Cambridge & Pearson Edexcel Past Paper Questions

The first three terms, in descending powers of x, of the expansion of (ax+3)(1-b/x)⁵ can be written as 32x⁵-160x⁴+cx³, where a, b and c are constan...

Solve the following simultaneous equations. x+5y=-4 3y-xy = 6

Solve the equation 4e^(2x-3) = 7e^(5-x).

In this question a and b are constants. The normal to the curve y = ax⁻³ + 3x - 2 at the point where x = 1 has equation y = -1/4 x + b. Find the va...

Solve the equation log₃(11x-8) = 1 + 2/logₓ3 given that x > 1.

DO NOT USE A CALCULATOR IN THIS QUESTION. Find the x-coordinates of the points of intersection of the curves y = x³-2x²-4x-16 and y = 7x³-7x²-17x-4.

A 4-digit code is to be formed using 4 different numbers selected from 2, 3, 4, 5, 6, 7, 8 and 9. Find how many possible codes there are if the cod...

Show that sinx / (1-cosx) + (1-cosx) / sinx = 2 cosecx.

In this question all lengths are in centimetres. The volume of a cylinder with radius r and height h is πr²h and its curved surface area is 2πrh. T...

In this question all lengths are in centimetres. The diagram shows triangle ABC which has area 2√5/3 cm². Angle A is acute. [Figure 9.1]

A geometric progression has third term 4.5 and sixth term 15.1875. Find the first term and the common ratio.

The coordinates of points A and B are (-5,6) and (4, – 6) respectively. The point C lies on the line AB, between A and B, such that AC/CB = 1/2.

[Figure 1.0] The diagram shows the graph of the cubic polynomial y = f(x).

The function g is defined by g(x) = 5 sin(3x/4) - 2 for all values of x.

When ln (y+2) is plotted against x² a straight line graph is obtained. The line passes through the points (2.25, 9.37) and (4.75, 3.92). Find y in ...

It is given that the first four terms, in ascending powers of x, in the expansion of (1 - x/2)^n can be written in the form 1-8x+px²+qx³, where n, ...

Solve the equation 3 sec² (2θ + π/6) = 4 for -π/2 < θ < π/2, giving your answers in terms of π.

The polynomial p(x) is such that p(x) = ax³ + bx² +cx-5, where a, b and c are integers. It is given that p'(0) = 12. It is also given that p(x) has...

A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit can be used only once in any 6-digit number. A 6-digi...

It is given that f : x → (3x+1)²−4 for x ≥ a, and that f⁻¹ exists. (i) Find the least possible value of a. (ii) Using this value of a, write down t...

Solve the equation 12x^(3/2) - 5x^(3/4) - 11 = 0 for x > 0. Give your answer correct to one decimal place.

In this question all lengths are in centimetres and all angles are in radians. [Figure 10.1] The diagram shows a badge which consists of a minor se...

[Figure 11.1] In the triangle OAB, OA = a_and OB = b. The mid-point of the line OB is X, and the mid-point of the line AB is Y. The lines OY and AX...

A curve has equation y = √(5x-2) / (x-3).

A straight line passes through the points (4, 23) and (-8, 29). Find the point of intersection, P, of this line with the line y = 2x+5.

Find the non-zero value of k for which the line y=-2x-6k-1 is a tangent to the curve y = x(x+2k).

DO NOT USE A CALCULATOR IN THIS QUESTION. A cylinder has base radius (2+ √3)m and volume π(16+9√3)m³. Find the exact value of its height, giving yo...

Find the equation of the normal to the curve y = x³ - 7x² + 12x - 5 at the point (1, 1).

Find the exact value of ∫₂³ ((x+2)² / x) dx.

A particle is travelling in a straight line. Its displacement, s metres, from the origin at time t seconds is given by s = 1.5e^(2t) + 2e^(-2t) - t.

A curve has equation y = xsin 2x.

An arithmetic progression has twelve terms. The sum of the first three terms is -36 and the sum of the last three terms is 72. Find the first term ...

By writing cotx and tanx in terms of cosx and sinx, show that sinx/(1-cotx) + cosx/(1-tanx) = sinx + cosx.

The curve y = acos bx+c, where a, b and c are integers, passes through the points (-π/6,-2) and (π/2, 1). The curve has a period of 2π/3.

It is given that y = f(x), where f(x) = (2x-5)(x-1)2.

In this question, all lengths are in centimetres and all angles are in radians. [Figure X.X] The diagram shows a circle with centre O and radius 12...

The function f is such that f(x) = 4ln(3x-2), for x > a, where a is as small as possible.

Show that (1+cot²θ)/cot²θ = sec²θ.

Find, in descending powers of x, the first 3 terms in the expansion of (x + 2/x²)¹⁰. Simplify each term as far as possible.

It is given that y = ln(3x²-1)/(x+2), for x > 1/√3. When x = 1, y is increasing at the rate of h units per second. Find, in terms of h, the corresp...

The tangent to the curve y = e^(2x+5)^(1/2) at the point where x = 2 meets the x-axis at the point X and the y-axis at the point Y. Find the coordi...

The diagram shows part of the curve y = 4/(2x+1) and the straight line 2y = 6x+1. Find the area of the shaded region, giving your answer in the for...

The first 3 terms of an arithmetic progression are 2 tan 2x, 5 tan 2x, 8 tan2x. Find the values of x, where -180° ≤ x ≤ 180°, for which the sum to ...

Solve the following simultaneous equations. y/x = 3/2 y^4/x^5 = 27/16

Variables x and y are related by the equation y = x√1+2x.

DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is defined by p(x) = ax³ −3x² – 3x+b, where a and b are constants.

Use a graphical method to solve the inequality |2x-8|>4.

DO NOT USE A CALCULATOR IN THIS QUESTION. Write (5-√3)(√6+ √2)⁻² in the form a+b√3, where a and b are constants.

A class of 10 students includes Abby and Ben.

Solve the equation cot²2θ+3 cosec 2θ = 9 for -90° ≤ θ ≤ 90°.