Algebra and functions: Edexcel International A Level Maths questions

Every Edexcel International A Level Maths exam question on P1.1 Algebra and functions, 2019–2025, with its mark scheme and examiner’s report.

All 92 questions on Algebra and functions, as a list

June 2025, AS Pure 1 (P1), Q1 (5 marks): Given that p = 1 16 x 4 q = 40 3x express each of the following in the form kx n where k and n are fully simplified constants. (a) p 1 2 (b) (pq) –1 (c) pq 2
June 2025, AS Pure 1 (P1), Q7 (10 marks): y x O C1 Figure 3 Figure 3 shows a sketch of part of the curve C1 Given that C1 • has equation y = f (x) where f (x) is a cubic function • touches the x-axis at
June 2025, AS Pure 1 (P1), Q9 (10 marks): y O x C2 C1 P 2 y x 12 y x Figure 4 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Fi
June 2025, AS Pure 1 (P1), Q10 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (k – 1)x 6 + 4x 3 + (k – 4) = 0 where
June 2025 (A), AS Pure 1 (P1), Q1 (5 marks): O –1 C P(2, 5) y = 3 x y Figure 1 The curve C, shown in Figure 1, • has equation y = f (x) , x ∈  • cuts the x-axis at –1 • has a maximum turning point at P (2
June 2025 (A), AS Pure 1 (P1), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A vessel that contained some
June 2025 (A), AS Pure 1 (P1), Q4 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) Using the laws of indices, solve 2
June 2025 (A), AS Pure 1 (P1), Q6 (5 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C1 has equation y = (x + 5)(
June 2025 (A), AS Pure 1 (P1), Q7 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Sketch the curve C with e
June 2025 (A), AS Pure 1 (P1), Q8 (9 marks): y x –6 –3 C l (2, 18) O R Figure 3 Figure 3 shows a sketch of a line l and a quadratic curve C. Given that l passes through (–3, 0) and (2, 18) (a) find an equa
January 2025, AS Pure 1 (P1), Q3 (5 marks): The population of a town was monitored. Exactly 5 years after monitoring began, the population was 58 000 Exactly 10 years after monitoring began, the populatio
January 2025, AS Pure 1 (P1), Q4 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Given that y = a x where
January 2025, AS Pure 1 (P1), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve C has equation y x
January 2025, AS Pure 1 (P1), Q9 (13 marks): O A B P x y C2 C1 R Figure 2 (a) Express 6 27 4 2 x x − − in the form a + b(x + c) 2 where a, b and c are constants to be found. Figure 2 shows part of a sketch
October 2024, AS Pure 1 (P1), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) Simplify fully 3 2 4 3 4 2 4 3 y x
October 2024, AS Pure 1 (P1), Q4 (10 marks): P 4 C2 O C1 x y Figure 1 Figure 1 shows a sketch of part of the curves C1 and C2 Given that C1 • has equation y = f(x) where f(x) is a quadratic function • cuts
October 2024, AS Pure 1 (P1), Q6 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Sketch the curve C with equation y
June 2024, AS Pure 1 (P1), Q2 (6 marks): (i) Given that m = 2 n, express each of the following in simplest form in terms of m. (a) 2 n + 3 (b) 16 3n (ii) In this question you must show all stages of yo
June 2024, AS Pure 1 (P1), Q3 (6 marks): O 2 3 x y –1 Figure 1 Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the points (–1, 0) and (0, 2) and touches the x‑axis
June 2024, AS Pure 1 (P1), Q4 (6 marks): The curve C1 has equation y = x 2 + kx – 9 and the curve C2 has equation y = –3x 2 – 5x + k where k is a constant. Given that C1 and C2 meet at a single point P
June 2024, AS Pure 1 (P1), Q6 (7 marks): P R Q O x y C l Figure 3 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 3 show
