 3 4 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10
June 2024, Paper 1 Higher, Q21 (2 marks): A curve has equation y = f (x) There is one minimum point on this curve. The coordinates of this minimum point are (5, ‒4) Write down the coordinates of the min
June 2024, Paper 2 Foundation, Q18 (4 marks): (a) On the grid, draw the straight line with equation (i) y = 2 (ii) x = 6 (iii) y = x + 1 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6
June 2024, Paper 2 Higher, Q2 (4 marks): (a) On the grid, draw the straight line with equation (i) y = 2 (ii) x = 6 (iii) y = x + 1 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6
June 2024, Paper 2 Higher, Q18 (2 marks): The straight line P has equation 5y + 2x = 7 Find the gradient of a straight line that is perpendicular to P
June 2024, Paper 2 Higher, Q25 (2 marks): The diagram shows a sketch of the graph of y = 2sin (x + 60)° y A B x O (i) Find the coordinates of the point A ( , ) (ii) Find the coordinates of the point B (
November 2023, Paper 1 Foundation, Q4 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y 7 A 6 5 4 3 2 1 O x −5 −4 −3 −2 −1 1 2 3 4 5 6 7 −1 B −2 C −3 (a) Write down the coordinates of
November 2023, Paper 1 Foundation, Q12 (3 marks): On the grid below, draw the graph of y = 5 − 3x for values of x from − 2 to 3 y 12 11 10 9 8 7 6 5 4 3 2 1 O x −2 −1 1 2 3 −1 −2 −3 −4 −5 −6
November 2023, Paper 1 Foundation, Q22 (5 marks): (a) Solve the inequality 8 x − x − 4 3 10 The region R, shown shaded in the diagram, is bounded by three straight lines. y 9 8 7 6 5 4 R 3 2 1 O x 1 2 3 4 5 6 7
November 2023, Paper 1 Higher, Q8 (5 marks): (a) Solve the inequality 8 x − x − 4 3 10 The region R, shown shaded in the diagram, is bounded by three straight lines. y 9 8 7 6 5 4 R 3 2 1 O x 1 2 3 4 5 6 7
November 2023, Paper 1 Higher, Q12 (5 marks): (a) Complete the table of values for y = x3 − 3x + 1 −2 −1 0 1 2 x y −1 (b) On the grid, draw the graph of y = x3 − 3x + 1 for values of x from − 2 to 2 y 6 5 4
November 2023, Paper 1 Higher, Q22 (6 marks): [In this question 1 cm = 1 unit on the x-axis and 1 cm = 1 unit on the y-axis] P is a point on a circle with centre (0, 0) The coordinates of P are (8, -10) The
November 2023, Paper 1 Higher, Q24 (4 marks): The curve with equation f(x) = 5 is transformed to the curve with equation x 2 + x + 9 2 by the translation a 2 g(x) = 5 x 4 9 x 4 8 b (a) Write down the val
November 2023, Paper 2 Foundation, Q11 (4 marks): The graph below can be used to change between Australian dollars and euros. 50 40 30 euros 20 10 0 0 10 20 30 40 50 60 70 Australian dollars (a) Use the graph t
November 2023, Paper 2 Foundation, Q25 (2 marks): A straight line passes through the points with coordinates (0, –3) and (2, 0) Find an equation of the line.
November 2023, Paper 2 Higher, Q9 (2 marks): A straight line passes through the points with coordinates (0, –3) and (2, 0) Find an equation of the line.
