plumiAlgebra and functions: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P3.1 Algebra and functions, 2019–2025, with its mark scheme and examiner’s report.
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All 41 questions on Algebra and functions, as a list
- June 2025, Pure 3 (P3), Q1 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The functions f and g are def
- June 2025, Pure 3 (P3), Q4 (5 marks): The function f is defined by f ( ) x x x x x x 49 12 7 4 2 x > 3 (a) Show that f ( ) x x x 7 3 x > 3 (b) Hence find fʹ(x) giving your answer in simplest form.
- June 2025, Pure 3 (P3), Q10 (10 marks): x y A O P Figure 3 Figure 3 shows a sketch of part of the graph with equation y = f (x), where f (x) = ½kx – 10½+ k x ∈ and k is a positive constant. The grap
- June 2025 (A), Pure 3 (P3), Q1 (5 marks): The point P(6, –2) lies on the continuous curve with equation y = f (x), x ∈ . Find the point to which P is mapped when the curve with equation y = f (x) is tr
- June 2025 (A), Pure 3 (P3), Q4 (8 marks): R C O x y 2 3 Figure 1 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 1 shows
- June 2025 (A), Pure 3 (P3), Q8 (12 marks): The functions f and g are defined by f (x) = ln(2x – 3) x ∈ x > 2 g( ) x x a x a 3 2 x ∈ x ≠ a where a is a positive constant. (a) Find the exact value of f
- January 2025, Pure 3 (P3), Q4 (9 marks): Given that 4 2 3 8 4 4 3 2 2 2 x x x x Ax B Cx D x (a) (i) find the values of the constants A, B and C (ii) show that D = 0 (b) Hence, using algebraic integrati
- January 2025, Pure 3 (P3), Q6 (8 marks): The function f is defined by f (x) = 4 3 2 x x x ≠ 2 (a) Find f –1 (b) Show that f f (x) = ax b cx d + + where a, b, c and d are integers to be found. The point
- January 2025, Pure 3 (P3), Q7 (8 marks): Given that a and b are positive constants with a > b , (a) sketch, on separate diagrams, the graph with equation (i) y = |3x – a| (ii) y = |3x – a| – b Show on
- October 2024, Pure 3 (P3), Q3 (7 marks): y x O Figure 2 In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 2 shows
- October 2024, Pure 3 (P3), Q6 (8 marks): The functions f and g are defined by f (x) = 6 – 21 2 3 x + x 0 g (x) = x 2 + 5 x ∈ (a) Find gf (b) Find f –1 (c) Solve the equation gg(x) = 126
- June 2024, Pure 3 (P3), Q1 (6 marks): y x O P y = f (x) Figure 1 Figure 1 shows a sketch of the graph with equation y = f (x) where f (x) = 2| x – 5| + 10 The point P, shown in Figure 1, is the vert
- June 2024, Pure 3 (P3), Q2 (7 marks): g( ) x x x x 2 5 8 2 2 (a) Write g (x) in the form Ax B C x 2 where A, B and C are integers to be found. (b) Hence use algebraic integration to show that 8 4 g(
- June 2024, Pure 3 (P3), Q5 (10 marks): The functions f and g are defined by f ( ) ln x x x 2 5 0 > g( ) x x x x 6 2 2 1 1 3 > (a) Find f –1 (b) Use differentiation to prove that g is an increasing fu
- January 2024, Pure 3 (P3), Q1 (4 marks): The point P(–4, –3) lies on the curve with equation y = f(x), x ∈ Find the point to which P is mapped when the curve with equation y = f(x) is transformed to
- January 2024, Pure 3 (P3), Q4 (13 marks): The function f is defined by f(x) = 2 32 3 7 20 8 3 5 2 2 x x x x x ∈ x > 2 (a) Show that f(x) = 2 3 5 x x − (b) Show, using calculus, that f is a decreasing
- January 2024, Pure 3 (P3), Q8 (11 marks): O x y Figure 2 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The graph shown in Figu
- October 2023, Pure 3 (P3), Q2 (8 marks): The function f is defined by f (x) = x x 3 4 x ∈ , x ≠ 4 (a) Find ff (b) Find f –1 The function g is defined by g (x) = x 2 + 5 x ∈ , x > 0 (c) Find the exact
- October 2023, Pure 3 (P3), Q9 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. y y = f (x) x = k B A O x Figure 2 Fig
- June 2023, Pure 3 (P3), Q4 (6 marks): The function f is defined by f(x) = 2x 2 – 5 x 0 x ∈ (a) State the range of f On the following page there is a diagram, labelled Diagram 1, which shows a sk
- June 2023, Pure 3 (P3), Q6 (9 marks): y O x P Figure 2 Figure 2 shows a sketch of the graph y = f(x), where f(x) = 3½x – 2½ – 10 The vertex of the graph is at point P, shown in Figure 2. (a) Find th