June 2024, AS Pure 1 (P1), Q8 (7 marks): The curve C1 has equation y = x(4 – x 2) (a) Sketch the graph of C1 showing the coordinates of any points of intersection with the coordinate axes. The curve C2
June 2024 (R), AS Pure 1 (P1), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Solve 5 (x + 3) > 4 (2x –5) (b) (i
June 2024 (R), AS Pure 1 (P1), Q4 (5 marks): The curve C has equation y = 2 x + 3x – 4 x ≠ 0 The straight line l has equation y = kx + 2 where k is a constant. (a) Show that l meets C when (k – 3) x 2 + 6x
June 2024 (R), AS Pure 1 (P1), Q5 (5 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Fully factorise 9x 3 – 10x 2 + x (
June 2024 (R), AS Pure 1 (P1), Q8 (11 marks): A curve C with equation y = f (x) passes through the point R(4, 13). Given that f′ (x) = 2(x – 3)(3x + 2) (a) use integration to find f (x), giving your answer
January 2024, AS Pure 1 (P1), Q4 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) By substituting p = 2 x, show that
January 2024, AS Pure 1 (P1), Q7 (9 marks): (a) Sketch the graph of the curve C with equation y x k 4 where k is a positive constant. Show on your sketch • the coordinates of any points where C cuts the c
January 2024, AS Pure 1 (P1), Q9 (10 marks): The curve C1 has equation y = f (x). Given that • f (x) is a quadratic expression • C1 has a maximum turning point at (2, 20) • C1 passes through the origin (a)
October 2023, AS Pure 1 (P1), Q2 (4 marks): Given that a x b x = = 1 64 16 2 express each of the following in the form kx n where k and n are simplified constants. (a) a 1 2 (b) 16 3 b (c) ab 2 4 3
October 2023, AS Pure 1 (P1), Q3 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Write 8 15 2 3 5 in the form a b 3
October 2023, AS Pure 1 (P1), Q4 (7 marks): O C x y Figure 1 Figure 1 shows a sketch of part of the curve C with equation y = 1 2 x + (a) State the equation of the asymptote of C that is parallel to the y
October 2023, AS Pure 1 (P1), Q6 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The equation 4 2 12 15 ( ) p x p x p x
October 2023, AS Pure 1 (P1), Q8 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The curve C1 has equation xy x 15 2 5
October 2023, AS Pure 1 (P1), Q11 (10 marks): O R P l C x y (–1, 28) Figure 5 Figure 5 shows part of the curve C with equation y = f(x) where f ( ) x x x 2 12 14 2 (a) Write 2 12 14 2 x x in the form a x b
June 2023, AS Pure 1 (P1), Q1 (4 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Solve the inequality 4x 2 – 3x + 7  4
June 2023, AS Pure 1 (P1), Q2 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A rectangular sports pitch ha
June 2023, AS Pure 1 (P1), Q3 (6 marks): (a) Express 3x 2 + 12x + 13 in the form a(x + b) 2 + c where a, b and c are integers to be found. (b) Hence sketch the curve with equation y = 3x 2 + 12x + 13 O
June 2023, AS Pure 1 (P1), Q4 (7 marks): In this question you must show all stages of your working. (a) Write y x x x 5 8 2 3 3 in the form y = Ax p + Bx q where A, B, p and q are constants to be found
June 2023, AS Pure 1 (P1), Q6 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Expand and simplify r r 1 2 (
June 2023, AS Pure 1 (P1), Q7 (6 marks): O R1 R2 x y y = kx y = 2 x = a y = 10 – 2x Figure 2 The region R1 , shown shaded in Figure 2, is defined by the inequalities 0  y  2 y  10 – 2x y  kx where
June 2023, AS Pure 1 (P1), Q10 (10 marks): C P O l1 l2 x y Figure 5 Figure 5 shows a sketch of the quadratic curve C with equation y = – 1 4 (x + 2)(x – b) where b is a positive constant The line l1 also
January 2023, AS Pure 1 (P1), Q4 (4 marks): Given that the equation kx 2 + 6kx + 5 = 0 where k is a non zero constant has no real roots, find the range of possible values for k.