November 2023, Paper 2 Higher, Q14 (3 marks): Here is the graph of the equation y x 2 1 drawn on a grid. y 5 4 3 2 1 O x −3 −2 −1 1 2 3 4 5 −1 −2 −3 −4 By drawing another straight line on the grid, solve th
June 2023 (R), Paper 1 Foundation, Q12 (3 marks): On the grid, draw the graph of y = 4 – 2x for values of x from –1 to 4 y 8 7 6 5 4 3 2 1 O x –1 1 2 3 4 –1 –2 –3 –4 –5
June 2023 (R), Paper 1 Higher, Q20 (7 marks): Curve C has equation y = f (x) The graph of curve C has one maximum point. The coordinates of this maximum point are (3, 5) (a) Write down the coordinates of th
June 2023 (R), Paper 2 Foundation, Q4 (3 marks): y 7 P 6 5 4 Q 3 2 1 O x –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 R –2 (a) Write down the coordinates of the point (i) P ( , ) (ii) Q ( , ) (b) On the grid above, mark wi
June 2023 (R), Paper 2 Foundation, Q23 (5 marks): (a) Solve 9 – 4x > 17 y 8 7 6 5 4 R 3 2 1 O 1 2 3 4 5 6 7 8 9 10 x (b) Write down the three inequalities that represent the shaded region R
June 2023 (R), Paper 2 Higher, Q8 (5 marks): (a) Solve 9 – 4x > 17 y 8 7 6 5 4 R 3 2 1 O 1 2 3 4 5 6 7 8 9 10 x (b) Write down the three inequalities that represent the shaded region R
June 2023 (R), Paper 2 Higher, Q12 (3 marks): Here are six graphs. Graph A Graph B Graph C y y y O x O x O x Graph D Graph E Graph F y y y O x O x O x Write down the letter of the graph of (a) y = 10 2x (b)
June 2023 (R), Paper 2 Higher, Q25 (6 marks): The straight line with equation y – 2x = 7 is the perpendicular bisector of the line AB where A is the point with coordinates ( j, 7) and B is the point with co
June 2023 (R), Paper 2 Higher, Q26 (3 marks): Here is a sketch of the curve with equation y = a cos bx° + c where –90  x  450 y 4 3 2 1 x O –90 90 180 270 360 450 –1 –2 Find the value of a, the value of b
June 2023, Paper 1 Foundation, Q22 (4 marks): y 9 8 7 6 5 4 3 2 1 R –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 The region R, shown shaded in the diagram, is bounded by three straight lines. Find the inequalities th
June 2023, Paper 1 Higher, Q7 (4 marks): y 9 8 7 6 5 4 3 2 1 R –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 The region R, shown shaded in the diagram, is bounded by three straight lines. Find the inequalities th
June 2023, Paper 1 Higher, Q13 (3 marks): A is the point with coordinates (–5, 12) B is the point with coordinates (19, –48) Find an equation of the straight line that passes through the points A and B
June 2023, Paper 1 Higher, Q21 (2 marks): A curve has equation y = f(x) There is only one turning point on the curve. The coordinates of this turning point are (6, 5) Write down the coordinates of the t
June 2023, Paper 2 Foundation, Q5 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y 5 4 A 3 2 B 1 O x –1 1 2 3 4 5 6 7 –1 C –2 (a) Write down the coordinates of point A ( , ) (b) O
June 2023, Paper 2 Foundation, Q20 (4 marks): (a) Complete the table of values for y = x2 – x – 4 –3 –2 –1 0 1 2 3 x y 2 –4 (b) On the grid below, draw the graph of y = x2 – x – 4 for values of x from –3 to
June 2023, Paper 2 Higher, Q4 (4 marks): (a) Complete the table of values for y = x2 – x – 4 –3 –2 –1 0 1 2 3 x y 2 –4 (b) On the grid below, draw the graph of y = x2 – x – 4 for values of x from –3 to
June 2023, Paper 2 Higher, Q18 (3 marks): Here are 6 graphs. Graph A Graph B Graph C y y y O x O x O x Graph D Graph E Graph F y y y O x O x O x Complete the table below with the letter of the graph tha
June 2023, Paper 2 Higher, Q24 (6 marks): ABCD is a kite with AB = AD and CB = CD A is the point with coordinates (–2, 10) 27 B is the point with coordinates , 4 5 C is the point with coordinates (
January 2023 (R), Paper 1 Foundation, Q10 (4 marks): The graph below can be used to change between dollars and Danish krone. 400 300 Danish krone 200 100 0 0 10 20 30 40 50 60 70 dollars (a) Change 40 dollars to D
January 2023 (R), Paper 1 Higher, Q15 (7 marks): (a) Complete the table of values for y = x3 – 3x + 2 –2 –1 –0.5 0 1 1.5 2 x y 4 3.4 0 0.9 (b) On the grid, draw the graph of y = x3 – 3x + 2 for values of x fro
