plumiAlgebra and functions: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.2 Algebra and functions, 2019–2025, with its mark scheme and examiner’s report.
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All 20 questions on Algebra and functions, as a list
- June 2025, AS Pure 2 (P2), Q4 (9 marks): The function f (x) is defined by f (x) = ax 3 + bx 2 + 5x – 3 where a and b are constants. Given that (x + 3) is a factor of f (x), (a) show that b = 3a + 2 Giv
- June 2025 (A), AS Pure 2 (P2), Q3 (7 marks): f (x) = (3x 2 – 4x – 5)(x – k) – 5 where k is a constant. (a) Deduce the value of the remainder when f (x) is divided by (x – k) Given that the remainder when f
- January 2025, AS Pure 2 (P2), Q5 (9 marks): f(x) = 3x 3 + ax 2 – 10x + b where a and b are constants. Given that (3x – 4) is a factor of f(x), (a) show that 16a + 9b = 56 Given further that when f(x) is d
- October 2024, AS Pure 2 (P2), Q3 (7 marks): f (x) = 2x 3 – x 2 + Ax + B where A and B are integers. Given that when f (x) is divided by (x + 3) the remainder is 55 (a) show that 3A – B = –118 Given also t
- June 2024, AS Pure 2 (P2), Q4 (8 marks): f (x) = (x – 2)(2x 2 + 5x + k) + 21 where k is a constant. (a) State the remainder when f (x) is divided by (x – 2) Given that (2x – 1) is a factor of f (x) (b)
- June 2024 (R), AS Pure 2 (P2), Q6 (9 marks): f (x) = 4x 3 + px 2 + 8x + q where p and q are constants. Given that • (2x + 3) is a factor of f (x) • f (x) has a remainder of –5 when divided by (x + 2) (a) (
- January 2024, AS Pure 2 (P2), Q1 (3 marks): f(x) = ax 3 + 3x 2 – 8x + 2 where a is a constant Given that when f(x) is divided by (x – 2) the remainder is 3, find the value of a.
- January 2024, AS Pure 2 (P2), Q6 (8 marks): (a) Given that 2 3 4 2 1 2 4 4 4 log log log x x x show that x 3 + 6x 2 + x – 4 = 0 (b) Given also that –1 is a root of the equation x 3 + 6x 2 + x – 4 = 0 (i)
- October 2023, AS Pure 2 (P2), Q4 (9 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. f (x) = 4x 3 + ax 2 – 29x + b where a
- June 2023, AS Pure 2 (P2), Q2 (6 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. f(x) = 4x 3 – 8x 2 + 5x + a where a is
- January 2023, AS Pure 2 (P2), Q5 (9 marks): f (x) = x3 + ( p + 3) x2 – x + q where p and q are constants and p > 0 Given that (x – 3) is a factor of f (x) (a) show that 9p + q = –51 Given also that when f
- June 2022, AS Pure 2 (P2), Q7 (7 marks): f(x) = Ax3 + 6x2 − 4x + B where A and B are constants. Given that • (x + 2) is a factor of f(x) • f d ( ) x x = ∫ 176 3 5 find the value of A and the value of B
- January 2022, AS Pure 2 (P2), Q5 (8 marks): f(x) = 3x 3 + Ax 2 + Bx – 10 where A and B are integers. Given that • when f(x) is divided by (x – 1) the remainder is k • when f(x) is divided by (x + 1) the r
- October 2021, AS Pure 2 (P2), Q4 (8 marks): f (x) = (x2 − 2)(2x − 3) − 21 (a) State the value of the remainder when f (x) is divided by (2x − 3) (b) Use the factor theorem to show that (x − 3) is a factor
- June 2021, AS Pure 2 (P2), Q7 (10 marks): (a) Given that 3 log3(2x – 1) = 2 + log3(14x – 25) show that 2x3 – 3x2 – 30x + 56 = 0 (b) Show that –4 is a root of this cubic equation. (c) Hence, using algebr
- January 2021, AS Pure 2 (P2), Q1 (6 marks): f (x) = x4 + ax3 − 3x2 + bx + 5 where a and b are constants. When f (x) is divided by (x + 1) , the remainder is 4 (a) Show that a + b = −1 When f (x) is divide
- October 2020, AS Pure 2 (P2), Q3 (10 marks): f(x) = ax3 – x2 + bx + 4 where a and b are constants. When f(x) is divided by (x + 4), the remainder is –108 (a) Use the remainder theorem to show that 16a + b
- October 2020, AS Pure 2 (P2), Q6 (9 marks): B A R C1 C2 O x y Figure 1 Figure 1 shows a sketch of part of the curves C1 and C2 with equations C1 : y = x3 – 6x + 9 x 0 C2 : y = –2x2 + 7x – 1 x 0 The cu
- January 2020, AS Pure 2 (P2), Q3 (8 marks): . f(x) = 6x3 + 17x2 + 4x – 12 (a) Use the factor theorem to show that (2x + 3) is a factor of f(x). (b) Hence, using algebra, write f(x) as a product of three l
- June 2019, AS Pure 2 (P2), Q6 (8 marks): f(x) = kx3 – 15x2 – 32x – 12 where k is a constant Given (x – 3) is a factor of f(x), (a) show that k = 9 (b) Using algebra and showing each step of your workin
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