Cambridge & Pearson Edexcel Past Paper Questions

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]

A geometric progression has first term a and common ratio r, where r > 0. The second term of this progression is 8. The sum of the third and fourth...

The diagram shows part of the line y = 1 and one complete period of the curve y = 1+cosx, where x is in radians. The line PQ is a tangent to the cu...

A curve is such that d²y/dx² = ((√x+1)/√x)². Given that the gradient of the curve is 4/3 at the point (1, −1), find the equation of the curve.

1 (a) Write 5x²-14x+8 in the form a(x+b)² +c, where a, b and c are constants to be found.

2 The polynomial p is such that p(x) = ax³ +7x²+bx+c, where a, b and c are integers.

3 The points A and B have coordinates (2,5) and (10, -15) respectively. The point P lies on the perpendicular bisector of the line AB. The y-coordi...

4 The diagram shows the velocity-time graph for a particle travelling in a straight line with velocity, vms⁻¹, at time t seconds. When t = 30 the v...

5 DO NOT USE A CALCULATOR IN THIS QUESTION. In this question, all lengths are in centimetres.

6 Show that (cot θ + tan θ) / sec θ = cosec θ.

7 (a) A team of 8 people is to be chosen from a group of 15 people.

8 A curve has the equation y = (3x-4)¹ᐟ³ / (2x+1).

9 The first three terms of an arithmetic progression are ln q, ln q⁴ and ln q⁷, where q is a positive constant. The sum to n terms of this progress...

10 It is given that y = (3x+1)²ln(3x+1).

The diagram shows the graph of y = a cos bx+c. Find the values of the constants a, b and c.

DO NOT USE A CALCULATOR IN THIS QUESTION. Solve the equation (2+√5)x² = 4x+3(2-√5), giving your answers in the form a+b√5 where a and b are integers.

The diagram shows the graph of y = |f(x)|, where f(x) is a cubic polynomial. Find, in factorised form, the possible expressions for f(x).