January 2023 (R), Paper 1 Higher, Q20 (2 marks): Here is a sketch of the curve y = a cos(x + b)° for 0  x  360 y 2 1 O x 90 180 270 360 –1 –2 Given that 0 < b < 180 find the value of a and the value of b a =
January 2023 (R), Paper 1 Higher, Q23 (5 marks): G is the point on the curve with equation y = 8x2 – 14x – 6 where the gradient is 10 The straight line Q passes through the point G and is perpendicular to the
January 2023 (R), Paper 2 Foundation, Q4 (5 marks): The diagram shows three points, A, B and C, and a line EF on a grid. y 4 E 3 F B 2 1 A O x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 C (a) Write down the coordinates
January 2023 (R), Paper 2 Foundation, Q19 (3 marks): On the grid, draw the graph of 5x + 2y = 10 for values of x from –2 to 4 y 11 10 9 8 7 6 5 4 3 2 1 O x –2 –1 1 2 3 4 –1 –2 –3 –4 –5 –6
January 2023 (R), Paper 2 Higher, Q5 (3 marks): On the grid, draw the graph of 5x + 2y = 10 for values of x from –2 to 4 y 11 10 9 8 7 6 5 4 3 2 1 O x –2 –1 1 2 3 4 –1 –2 –3 –4 –5 –6
January 2023 (R), Paper 2 Higher, Q21 (3 marks): The diagram shows the graph of y = f(x) y 6 4 P 2 O x –8 –6 –4 –2 2 4 6 8 –2 –4 The point P has x coordinate –2 Use the graph to find an estimate for the gradie
January 2023 (R), Paper 2 Higher, Q25 (6 marks): ABCD is a trapezium with AB parallel to DC A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8
January 2023, Paper 1 Foundation, Q11 (3 marks): On the grid below, draw the graph of y = 1 – 2x for values of x from –2 to 3 y 8 7 6 5 4 3 2 1 O –2 –1 1 2 3 x –1 –2 –3 –4 –5 –6
January 2023, Paper 1 Higher, Q11 (3 marks): y 8 7 6 5 4 3 2 R 1 x – 3 – 2 – 1 1 2 3 4 5 6 O – 1 – 2 – 3 – 4 The region R, shown shaded in the diagram, is bounded by the straight lines with equations 2x +
January 2023, Paper 1 Higher, Q14 (3 marks): (a) Complete the table of values for y x x x 0.5 1 2 3 4 5 y 8 3.1 2.4 1.9 2 5 1 for 0.5  x  5 (b) On the grid, draw the graph of y x x y 12 10 8
January 2023, Paper 1 Higher, Q23 (6 marks): ABCD is a kite. AB = AD and CB = CD The point B has coordinates (k, 1) where k is a negative constant. The point D has coordinates (8, 7) The straight line L pa
January 2023, Paper 2 Foundation, Q21 (3 marks): The points A and B are on a coordinate grid. The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant. The midpoint of AB has coor
January 2023, Paper 2 Foundation, Q24 (7 marks): (a) Write down the value of (m + 2)0 where m is a positive integer. (b) Simplify (3a2b4)3 (c) Factorise fully 14x2y4 + 21x3y2 The diagram shows a straight line
January 2023, Paper 2 Higher, Q6 (3 marks): The points A and B are on a coordinate grid. The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant. The midpoint of AB has coor
January 2023, Paper 2 Higher, Q9 (7 marks): (a) Write down the value of (m + 2)0 where m is a positive integer. (b) Simplify (3a2b4)3 (c) Factorise fully 14x2y4 + 21x3y2 The diagram shows a straight line
January 2023, Paper 2 Higher, Q11 (3 marks): Here are six graphs. Graph A Graph B Graph C y y y x x x Graph D Graph E Graph F y y y x x x Complete the table below with the letter of the graph that could re
January 2023, Paper 2 Higher, Q24 (2 marks): The graph of y = a sin x° + b is drawn on the grid. y 4 3 2 1 O x 60 120 180 240 300 360 –1 –2 –3 Find the value of a and the value of b a = b =
June 2022 (R), Paper 1 Foundation, Q7 (6 marks): The three points A, B and C are marked on a centimetre grid. y 5 4 A B 3 2 1 O x –4 –3 –2 –1 1 2 3 4 5 6 7 C –1 –2 –3 (a) Write down the coordinates of A ( , )
June 2022 (R), Paper 1 Foundation, Q26 (3 marks): Line L is drawn on the grid. y 6 L 5 4 3 2 1 O x –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 Find an equation for L Give your answer in the form y = mx + c
June 2022 (R), Paper 1 Higher, Q10 (3 marks): Line L is drawn on the grid. y 6 L 5 4 3 2 1 O x –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 Find an equation for L Give your answer in the form y = mx + c
June 2022 (R), Paper 1 Higher, Q23 (5 marks): (a) Express 2x 2 – 12x + 3 in the form a(x + b) 2 + c where a, b and c are integers. The curve C has equation y = 2(x + 4) 2 – 12(x + 4) + 3 The point M is the