January 2023, AS Pure 1 (P1), Q5 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) By substituting p = 3 x, show that
January 2023, AS Pure 1 (P1), Q7 (10 marks): (a) On Diagram 1, sketch a graph of the curve C with equation y x x = ≠ 6 0 The curve C is transformed onto the curve with equation y x x = − ≠ 6 2 2 (b) Fully
January 2023, AS Pure 1 (P1), Q8 (8 marks): R 4 –12 (7, –18) l O C x y Figure 2 Figure 2 shows a sketch of the straight line l and the curve C. Given that l cuts the y‑axis at –12 and cuts the x‑axis at 4
January 2023, AS Pure 1 (P1), Q10 (10 marks): l O C P x y Figure 4 Figure 4 shows a sketch of part of the curve C with equation y = f(x), where f(x) = (3x + 20)(x + 6)(2x – 3) (a) Use the given information
October 2022, AS Pure 1 (P1), Q3 (5 marks): The share price of a company is monitored. Exactly 3 years after monitoring began, the share price was £1.05 Exactly 5 years after monitoring began, the share p
October 2022, AS Pure 1 (P1), Q4 (6 marks): In this question you must show detailed reasoning. Solutions relying on calculator technology are not acceptable. f(x) = x2(2x + 1) – 15x (a) Solve f(x) = 0 (b)
October 2022, AS Pure 1 (P1), Q6 (6 marks): (a) Given that k is a positive constant such that 0 < k < 4 sketch, on separate axes, the graphs of (i) y = (2x – k)(x + 4)2 (ii) y = k x2 showing the coordinat
October 2022, AS Pure 1 (P1), Q7 (8 marks): O (–4, 6) (–1, 6) (2, 6) (3, 6) y = f(x) x y Figure 1 Figure 1 shows the curve with equation y = f(x). The points P(–4, 6), Q(–1, 6), R(2, 6) and S(3, 6) lie on
October 2022, AS Pure 1 (P1), Q9 (14 marks): O P l M C x y Figure 3 Figure 3 shows a sketch of the curve C with equation y = 1 2 x2 – 10x + 22 (a) Write 1 2 x2 – 10x + 22 in the form a(x + b) 2 + c where a
June 2022, AS Pure 1 (P1), Q3 (5 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) Show that 180 80 5 − is an integer
June 2022, AS Pure 1 (P1), Q4 (6 marks): y x O y = 1 y = f(x) Q P Figure 1 Figure 1 shows a sketch of a curve with equation y = f(x) The curve has a minimum at P(−1, 0) and a maximum at Q 3 2 2 ,  
June 2022, AS Pure 1 (P1), Q5 (9 marks): The curve C has equation y = f(x) Given that • f(x) is a quadratic expression • the maximum turning point on C has coordinates (−2, 12) • C cuts the negative x-
June 2022, AS Pure 1 (P1), Q6 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Given that 2xy − 3x2 = 50 and y −
January 2022, AS Pure 1 (P1), Q2 (6 marks): f(x) = 11 – 4x – 2x 2 (a) Express f(x) in the form a + b(x + c) 2 where a, b and c are integers to be found. (b) Sketch the graph of the curve C with equation y
January 2022, AS Pure 1 (P1), Q3 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) f(x) = (x + 2) 2 + (3x – 5 8) 2 Ex
January 2022, AS Pure 1 (P1), Q4 (7 marks): y Q l O R C x P Figure 1 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 1 show
January 2022, AS Pure 1 (P1), Q7 (11 marks): y O x Figure 3 Figure 3 shows a sketch of part of the curve with equation y = f(x), where f(x) = (x + 4)(x – 2)(2x – 9) Given that the curve with equation y = f
January 2022, AS Pure 1 (P1), Q10 (9 marks): The curve C has equation y = 1 2 x – 9 (a) Sketch the graph of C. On your sketch • show the coordinates of any points of intersection with the coordinate axes •
October 2021, AS Pure 1 (P1), Q3 (6 marks): (i) Solve 3 x > 4 (ii) y x O l R C Figure 1 Figure 1 shows a sketch of the curve C and the straight line l. The infinite region R, shown shaded in Figure 1, lie
October 2021, AS Pure 1 (P1), Q6 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve C has equation y = f(x) where
October 2021, AS Pure 1 (P1), Q8 (10 marks): y x O M C l1 Figure 4 Figure 4 shows a sketch of the curve C with equation y = 4 + 12x – 3x 2 The point M is the maximum turning point on C. (a) (i) Write 4 + 1
October 2021, AS Pure 1 (P1), Q9 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. y x O P(9, 3) y = f(x) Figure 5 Figure
June 2021, AS Pure 1 (P1), Q2 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. f(x) = ax3 + (6a + 8)x2 – a2x where a
June 2021, AS Pure 1 (P1), Q3 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Not drawn to scale B q m C A p m 60° 2
June 2021, AS Pure 1 (P1), Q5 (8 marks): O t PA P PB Figure 2 The share value of two companies, company A and company B, has been monitored over a 15-year period. The share value PA of company A, in mi
June 2021, AS Pure 1 (P1), Q8 (9 marks): The curve C1 has equation y = 3x2 + 6x + 9 (a) Write 3x2 + 6x + 9 in the form a(x + b) 2 + c where a, b and c are constants to be found. The point P is the mini
January 2021, AS Pure 1 (P1), Q2 (6 marks): A tree was planted. Exactly 3 years after it was planted, the height of the tree was 2 m. Exactly 5 years after it was planted, the height of the tree was 2.4 m
January 2021, AS Pure 1 (P1), Q4 (8 marks): O x y P Q C R l Figure 2 The points P and Q, as shown in Figure 2, have coordinates (–2, 13) and (4, –5) respectively. The straight line l passes through P and
January 2021, AS Pure 1 (P1), Q6 (10 marks): (a) Sketch the curve with equation y k x k x = − > ≠ 0 0 (b) On a separate diagram, sketch the curve with equation y k x k k x = − + > ≠ 0 0 stating the coordin
January 2021, AS Pure 1 (P1), Q7 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. f ( ) x x x x = − − > 2 3 5 0 (a) Solv
January 2021, AS Pure 1 (P1), Q8 (9 marks): O x y P Q C l Figure 4 Figure 4 shows a sketch of part of the curve C with equation y = f (x), where f (x) = (3x – 2)2 (x – 4) (a) Deduce the values of x for wh
October 2020, AS Pure 1 (P1), Q1 (3 marks): Given that (3pq2)4 ×2p q8 º apbqc find the values of the constants a, b and c.
