Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
In this question all lengths are in centimetres and all angles are in radians. The diagram shows a circle with centre O and radius r. The points A ...
Find the exact solutions of the equation 6p^(1/3) - 5p^(-1/3) - 13 = 0.
Given that cot²θ = 1/(y+2) and sec θ = x-4, find y in terms of x.
Find the number of ways in which 14 people can be put into 4 groups containing 2, 3, 4 and 5 people.
It is given that f(x) = 2ln(3x-4) for x > a.
The diagram shows part of the curve y = 3 + 4/(2x+1) and the straight line 3y = 2x+6. Find the area of the shaded region, giving your answer in exa...
The first three terms of an arithmetic progression are (2x+1), 4(2x+1) and 7(2x+1), where x ≠ -1/2. Show that the sum to n terms can be written in ...
Variables x and y are such that when lgy is plotted against √x a straight line passing through the points (1, 5) and (2.5, 8) is obtained. Show tha...
The function g is defined for 0° ≤ x ≤ 120° by g(x) = 2+4 cos 6x.
The diagram shows the graph of y = h(x) where h(x) = (x+a)²(b+cx) and a, b and c are integers. The curve meets the x-axis at the points (-2, 0) and...
Solve the equation 5^(2y-1) = 6×3^y, giving your answer correct to 3 decimal places.
The volume, V, of a sphere of radius r is given by V = (4/3)πr³. The volume of a sphere is increasing at a constant rate of 24 cm³ s⁻¹. Find the ra...
The position vectors of the points P, Q and R relative to an origin O are (4/7), (8/5) and (x/y) respectively. The point R lies on PQ extended such...
The diagram shows the curve y = 6x-x² for 0 ≤ x ≤ 5 and the line y = x. Find the area of the shaded region.
The diagram shows the graph of y = f(x) where f is defined by f(x) = 3x/√(5x+1) for 0 ≤ x ≤ 3.
In this question all lengths are in centimetres and all angles are in radians.
In the expansion of (ax + b/x²)⁹ where a and b are constants with a > 0, the term independent of x is -145152 and the coefficient of x⁶ is –6912. S...
The line with equation x+3y = k, where k is a positive constant, is a tangent to the curve with equation x²+y²+2y-9 = 0. Find the value of k and he...
Solve the inequality 3x²-12x+16 > 3x+4.
A curve has equation y = 32x² + 1/(8x²) where x ≠ 0.
Variables x and y are related by the equation y = 2+tan(1-x) where 0 ≤ x ≤ π/2. Given that x is increasing at a constant rate of 0.04 radians per s...
Variables P and T are known to be connected by the relationship P = Abᵀ, where A and b are constants. Values of P are found for certain values of t...
Find the first three terms in the expansion of (1 + x/7)⁵, in ascending powers of x. Simplify the coefficient of each term.
f(x) = √3 + (4x-2)⁵ where x > 1. Find an expression for f'(x), giving your answer as a simplified algebraic fraction.
A curve has equation y = cos(x/4) where x is in radians. The normal to the curve at the point where x = 4π/3 cuts the x-axis at the point P. Find t...
A particle travels in a straight line so that, t seconds after passing a fixed point, its velocity, v ms⁻¹, is given by v = e⁴ for 0 ≤ t ≤ 4, v = 1...
The diagram shows a triangle OAB. The point C is the mid-point of OA. The point D lies on CB such that CD : DB = 2 : 3. OC = c CB = b. The point E ...
1 (a) On the axes, sketch the graph of y=-=(x+2)(2x-1)(x+5), stating the intercepts with the axes. [Figure 1.1 - Graph axes with x and y labels, a...
2 DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is such that p(x) = 6x³ - 35x² +34x+45.
3 (a) Write 1+1g(x² - 1) - 21g(x-1), where x > 1, as a single logarithm to base 10. Give your answer in its simplest form. (b) Solve the equation 4...
4 (a) The first three terms, in ascending powers of x, in the expansion of (3+px)ⁿ are 243+810x+qx², where n, p and q are constants. Find the value...
5 (a) The diagram shows the graph of y = acos bx+c, for -360° ≤ x ≤ 360°, where a, b and c are constants. Find the values of a, b and c. [Figure 5...
6 Find ∫₄²(2/(2x-3) - 3/(3x-5)²) dx, giving your answer in exact form.
7 Given that 2+cotθ = 3x and sinθ = √y, find y in terms of x.
8 Solve the equation 4 sin²(2α-π/3) = 1 for -π/2 < α < π/2. Give your answers in terms of π.
9 (a) Solve the following simultaneous equations. ex+y × e3x-2y = 1 x²y = 256
10 In this question, all distances are in metres and time, t, is in seconds. A particle P is at a fixed point O at time t = 0. The velocity, v, of ...
11 The tangent to the curve y = (3x-1)¹/² at the point where x = 3 meets the coordinate axes at the points A and B. The point with coordinates (a, ...
12 (a) It is given that y = (ln 3x) / x² for x > 0. Find dy/dx. Give your answer in the form (A+B ln 3x) / x³, where A and B are integers. (b) Henc...
The diagram shows the graph of y = a sinbx+c for -360°≤x≤ 360°, where a, b and c are constants. Find the values of a, b and c. [Figure 1.1]
Given that log₃r+2log₉s = 8, find the value of rs.
Given that y = tan(x/2), find the exact value of dy/dx when x = π/3.
A team of 8 people is to be formed from 6 teachers, 5 doctors and 4 police officers.
DO NOT USE A CALCULATOR IN THIS QUESTION. In this question, all lengths are in centimetres. The diagram shows the trapezium ABCD. The lengths of AB...
In this question, all lengths are in metres and all angles are in radians. The diagram shows a circle with centre O and radius 5. The points A, B, ...
The line y = 3x-2 intersects the curve 2x²-xy+y² = 2 at the points A and B. The point C with coordinates (k, 7/8) lies on the perpendicular bisecto...
A curve has equation y = (3x²-5)^(1/2) / (x+4).
In this question, all distances are in metres and time, t, is in seconds.
10 (a) The first 3 terms of an arithmetic progression are 3 sin 2x, 5 sin 2x, 7 sin2x.
11 (a) Given that y = x²lnx, find dy/dx.