June 2022 (R), Paper 2 Foundation, Q14 (3 marks): On the grid, draw the graph of y = 2x – 1 for values of x from –1 to 4 y 9 8 7 6 5 4 3 2 1 O x –1 1 2 3 4 –1 –2 –3 –4
June 2022 (R), Paper 2 Higher, Q16 (3 marks): Here are nine graphs. Graph A Graph B Graph C y y y O x O x O x Graph D Graph E Graph F y y y x O O x O x Graph G Graph H Graph I y y y O x O x O x Complete the
June 2022 (R), Paper 2 Higher, Q20 (4 marks): The centre O of a circle has coordinates (4, 7) The point A, on the circle, has coordinates (6, 11) and AOP is a diameter of the circle. Find an equation of the
June 2022 (R), Paper 2 Higher, Q22 (4 marks): The point A with coordinates (–3, 2) lies on the straight line with equation y = f(x) (a) Find the coordinates of the image of the point A on the straight line
June 2022, Paper 1 Foundation, Q13 (3 marks): On the grid, draw the graph of y = −2x + 3 for values of x from −1 to 5 y 6 5 4 3 2 1 O −1 1 2 3 4 5 6 x −1 −2 −3 −4 −5 −6 −7 −8 −9 −10
June 2022, Paper 1 Foundation, Q25 (4 marks): Two circles, C1 and C2 , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis. The centre of circle C1 is at the point with coordinates
June 2022, Paper 1 Higher, Q10 (4 marks): Two circles, C1 and C2 , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis. The centre of circle C1 is at the point with coordinates
June 2022, Paper 1 Higher, Q20 (2 marks): The diagram shows a sketch of part of the curve with equation y = f (x) y (s, t) y = f (x) O x There is one maximum point on this curve. The coordinates of this
June 2022, Paper 2 Foundation, Q18 (4 marks): (a) On the grid, draw and label with its equation the straight line with equation (i) y = 1 (ii) x = 2 (iii) x + y = 7 y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8 (b)
June 2022, Paper 2 Higher, Q2 (4 marks): (a) On the grid, draw and label with its equation the straight line with equation (i) y = 1 (ii) x = 2 (iii) x + y = 7 y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8 (b)
June 2022, Paper 2 Higher, Q22 (7 marks): ABCD is a kite, with diagonals AC and BD, drawn on a centimetre square grid, with a scale of 1 cm for 1 unit on each axis. A is the point with coordinates (−3,
June 2022, Paper 2 Higher, Q23 (2 marks): The diagram shows a sketch of the graph of y = cos x     2 ° y y = cos x     2 A O x B (i) Find the coordinates of the point A ( , ) (ii) Find the c
January 2022 (R), Paper 1 Foundation, Q18 (4 marks): (a) Complete the table of values for y = x2 – 4x + 3 x –2 –1 0 1 2 3 4 y 8 3 0 (b) On the grid, draw the graph of y = x2 – 4x + 3 for values of x from –2 to 4 y
January 2022 (R), Paper 1 Higher, Q4 (4 marks): (a) Complete the table of values for y = x2 – 4x + 3 x –2 –1 0 1 2 3 4 8 3 0 y (b) On the grid, draw the graph of y = x2 – 4x + 3 for values of x from –2 to 4 y
January 2022 (R), Paper 1 Higher, Q20 (6 marks): The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (– 6, – 4) (a) Write down the coordinates of the turning point
January 2022 (R), Paper 2 Foundation, Q2 (5 marks): The diagram shows three points, A, B and C, on a grid. y 6 5 A 4 3 B 2 1 C O x –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 (a) Write down the coordinates of (i) point A ( , )
January 2022 (R), Paper 2 Foundation, Q24 (5 marks): (a) Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5) (b) Show, by shading on the grid, th
January 2022 (R), Paper 2 Higher, Q7 (5 marks): (a) Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5) (b) Show, by shading on the grid, th
January 2022 (R), Paper 2 Higher, Q11 (4 marks): (a) Complete the table of values for y = 6 x x 0.5 1 2 3 4 5 6 y 6 2 1 (b) On the grid, draw the graph of y = 6 x for 0.5  x  6 y 12 10 8 6 4 2 O x 2 4 6
January 2022 (R), Paper 2 Higher, Q17 (3 marks): Part of the curve with equation y = f (x) is shown on the grid. y 6 5 4 3 2 1 x –2 –1 O 1 2 3 4 –1 –2 –3 Find an estimate for the gradient of the curve at the p
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, Q14 (3 marks): On the grid, draw the graph of y = 2x – 3 for values of x from –2 to 4 y 6 5 4 3 2 1 O x –2 –1 1 2 3 4 –1 –2 –3 –4 –5 –6 –7