October 2020, AS Pure 1 (P1), Q2 (7 marks): f(x) = 3 + 12x – 2x 2 (a) Express f(x) in the form a – b(x + c)2 where a, b and c are integers to be found. The curve with equation y = f(x) – 7 crosses the x‑a
October 2020, AS Pure 1 (P1), Q4 (7 marks): Use algebra to solve the simultaneous equations y – 3x = 4 x 2 + y 2 + 6x – 4y = 4 You must show all stages of your working.
October 2020, AS Pure 1 (P1), Q5 (9 marks): (i) 2 –5 –3 y = f(x) O x y Figure 2 Figure 2 shows a sketch of the curve with equation y = f(x). The curve passes through the points (–5, 0) and (0, –3) and tou
October 2020, AS Pure 1 (P1), Q7 (11 marks): The curve C has equation y = 1 2 −x (a) Sketch the graph of C. On your sketch you should show the coordinates of any points of intersection with the coordinate
January 2020, AS Pure 1 (P1), Q2 (5 marks): Given y = 3 x, express each of the following in terms of y. Write each expression in its simplest form. (a) 3 3x (b) 1 3 2 x− (c) 81 9 2 3 −x
January 2020, AS Pure 1 (P1), Q5 (7 marks): (a) Find, using algebra, all solutions of 20x3 – 50x2 − 30x = 0 (b) Hence find all real solutions of 20( y + 3) 3 2 – 50( y + 3) − 30( y + 3) 1 2 = 0
January 2020, AS Pure 1 (P1), Q8 (6 marks): The straight line l has equation y = k(2x – 1), where k is a constant. The curve C has equation y = x2 + 2x + 11 Find the set of values of k for which l does no
January 2020, AS Pure 1 (P1), Q10 (8 marks): The curve C1 has equation y = f(x), where . f(x) = (4x – 3)(x – 5) 2 (a) Sketch C1 showing the coordinates of any point where the curve touches or crosses the c
June 2019, AS Pure 1 (P1), Q2 (5 marks): Answer this question showing each stage of your working. (a) Simplify 1 4 2 2 − giving your answer in the form a + b 2 where a and b are rational numbers. (b) H
June 2019, AS Pure 1 (P1), Q3 (9 marks): 2xí 5x 2x 6xí Not to scale Figure 1 )LJXUHVKRZVWKHSODQRIDJDUGHQ7KHPDUNHGDQJOHVDUHULJKWDQJOHV The six edges are straight lines. The length
June 2019, AS Pure 1 (P1), Q5 (7 marks): (a) Find, using algebra, all real solutions of 2xx2íx = 0 (b) Hence find all real solutions of 2( yí 6 yí 4í yí 2 = 0
June 2019, AS Pure 1 (P1), Q6 (7 marks): The line with equation y = 4x + c, where c is a constant, meets the curve with equation y = x(xí DWRQO\RQHSRLQW (a) Find the value of c. (b) Hence find
January 2019, AS Pure 1 (P1), Q2 (3 marks): Given 3 3 27 3 4 x y = find y as a simplified function of x.
January 2019, AS Pure 1 (P1), Q4 (3 marks): y x R C l1 O l2 Figure 1 Figure 1 shows a line l1 with equation 2y = x and a curve C with equation y = 2x − 1 8 x2 The region R, shown unshaded in Figure 1, is
January 2019, AS Pure 1 (P1), Q8 (6 marks): y O y = 4 y = f ( x ) (4, 9) (0, 6) (−3, 0) x Figure 4 The curve C with equation y = f ( x ) is shown in Figure 4. The curve C • has a single turning point, a m
January 2019, AS Pure 1 (P1), Q9 (7 marks): The equation 3 x + 5 = −2x + c where c is a constant, has no real roots. Find the range of possible values of c.
January 2019, AS Pure 1 (P1), Q11 (12 marks): (a) On Diagram 1 sketch the graphs of (i) y = x(3 − x) (ii) y = x(x − 2)(5 − x) showing clearly the coordinates of the points where the curves cross the coordin

Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International A Level Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.

1,251 questions