Cambridge & Pearson Edexcel Past Paper Questions

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).

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.