January 2022, Paper 1 Foundation, Q25 (3 marks): The straight line L has equation 2y + 7x = 10 (a) Find the gradient of L (b) Find the coordinates of the point where L crosses the y‑axis. ( , )
January 2022, Paper 1 Higher, Q10 (3 marks): The straight line L has equation 2y + 7x = 10 (a) Find the gradient of L (b) Find the coordinates of the point where L crosses the y‑axis. ( , )
January 2022, Paper 1 Higher, Q20 (4 marks): (a) Express 7 + 12x – 3x2 in the form a + b(x + c)2 where a, b and c are integers. C is the curve with equation y = 7 + 12x – 3x2 The point A is the maximum poi
January 2022, Paper 1 Higher, Q23 (2 marks): The diagram shows a sketch of the curve with equation y = f(x) y (5, 7) y = f(x) O x There is only one maximum point on the curve. The coordinates of this maxim
January 2022, Paper 2 Foundation, Q5 (4 marks): The diagram shows points A and B marked on a grid of squares. y 6 5 4 B 3 2 A 1 O x −5 −4 −3 −2 −1 1 2 3 4 5 6 7 −1 −2 −3 (a) On the grid, draw the line with eq
January 2022, Paper 2 Foundation, Q13 (5 marks): Here is a conversion graph to change between Canadian dollars and pounds (£) 30 20 pounds (£) 10 0 0 10 20 30 40 50 60 Canadian dollars (a) Use the graph to cha
January 2022, Paper 2 Higher, Q21 (5 marks): Part of the graph of y = 2x2 − 4x − 1 is shown on the grid. y 4 2 O −1 1 2 3 x −2 −4 (a) Use the graph to find estimates for the solutions of the equation 2x2 −
November 2021, Paper 1 Foundation, Q6 (7 marks): The accurate scale diagram shows the map of an island drawn on a centimetre grid. y North 8 B 6 A 4 2 O x 2 4 6 8 The position of Aaron’s house is A. The positi
November 2021, Paper 1 Higher, Q20 (7 marks): The straight line L passes through point A (– 6, 2) and point B (5, 3) The straight line M is perpendicular to L and passes through the midpoint of A and B. The
November 2021, Paper 2 Foundation, Q14 (3 marks): On the grid below, draw the graph of y = 1 – 3x for values of x from – 2 to 3 y 10 9 8 7 6 5 4 3 2 1 O x –2 –1 1 2 3 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10
November 2021, Paper 2 Higher, Q19 (6 marks): The straight line L has equation x – y = 3 The curve C has equation 3x2 – y2 + xy = 9 L and C intersect at the points P and Q. Find the coordinates of the midpo
November 2021, Paper 2 Higher, Q21 (6 marks): The curve C has equation y = f(x) where f(x) = 9 – 3(x + 2)2 The point A is the maximum point on C. (a) Write down the coordinates of A. ( , ) 4 The curve C is
June 2021, Paper 2 Foundation, Q4 (5 marks): The points A, B and C, shown on the grid, are the vertices of triangle ABC. y 5 4 B 3 2 1 A O −5 −4 −3 −2 −1 1 2 3 4 5 x C −1 −2 −3 −4 −5 (a) Write down the coo
June 2021, Paper 2 Higher, Q15 (4 marks): (a) Complete the table of values for y = x x ( 2 + 4 ) x 0.25 0.5 1 2 4 8 y 16.25 8.5 1 ) for 0.25  x  8 (b) On the grid, draw the graph of y = x x ( 2 + 4 y
June 2021, Paper 2 Higher, Q17 (4 marks): The straight line L passes through the points (4, −1) and (6, 4) The straight line M is perpendicular to L and intersects the y-axis at the point (0, 8) Find th
June 2021, Paper 2 Higher, Q22 (4 marks): The curve S has equation y = f(x) where f(x) = x2 The curve T has equation y = g(x) where g(x) = 2x2 – 12x + 13 By writing g(x) in the form a(x – b)2 – c, where
January 2021 (R), Paper 1 Foundation, Q5 (3 marks): The diagram shows the point A and the line CD on a grid. y 5 4 3 A 2 1 O x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 C D –4 –5 (a) Write down the coordinates of point A
January 2021 (R), Paper 1 Foundation, Q11 (3 marks): On the grid, draw the graph of y = 3 – 2x for values of x from –2 to 3 y 8 7 6 5 4 3 2 1 O x –2 –1 1 2 3 –1 –2 –3 –4 –5
January 2021 (R), Paper 1 Higher, Q22 (5 marks): ABC is an isosceles triangle with AB = AC. B is the point with coordinates (–1, 5) C is the point with coordinates (2, 10) M is the midpoint of BC. Find an equa
January 2021, Paper 1 Higher, Q13 (3 marks): Point A has coordinates (5, 8) Point B has coordinates (9, –4) (a) Work out the gradient of AB. The straight line L has equation y = –4x + 5 (b) Write down the
