Cambridge & Pearson Edexcel Past Paper Questions

The polynomial p(x) = mx³-29x2+39x+n, where m and n are constants, has a factor 3x-1, and remainder 6 when divided by x-1. Show that x-2 is a facto...

The function f is defined, for 0° ≤ x ≤ 810°, by f(x)=-2+cos(2x/3).

The points A(5, -4) and C(11, 6) are such that AC is the diagonal of a square, ABCD.

DAB is a sector of a circle, centre A, radius 18 cm. The lines CB and CD are tangents to the circle. Angle DAB is (7π/9) radians. [Figure 7.1]

A particle moves in a straight line so that, t seconds after passing through a fixed point O, its velocity, v ms⁻¹, is given by v = 3t² - 30t+72.

Solve the following simultaneous equations. 4x² + 3xy + y² = 8 xy+4 = 0

Find ∫(e³x+1)³dx.

In this question all lengths are in centimetres. The volume and surface area of a sphere of radius r are (4/3)πr³ and 4πr² respectively. [Figure 11...

DO NOT USE A CALCULATOR IN THIS QUESTION. [Figure 12.1] The diagram shows part of the curve y=1/(2x+1) and part of the line 5y = x-1. The curve mee...

The functions f and g are defined, for x > 0, by f(x) = (2x²-1)/(3x) and g(x) = 1/x.

Find constants a, b and c such that √pq³r⁻³ / ((pq⁻¹)²)r⁻¹ = pᵃqᵇrᶜ.

A particle moves in a straight line such that its displacement, s metres, from a fixed point, at time t seconds, t≥ 0, is given by s = (1+3t)^(1/2).

A function f is such that f(x) = ln (2x+1), for x > -1/2. A function g is such that g(x) = 5x-7, for x ∈ R.

[Figure 4.a] The diagram shows the graph of y =|f(x)|, where f(x) is a cubic. Find the possible expressions for f(x).

Find the vector which is in the opposite direction to `( (15), (-8) )` and has a magnitude of 8.5.

Write down the values of k for which the line y = k is a tangent to the curve `y = 4 sin(x + π/4) + 10`.

The first three terms of an arithmetic progression are lg 3, 3 lg 3, 5 lg 3. Given that the sum to n terms of this progression can be written as 25...

A circle, centre O and radius r cm, has a sector OAB of fixed area 10 cm². Angle AOB is θ radians and the perimeter of the sector is P cm.

The normal to the curve `y = tan(3x + π/2)` at the point P with coordinates `(p, -1)`, where `0 < p < π/6`, meets the x-axis at the point A and the...

The diagram shows the graph of y = a sinbx+c, where a, b and c are integers, for -180° ≤ x ≤ 180°. Find the values of a, b and c.

Given that x = sec²θ and y+2 = cot²θ, find y in terms of x.

Variables x and y are such that, when lg(2y+1) is plotted against x², a straight line graph passing through the points (1, 1) and (2, 5) is obtained.

Find the unit vector in the same direction as (-15, 8).

The first three terms, in ascending powers of x, in the expansion of (1 + x/6)^12 (2−3x)^3 can be written in the form 8+px+qx², where p and q are c...

The polynomial p(x) = 6x³ + ax² + 6x + b, where a and b are integers, is divisible by 2x−1. When p(x) is divided by x−2, the remainder is 120.

Show that 2/(2x+3) - 1/(x-1) + 1/(x-1)² can be written as (8-3x)/((x-1)²(2x+3)).

A team of 6 people is to be chosen from 10 people. Two of the people are sisters who must not be separated. Find the number of different teams that...

The normal to the curve y = ln(3x² + 2)/(x + 1), at the point A on the curve where x = 0, meets the x-axis at point B. Point C has coordinates (0, ...

Given the simultaneous equations lg x + 2 lg y = 1, x - 3y² = 13, show that x² - 13x - 30 = 0.

In this question all lengths are in kilometres and time is in hours. A particle P moves in a straight line such that its displacement, s, from a fi...

Solve the equation 5ʷ⁻¹ = 12, giving your answer correct to 2 decimal places.

Write 2lgx-(lg(x+6)+lg3) as a single logarithm to base 10.

Variables x and y are such that when √y is plotted against x², a straight line passing through the points (9, 8) and (16, 1) is obtained. Find y as...

The polynomial p(x) = mx³ - 17x²+nx+6 has a factor x-3. It has a remainder of -12 when divided by x + 1. Find the remainder when p(x) is divided by...

Write down, in ascending powers of x, the first three terms in the expansion of (1+4x)ⁿ. Simplify each term.

A 5-digit number is to be formed from the seven digits 0, 1, 2, 3, 4, 5, 6. Each digit can be used at most once in any number and the number does n...

Variables x and y are such that y = (1 + sin 3x)⁴ / √x. Use differentiation to find the approximate change in y when x increases from 1.9 to 1.9+h,...

In this question, i is a unit vector due east and j is a unit vector due north. Distances are measured in kilometres and time is measured in hours....

In this question all lengths are in metres. [Figure 9.1] The diagram shows a water container in the shape of a triangular prism. The depth of water...

Differentiate xlnx-2x with respect to x. Simplify your answer.

The diagram shows part of the curves y = eˣᐟ² and y = cos 5x and part of the line x = π/4. The curves intersect at A. The curve y = cos 5x cuts the...

DO NOT USE A CALCULATOR IN THIS QUESTION. A curve has equation y = 6+ √x / 3+√x where x ≥ 0. Find the exact value of y when x = 6. Give your answer...

The diagram shows the graphs of y = |f(x)| and y = g(x), where y = f(x) and y = g(x) are straight lines. Solve the inequality |f(x)|≤g(x). [Figure 2]

Find the possible values of k for which the equation kx² + (k+5)x-4 = 0 has real roots.

Variables x and y are related by the equation y = 1+2/x+1/x² where x > 0. Use differentiation to find the approximate change in x when y increases ...

Solve the equation 625^((x³-1)/2) / 125^(x³) = 5.

In this question, i is a unit vector due east and j is a unit vector due north. A cyclist rides at a speed of 4ms⁻¹ on a bearing of 015°. Write the...

Differentiate y = (e^(4x) tanx) / lnx with respect to x.

The function f is defined by f(x) = 3 sin²x-2cosx for 2≤x≤4, where x is in radians.

In this question all lengths are in centimetres. [Figure 9]