- January 2023, Pure 3 (P3), Q1 (6 marks): The functions f and g are defined by (a) Write down the range of f (b) Find the value of fg (1.5) (c) Find g−1
- January 2023, Pure 3 (P3), Q4 (7 marks): f x x x x x x x x 2 15 35 21 4 3 3 4 3 2 2 (a) Find the values of the constants A, B, C and D such that f x Ax Bx C D x 2 2 3 (b) Hence find, f d x x
- January 2023, Pure 3 (P3), Q6 (8 marks): y P Q S R x O Figure 2 Figure 2 shows a sketch of the graph with equation y x a a 3 5 2 where a is a positive constant. The graph • cuts the y-axis at the point
- October 2022, Pure 3 (P3), Q1 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f(x) = 2 4 15 3 4 3 2 x x x x
- October 2022, Pure 3 (P3), Q2 (7 marks): The functions f and g are defined by f(x) = 5 − 4 3 2 x + x 0 g(x) = 4sin 3 6 x π + x ∈ (a) Find the range of f (b) (i) Find f −1(x) (ii) Write
- October 2022, Pure 3 (P3), Q7 (12 marks): y C1 x O Figure 3 Figure 3 shows a sketch of the graph of C1 with equation y = 5 − | 3x − 22 | (a) Write down the coordinates of (i) the vertex of C1 (ii) the i
- June 2022, Pure 3 (P3), Q2 (9 marks): The functions f and g are defined by f(x) = 5 3 2 − + x x x ∈ , x ≠ – 2 3 g(x) = 2x – 7 x ∈ (a) Find the value of fg (b) Find f –1 (c) Solve the equation f
- June 2022, Pure 3 (P3), Q5 (8 marks): O A B y = f(x) y x Figure 2 Figure 2 shows part of the graph with equation y = f(x), where f(x) = ½kx – 9½ – 2 x ∈ and k is a positive constant. The graph int
- January 2022, Pure 3 (P3), Q6 (11 marks): The function f is defined by f(x) = 5 3 4 x x − − x > 4 (a) Show, by using calculus, that f is a decreasing function. (b) Find f –1 (c) (i) Show that ff(x) = ax
- January 2022, Pure 3 (P3), Q7 (10 marks): y x O y = f(x) V Figure 2 Figure 2 shows a sketch of part of the graph with equation y = f(x), where f(x) = 1 2 ½2x + 7½ – 10 (a) State the coordinates of the v
- October 2021, Pure 3 (P3), Q1 (9 marks): The function f is defined by f ( ) x x x x x x = + + + + 5 7 12 5 4 2 x > 0 (a) Show that f ( ) x x x = + 5 3 (b) Find f –1 (c) (i) Find, in simplest form, f′(x
- October 2021, Pure 3 (P3), Q2 (10 marks): O x P y Figure 1 Figure 1 shows a sketch of part of the graph with equation y = f(x), where f(x) = ½3x – 13½ + 5 x ∈ The vertex of the graph is at point P, as
- June 2021, Pure 3 (P3), Q4 (10 marks): The functions f and g are defined by f (x) = 4 6 5 x x + − x , x ¹ 5 g (x) = 5 − 2x2 x , x 0 (a) Solve the equation fg(x) = 3 (b) Find f −1 (c) Sketch a
- June 2021, Pure 3 (P3), Q6 (8 marks): Given that k is a positive constant, (a) on separate diagrams, sketch the graph with equation (i) y = k − 2| x | (ii) y = | 2x − k 3 | Show on each sketch the c
- January 2021, Pure 3 (P3), Q2 (6 marks): O x y (1, 2) (3,0) Figure 1 Figure 1 shows a sketch of the curve with equation y = f(x), where x ∈ and f(x) is a polynomial. The curve passes through the orig
- January 2021, Pure 3 (P3), Q3 (8 marks): f ( ) x x x x x x x = − − + + + − − 3 2 1 5 26 2 3 5 4 2 > (a) Show that f ( ) x ax b cx d x = + + > 4 where a, b, c and d are integers to be found. (b) Hence f
- January 2021, Pure 3 (P3), Q4 (9 marks): O y x P Figure 2 Figure 2 shows a sketch of the graph with equation y = f(x), where f(x) = | 3x + a | + a and where a is a positive constant. The graph has a ve
- October 2020, Pure 3 (P3), Q4 (8 marks): y x O y = f (x) Figure 2 Figure 2 shows a sketch of part of the graph with equation y = f (x) where f (x) = 21 − 2 | 2 − x | x 0 (a) Find f f (b) Solve the eq
- January 2020, Pure 3 (P3), Q2 (8 marks): The function f and the function g are defined by f(x) = 12 1 x + x > 0, x ∈ g(x) = 5 2 ln x x > 0, x ∈ (a) Find, in simplest form, the value of fg(e2) (b) F
- January 2020, Pure 3 (P3), Q6 (9 marks): y O P y = f(x) x Figure 2 Figure 2 shows part of the graph with equation y = f(x), where f(x) = 2 ½ 2x – 5 ½ + 3 x 0 The vertex of the graph is at point P as
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