January 2021, Paper 1 Higher, Q21 (4 marks): A curve has equation y = f(x) The coordinates of the minimum point on this curve are (–9, 15) (a) Write down the coordinates of the minimum point on the curve w
January 2021, Paper 2 Foundation, Q18 (4 marks): y 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 (a) On the grid, draw and label the straight line with equation (i) x = 1.5 (ii) y = x (iii) x + y = 6 (b) Show, by shading on
January 2021, Paper 2 Higher, Q4 (4 marks): y 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 (a) On the grid, draw and label the straight line with equation (i) x = 1.5 (ii) y = x (iii) x + y = 6 (b) Show, by shading on
January 2021, Paper 2 Higher, Q18 (7 marks): A rectangle ABCD is to be drawn on a centimetre grid such that A has coordinates (–4, –2) B has coordinates (1, 10) C has coordinates (19, a) D has coordinates
November 2020 (R), Paper 1 Foundation, Q11 (3 marks): On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 4 y 10 9 8 7 6 5 4 3 2 1 O x –1 1 2 3 4 –1 –2 –3 –4 –5 –6
November 2020 (R), Paper 1 Foundation, Q16 (3 marks): The graph below can be used to change between euros and dirham. 300 250 200 dirham 150 100 50 0 0 10 20 30 40 50 60 euros (a) Use the graph to change 200 dirham
November 2020 (R), Paper 1 Foundation, Q22 (2 marks): Point A has coordinates (–3, 11) Point B has coordinates (47, b) The midpoint of AB has coordinates (a, –19) Find the value of a and the value of b. a = b =
November 2020 (R), Paper 1 Higher, Q6 (2 marks): Point A has coordinates (–3, 11) Point B has coordinates (47, b) The midpoint of AB has coordinates (a, –19) Find the value of a and the value of b. a = b =
November 2020 (R), Paper 1 Higher, Q20 (2 marks): A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (–3, 4) Write down the coordinates of the
November 2020 (R), Paper 2 Foundation, Q24 (3 marks): Show, by shading on the grid, the region that satisfies all three of the inequalities x  4 and y  –2 and y  x Label the region R. y 7 6 5 4 3 2 1 O x –5 –4 –
November 2020 (R), Paper 2 Foundation, Q25 (2 marks): Find the gradient of the straight line with equation 5x + 2y = 7
November 2020 (R), Paper 2 Higher, Q11 (3 marks): Show, by shading on the grid, the region that satisfies all three of the inequalities x  4 and y  –2 and y  x Label the region R. y 7 6 5 4 3 2 1 O x –5 –4 –
November 2020 (R), Paper 2 Higher, Q12 (2 marks): Find the gradient of the straight line with equation 5x + 2y = 7
November 2020 (R), Paper 2 Higher, Q18 (6 marks): (a) Complete the table of values for y = 1 2 x3 – 2x + 3 x –3 –2 –1 0 1 2 3 y –4.5 3 3 (b) On the grid, draw the graph of y = 1 2 x3 – 2x + 3 for –3  x  3 y 1
November 2020 (R), Paper 2 Higher, Q23 (6 marks): P and Q are two points. The coordinates of P are (–1, 6) The coordinates of Q are (5, –4) Find an equation of the perpendicular bisector of PQ. Give your answer
November 2020, Paper 1 Foundation, Q16 (3 marks): On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3 y 16 14 12 10 8 6 4 2 O x −2 −1 1 2 3 −2 −4 −6 −8
November 2020, Paper 1 Higher, Q3 (3 marks): On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3 y 16 14 12 10 8 6 4 2 O x −2 −1 1 2 3 −2 −4 −6 −8
November 2020, Paper 1 Higher, Q22 (4 marks): ABCD is a rhombus. The diagonals, AC and BD, intersect at the point M. The coordinates of M are (6, −11) The points A and C both lie on the line with equation 2
November 2020, Paper 1 Higher, Q25 (3 marks): The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by the single transformation T. (a) Describe fully the transformation T. Th
November 2020, Paper 2 Foundation, Q7 (5 marks): The diagram shows three points, A, B and C, marked on a grid. y 5 4 C 3 2 1 B O –5 –4 –3 –2 –1 1 2 3 4 5 x –1 A –2 –3 –4 –5 (a) Write down the coordinates of po
November 2020, Paper 2 Foundation, Q9 (4 marks): Below is a conversion graph to change between metres and feet. 80 70 60 50 feet 40 30 20 10 0 0 5 10 15 20 25 metres (a) Use the graph to change (i) 10 metres t
November 2020, Paper 2 Higher, Q6 (2 marks): The line L is shown on the grid. y 6 5 L 4 3 2 1 O –3 –2 –1 1 2 3 x –1 –2 –3 –4 –5 –6 Find an equation for L.
