Cambridge & Pearson Edexcel Past Paper Questions

Express 4x² + 8x - 5 in the form p(x+q)² + r, where p, q and r are constants to be found.

O, P, Q and R are four points such that OP = p, OQ = q and OR = 3q - 2p.

Use the Binomial Theorem to expand (a + b)⁴, giving each term in its simplest form.

Given that y = atan bx + c has period π/4 radians and passes through the points (0, -2) and (π/16, 0), find the value of each of the constants a, b...

Find how many 5-digit even numbers can be made using each of the digits 1, 2, 3, 4, 5 once only.

The diagram shows part of the curve y = 3x - x³ and the lines y = 3x and 2y = 27 - 3x. The curve and the line y = 3x meet the x-axis at O and the c...

A curve has equation y = (2x-5)/(x-1) - 12x.

Given that x² + 2kx + 4k − 3 = 0 has no real roots, show that k satisfies k² - 4k+3 < 0.

Variables x and y are related by the equation y = (5x-1) / (3-x).

A team of 3 people is to be selected from 7 women and 6 men. Find the number of different teams that could be selected if there must be more women ...

Do not use a calculator in this question. The polynomial p(x) = 2x³ – 3x² + qx + 56 has a factor x – 2.

The coordinates of three points are A(−2, 6), B(6, 10) and C(p, 0).

The diagram shows a sector of a circle with centre O and radius 5 cm. The length of the arc AB is 7 cm. Angle AOB is θ radians. [Figure 6.1]

The matrix A is (4 5 / 3 2) and the matrix B is (4 2 / 1 3).

Find the coordinates of the points of intersection of the curve 4 + 5/y + 3/x = 0 and the line y = 15x + 10.

Find ∫(x³ + x² + 1) / x² dx.

The graph of the curve y = p(4^(2x)) - q(4^x) passes through the points (0, 2) and (0.5, 14). Find the value of p and of q.

A function f is defined, for all real x, by f(x) = x - x². Find the greatest value of f(x) and the value of x for which this occurs.

Solve the equation 8 sin²A + 2 cosA = 7 for 0° ≤ A ≤ 180°.

The line y = kx – 5, where k is a positive constant, is a tangent to the curve y = x² + 4x at the point A.

It is given that p(x) = x³ + ax² + bx – 48. When p(x) is divided by x – 3 the remainder is 6. Given that p'(1) = 0, find the value of a and of b.

Simplify √x³y¹⁰ ÷ √x³y⁻⁶, giving your answer in the form xᵃyᵇ, where a and b are integers.

State the range of f.

(a) [Figure OABC diagram] The diagram shows a figure OABC, where OA = a, OB = b and OC = c. The lines AC and OB intersect at the point M where M is...

[Figure Circle with rectangle ABCD] The diagram shows a circle, centre O, radius 12 cm. The points A and B lie on the circumference of the circle a...

Show that the curve y = (3x² + 8)² has only one stationary point. Find the coordinates of this stationary point and determine its nature.

On the axes below sketch the graphs of y = |2x – 5| and 9y = 80x – 16x².

Show that 5 + 4 tan²(x/3) = 4 sec²(x/3) + 1.

Given that y = e³ˣ / (4x² + 1), find dy/dx.

On each of the Venn diagrams below, shade the region which represents the given set. [Figure 1.1 - Three Venn diagrams are shown, with overlapping ...

It is given that y = (5x²+4)^(1/2) / (x+1). Showing all your working, find the exact value of dy/dx when x = 3.

Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.

The first 3 terms in the expansion of (3 - x/6)^n are 81 + ax + bx². Find the value of each of the constants n, a and b.

A particle P moves in a straight line, such that its displacement, x m, from a fixed point O, t s after passing O, is given by x = 4 cos (3t) – 4.

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

It is given that y = A(10^bx), where A and b are constants. The straight line graph obtained when lgy is plotted against x passes through the point...

(a) A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the...

(a) Given that A = [-3 1; -1 2; 4 5], B = [-2 0; 1 3] and C = AB, (b) The matrix X = [5 -12; 4 -7]

The diagram shows a circle, centre O, radius 8 cm. The points A, B, C and D lie on the circumference of the circle such that AB is parallel to DC. ...

The curve y = f(x) passes through the point (1/2, 7/2) and is such that f'(x) = e^(2x-1).

Find the equation of the curve which passes through the point (2, 17) and for which dy/dx = 4x³ + 1.

The variables x and y are such that y = ln(x² + 1).

Given that y = 7 cos 10x – 3, where the angle x is measured in degrees, state the period of y,

Given that a is a constant, expand (2 + ax)⁴, in ascending powers of x, simplifying each term of your expansion.

Four cinemas, P, Q, R and S each sell adult, student and child tickets. The number of tickets sold by each cinema on one weekday were P: 90 adult, ...

On each of the Venn diagrams below shade the region which represents the given set. [Figure 7.1]

A football club has 30 players. In how many different ways can a captain and a vice-captain be selected at random from these players?

The curve 3x² + xy - y² + 4y – 3 = 0 and the line y = 2(1 – x) intersect at the points A and B.

The table shows values of the variables t and P. t: 1, 1.5, 2, 2.5 P: 4.39, 8.33, 15.8, 30.0

Prove that sinx(cotx + tanx) = secx.