Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
Find the values of the positive constants p and q such that, in the binomial expansion of (p + qx)¹⁰, the coefficient of x⁵ is 252 and the coeffici...
Variables x and y are such that y = e^(2x) + e^(-2x).
Answer only one of the following two alternatives. EITHER The diagram shows part of the curve y = 9x² – x³, which meets the x-axis at the origin O...
Answer only one of the following two alternatives. OR The diagram shows part of the curve y = 2sin 3x . The normal to the curve y = 2sin 3x at the...
Find ∫√7x-5 dx.
Using the substitution u = 2ˣ, find the values of x such that 2²ˣ⁺² = 5 (2ˣ) – 1 .
Show that cot A + (sin A) / (1 + cos A) = cosec A.
Solve the simultaneous equations 5x + 3y = 2 and 2/x - 3/y = 1 .
Differentiate the following with respect to x.
You must not use a calculator in this question.
Sketch the graph of y = |x² − x −6|, showing the coordinates of the points where the graph meets the coordinate axes.
[Figure X.X] The figure shows a circle, centre O, with radius 10cm. The lines XA and XB are tangents to the circle at A and B respectively, and ang...
Variables N and x are such that N = 200 + 50e^(x/100).
It is given that f(x) = 1/(2+x) for x ≠ −2, x ∈R. Find f'(x).
The point P lies on the line joining A(−1, –5) and B(11, 13) such that AP = (1/3)AB.
Answer only one of the following two alternatives. EITHER At 1200 hours, a ship has position vector (54i + 16j) km relative to a lighthouse, where...
Given that A = ( 4 -3 / 2 5 ) find the inverse matrix A⁻¹.
A cuboid has a square base of side (2 + √3) cm and a volume of (16 + 9 √3) cm³. Without calculator, find the height of the cuboid in the form (a + ...
The diagram shows a sketch of the curve y = asin(bx) + c for 0° ≤ x ≤ 180°. Find the values of a, b and c.
Find d/dx (x² lnx).
Solve the equation 3²ˣ = 1000, giving your answer to 2 decimal places.
By shading the Venn diagrams below, investigate whether each of the following statements is true or false. State your conclusions clearly.
Given that f(x) = x² - 648/√x, find the value of x for which f''(x) = 0.
Relative to an origin O, the position vectors of the points A and B are 2i – 3j and 11i + 9j respectively.
The diagram shows a trapezium ABCD with vertices A(11, 4), B(7, 7), C(–3, 2) and D. The side AD is parallel to BC and the side CD is perpendicular ...
The diagram shows a right-angled triangle ABC and a sector CBDC of a circle with centre C and radius 12 cm. Angle ACB = 1 radian and ACD is a strai...
Answer only one of the following two alternatives. EITHER The equation of a curve is y = 2x² – 20x + 37.
Answer only one of the following two alternatives. OR A function g is defined by g : x → 5x² + px + 72, where p is a constant. The function can als...
It is given that P is the set of prime numbers, S is the set of square numbers and N is the numbers between 10 and 90. Write each of the following ...
Given that y = √(4x + 1)³, find dy/dx
Find the values of m for which the line y = mx – 5 is a tangent to the curve y = x² + 3x + 4.
In a competition the contestants search for hidden targets which are classed as difficult, medium or easy. In the first round, finding a difficult ...
It is given that x – 2 is a factor of f(x) = x³ + kx² – 8x – 8.
(1 – 2x)⁷,
The table shows experimental values of variables x and y. X | 5 | 30 | 150 | 400 y | 8.9 | 21.9 | 48.9 | 80.6
An open rectangular cardboard box with a square base is to have a volume of 256 cm³. Find the dimensions of the box if the area of cardboard used i...
3 sin x – 5 cos x = 0 for 0° < x < 360°,
A team of 7 people is to be chosen from 5 women and 7 men. Calculate the number of different ways in which this can be done if
Answer only one of the following two alternatives. EITHER The diagram shows part of the curve y = sin(½x). The tangent to the curve at the point P ...
Answer only one of the following two alternatives. OR The diagram shows part of the curve y = xe⁻ˣ and the tangent to the curve at the point R (2, ...
On the axes below sketch, for 0 ≤ x ≤ 2π, the graph of y = cosx - 1. Which of the following best describes the graph?
On the axes below sketch, for 0 ≤ x ≤ 2π, the graph of y = sin 2x. Which of the following best describes the graph?
State the number of solutions of the equation cosx - sin 2x = 1, for 0 ≤ x ≤ 2π.
Variables x and y are such that y = Abˣ, where A and b are constants. The diagram shows the graph of In y against x, passing through the points (2,...
A committee of 6 members is to be selected from 5 men and 9 women. Find the number of different committees that could be selected if there are no r...
Given that log₄x = 1/2, find the value of x.
Solve 2log₄y - log₄(5y – 12) = 1/2. Which of the following is the smaller value of y?
Solve 2log₄y - log₄(5y – 12) = 1/2. Which of the following is the larger value of y?
Find ∫(1 - 6/x²)dx.
Find the value of the positive constant k for which ∫_k^3k (1 - 6/x²)dx = 2.