January 2020 (R), Paper 1 Foundation, Q11 (3 marks): On the grid, draw the graph of y = 3x + 2 for values of x from −2 to 4 y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 x −2 −1 O 1 2 3 4 −1 −2 −3 −4 −5
January 2020 (R), Paper 1 Higher, Q18 (7 marks): The diagram shows the graph of y = f (x) for −4  x  12 4 P 2 −4 −2 O 2 4 6 8 10 12 −2 The point P on the curve has x coordinate 2 (a) (i) Use the graph to fin
January 2020 (R), Paper 1 Higher, Q22 (4 marks): The graph of y = a cos(x + b)° for 0  x  360 is drawn on the grid. y 3 2 1 O x 60 120 180 240 300 360 −1 −2 −3 (a) Find the value of a and the value of b. a =
January 2020 (R), Paper 2 Foundation, Q7 (4 marks): P, Q and R are three points marked on a grid. y 5 4 P 3 Q 2 1 O x –4 –3 –2 –1 1 2 3 4 –1 R –2 –3 (a) Write down the coordinates of point Q. ( , ) S is the point
January 2020 (R), Paper 2 Higher, Q15 (4 marks): (a) Complete the table of values for y = x 2 − − 3 2 x –3 –2 –1 0 1 2 3 y 7.5 –2.5 4.5 x (b) On the grid, draw the graph of y x 2 3 for values of x from –3 to 3
January 2020 (R), Paper 2 Higher, Q24 (5 marks): L1 and L2 are two straight lines. The origin of the coordinate axes is O. L1 has equation 5x + 10y = 8 L2 is perpendicular to L1 and passes through the point wi
January 2020, Paper 1 Foundation, Q14 (4 marks): The point A has coordinates (5, −4) The point B has coordinates (13, 1) (a) Work out the coordinates of the midpoint of AB. ( , ) Line L has equation y = 2 − 3x
January 2020, Paper 1 Higher, Q1 (4 marks): The point A has coordinates (5, −4) The point B has coordinates (13, 1) (a) Work out the coordinates of the midpoint of AB. ( , ) Line L has equation y = 2 − 3x
January 2020, Paper 1 Higher, Q20 (4 marks): The curve C has equation y = 4(x − 1)2 − a where a > 4 Using the axes below, sketch the curve C. On your sketch show clearly, in terms of a, (i) the coordinates
January 2020, Paper 1 Higher, Q22 (6 marks): Triangle HJK is isosceles with HJ = HK and JK = 80 H is the point with coordinates (−4, 1) J is the point with coordinates ( j, 15) where j < 0 K is the point w
January 2020, Paper 2 Foundation, Q8 (4 marks): (a) Complete the table of values for y = 3x – 1 x –1 0 1 2 3 4 5 6 y –1 5 14 (b) On the grid, draw the graph of y = 3x – 1 for values of x from –1 to 6 y 18 16
January 2020, Paper 2 Higher, Q15 (3 marks): Here are six graphs. Graph A Graph B Graph C y y y O O O x x x Graph D Graph E Graph F y y y O x O x O x Complete the table below with the letter of the graph t
January 2020, Paper 2 Higher, Q19 (5 marks): (a) Write down an equation of a line that is parallel to the line with equation y = 7 – 4x The line L passes through the points with coordinates (–3, 1) and (2,
January 2020, Paper 2 Higher, Q21 (4 marks): The diagram shows a sketch of part of the curve with equation y = f(x) y (4, 6) y = f(x) O x There is one maximum point on this curve. The coordinates of this m
June 2019 (R), Paper 1 Foundation, Q11 (3 marks): On the grid, draw the graph of y = 2x – 3 for values of xIURPíWR y 7 6 5 4 3 2 1 O x –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 –7
June 2019 (R), Paper 1 Higher, Q15 (4 marks): The straight line L1 has equation 2y = 6xí The straight line L2 is perpendicular to L1 DQGSDVVHVWKURXJKWKHSRLQW í Find an equation for L2 Give your a
June 2019 (R), Paper 1 Higher, Q21 (4 marks): A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (4, 3) (a) Write down the coordinates of t
June 2019 (R), Paper 2 Foundation, Q7 (4 marks): -4 B -3 -2 C -1 2 3 5 -5 -4 -3 -2 -1 1 -1 E D -2 --3 -4 (a) Write down the coordinates of point B. (. (b) Write down the letter of the point with coordinates (2
June 2019 (R), Paper 2 Foundation, Q15 (4 marks): This graph can be used to find the distance travelled, in kilometres, by Chuck's car and the amount of petrol, in litres, used. 200 - 150- Distance 100 - (kilom
June 2019 (R), Paper 2 Foundation, Q19 (4 marks): (a) Complete the table of values for y = 1 + 5x- x2 -1 1 2 3 4 5 6 1 7 7 1 (b) On the grid, draw the graph of y = 1 + 5x - x? for values of x from -1 to 6 4 3 2
June 2019 (R), Paper 2 Foundation, Q26 (3 marks): Line L is drawn on the grid. L 4 3 2 1 -2 1 2 3 -4 -3 -1 -1 -2 -3 Find an equation for L.
June 2019 (R), Paper 2 Higher, Q3 (4 marks): (a) Complete the table of values for y = 1 + 5xíx2 x í 0 1 2 3 4 5 6 y 1 7 7 1 (b) On the grid, draw the graph of y = 1 + 5xíx2 for values of xIURPíWR
June 2019 (R), Paper 2 Higher, Q11 (3 marks): Line L is drawn on the grid. y L 4 3 2 1 O x í í í í 1 2 3 í í í í Find an equation for L.
June 2019 (R), Paper 2 Higher, Q18 (9 marks): The functions f and g are defined as x f(x) = and g(x) = xí 4 x 3 − (a) State which value of x must be excluded from any domain of the function f. (b) Find f
June 2019, Paper 1 Foundation, Q15 (6 marks): Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is th
June 2019, Paper 1 Foundation, Q18 (4 marks): (a) Complete the table of values for y = x2íxí x í í 0 1 2 3 4 y í í 3 (b) On the grid, draw the graph of y = x2íxíIRUDOOYDOXHVRIxIURPí
June 2019, Paper 1 Higher, Q2 (6 marks): Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is th
June 2019, Paper 1 Higher, Q4 (4 marks): (a) Complete the table of values for y = x2íxí x í í 0 1 2 3 4 y í í 3 (b) On the grid, draw the graph of y = x2íxíIRUDOOYDOXHVRIxIURPí
June 2019, Paper 1 Higher, Q22 (6 marks): The graph of y = sinx° for 0 - x - 360 is drawn on the grid. y 3 2 1 O x 60 120 180 240 300 360 í í í (a) On the grid, draw the graph of y = 2sin(x + 30)° fo
June 2019, Paper 1 Higher, Q23 (5 marks): ABCD is a kite with AB = AD and CB = CD. B is the point with coordinates (10, 19) D is the point with coordinates (2, 7) Find an equation of the line AC. Give y
June 2019, Paper 2 Foundation, Q12 (3 marks): On the grid, draw the graph of y = 3x - 1 for values of x from -2 to 3 11- -10- 9 8 7 6 5 4 3 2 1 -2 -1 2 4 -2 -3 -4 -5 -6 -7 -8
June 2019, Paper 2 Foundation, Q22 (4 marks): The straight line L has gradient 5 and passes through the point with coordinates (0, -3) (a) Write down an equation for L. (b) 5 4 3 R 2 1 -1 -2 1 2 3 --1 --2-
June 2019, Paper 2 Higher, Q10 (4 marks): The straight line LKDVJUDGLHQWDQGSDVVHVWKURXJKWKHSRLQWZLWKFRRUGLQDWHV í (a) Write down an equation for L. (b) y 5 4 3 R 2 1 O x –2 –1 1 2 3 4 –1
January 2019 (R), Paper 1 Foundation, Q6 (5 marks): The diagram shows a triangle ABC drawn on a grid. •7- 6 •5 -4- -3 A -2 -1 4 5 6 -2 -1 1 2 3 7 -1 -2- (a) Write down the coordinates of point B. ( ) (b) On the g
January 2019 (R), Paper 1 Foundation, Q13 (6 marks): (a) Complete the table of values for y = 2x - 5 -2 -1 0 1 2 3 4 -7 1 -1 (b) On the grid, draw the graph of y= 2x - 5 for values of x from -2 to 4 5. -3. 2: 1 -2
January 2019 (R), Paper 2 Higher, Q11 (3 marks): The straight line L1 has equation x + 2y = 4 The straight line L2 passes through the points (−1, −7) and (7, 9) Michael says that the lines L1 and L2 are perpen
January 2019 (R), Paper 2 Higher, Q18 (4 marks): Here is the graph of y = sinx° for 0 ≤ x ≤ 360 -1- 450 ÷ 90 270 180 -90 360 -1 (a) On the grid above, sketch the graph of y = sin (x + 90)° for 0 ≤ x ≤ 360 I 0
January 2019 (R), Paper 2 Higher, Q21 (6 marks): The curve with equation y = (10x − 3)(x + 1) and the line with equation y − 6x = 0 intersect at the points A and B. Find the coordinates of the midpoint of AB.
January 2019, Paper 1 Foundation, Q12 (3 marks): On the grid, draw the graph of y = 2x - 3 for values of x from -1 to 4 6 4 3 2 -1 -1 -2 -3 -4 -5 -7
January 2019, Paper 1 Higher, Q6 (6 marks): (a) Complete the table of values for y = x2 – 5x + 6 x 0 1 2 3 4 5 y 6 0 0 2 (b) On the grid, draw the graph of y = x2 – 5x + 6 for 0  x  5 y 7 6 5 4 3 2 1 O
January 2019, Paper 1 Higher, Q18 (3 marks): The graph of y = f(x) is shown on the grid. y 4 2 O −8 −6 −4 −2 2 4 6 8 x −2 −4 −6 −8 1   (a) On the grid above, sketch the graph of y = f x   2 The graph
January 2019, Paper 2 Foundation, Q24 (3 marks): The line L is drawn on the grid. y 6 L 4 2 O x –4 –2 2 4 –2 –4 Find an equation for L.
January 2019, Paper 2 Higher, Q10 (3 marks): The line L is drawn on the grid. -4- -2 -4 --2 -4- Find an equation for L.
January 2019, Paper 2 Higher, Q21 (4 marks): Line L has equation 4y – 6x = 33 Line M goes through the point A (5, 6) and the point B (−4, k) L is perpendicular to M. Work out the value of k.

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