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.
Given that A = [[2, -1], [3, 5]], find the determinant of A.
Given that A = [[2, -1], [3, 5]], find the adjoint matrix of A.
Given that A = [[2, -1], [3, 5]], find A⁻¹.
Using your answer from part (i), or otherwise, find the value of a such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] where A = [[2, -1], [3, 5]].
Using your answer from part (i), or otherwise, find the value of b such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] where A = [[2, -1], [3, 5]].
Using your answer from part (i), or otherwise, find the value of c such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] where A = [[2, -1], [3, 5]].
Using your answer from part (i), or otherwise, find the value of d such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] where A = [[2, -1], [3, 5]].
Calculators must not be used in this question. The diagram shows a triangle ABC in which angle A = 90°. Sides AB and AC are √5 – 2 and √5+ 1 respec...
The diagram shows a square ABCD of side 16 cm. M is the mid-point of AB. The points E and F are on AD and BC respectively such that AE = BF = 6 cm....
The figure shows points A, B and C with position vectors a, b and c respectively, relative to an origin O. The point P lies on AB such that AP:AB =...
The point A, whose x-coordinate is 2, lies on the curve with equation y = x³ – 4x² + x + 1. What is the y-coordinate of point A?
The point A, whose x-coordinate is 2, lies on the curve with equation y = x³ – 4x² + x + 1. Find the gradient of the tangent to the curve at A.
The point A, whose x-coordinate is 2, lies on the curve with equation y = x³ – 4x² + x + 1. The tangent to the curve at A meets the curve again at ...
Find the equation of the perpendicular bisector of the line AB, where A is (2, -5) and B is (0, 1).
Solve 2sin(x + π/3) = -1 for 0 ≤ x ≤ 2π. Which of the following is the smaller value of x?
Solve 2sin(x + π/3) = -1 for 0 ≤ x ≤ 2π. Which of the following is the larger value of x?
Solve tany - 2 = coty for 0° ≤ y ≤ 180°. Which of the following is the smaller value of y, correct to 1 decimal place?
Solve tany - 2 = coty for 0° ≤ y ≤ 180°. Which of the following is the larger value of y, correct to 1 decimal place?
Find the y-intercept of the tangent to the curve y = x³ – 4x² + x + 1 at point A (2, -5).
The Venn diagram shows the universal set &, the set A and the set B. Given that n(B) = 5, n(A') = 10 and n(&) = 26, find
A 4-digit number is to be formed from the digits 1, 2, 5, 7, 8 and 9. Each digit may only be used once. Find the number of different 4-digit number...
Show that (1 – cos θ – sin θ)² – 2(1 – sin θ)(1 – cos θ) = 0.
Find the set of values of k for which the curve y = 2x² + kx + 2k – 6 lies above the x-axis for all values of x.
The line 3x + 4y = 15 cuts the curve 2xy = 9 at the points A and B. Find the length of the line AB.
The normal to the curve y + 2 = 3 tan x, at the point on the curve where x = 3π/4, cuts the y-axis at the point P. Find the coordinates of P.
It is given that f(x) = 6x³ – 5x² + ax + b has a factor of x + 2 and leaves a remainder of 27 when divided by x – 1.
(a) Given that the matrix A = (4 2 \ 3 -5), find
(i) Given that n is a positive integer, find the first 3 terms in the expansion of (1 + x/2)^n in ascending powers of x.
(a) (i) Find ∫√2x - 5dx. Find ∫√2x - 5dx.
(a) Solve cos 2x + 2sec 2x + 3 = 0 for 0° ≤ x ≤ 360°.
A particle P moves in a straight line such that, t s after leaving a point O, its velocity v m s⁻¹ is given by v = 36t –3t² for t ≥ 0.
Prove that ( (1 + sin θ)² / cos² θ ) + ( (1 - sin θ)² / cos² θ ) = 2 + 4 tan² θ.
The velocity-time graph represents the motion of a particle moving in a straight line. [Figure 2.1]
Variables x and y are related by the equation y = 10 − 4sin² x, where 0 ≤ x ≤ π/2. Given that x is increasing at a rate of 0.2 radians per second, ...
Sketch the graph of y = |4x - 2| on the axes below, showing the coordinates of the points where the graph meets the axes. [Figure 4.1]
A piece of wire of length 96cm is formed into the rectangular shape PQRSTU shown in the diagram. It is given that PQ = TU = SR = xcm. It may be ass...
Find the equation of the normal to the curve y = (x² + 8) / (x - 2) at the point on the curve where x = 4.
Find the first four terms in the expansion of (2 + x)⁶ in ascending powers of x.
The line y = 2x - 8 cuts the curve 2x² + y² - 5xy + 32 = 0 at the points A and B. Find the length of the line AB.
It is given that x ∈ R and that E = {x:-5 < x < 12}, S = {x: 5x + 24 > x²}, T= {x:2x + 7 > 15}.
A plane, whose speed in still air is 240kmh⁻¹, flies directly from A to B, where B is 500km from A on a bearing of 032°. There is a constant wind o...
A one-one function f is defined by f(x) = (x - 1)² – 5 for x ≥ k.
The function f(x) = x³ + x² + ax + b is divisible by x - 3 and leaves a remainder of 20 when divided by x + 1.
Variables x and y are such that when √y is plotted against x² a straight line graph passing through the points (1, 3) and (4, 18) is obtained. Expr...
Solve the equation 3^(p+1) = 0.7, giving your answer to 2 decimal places.
The diagram shows the graph of a function y = f(x).
The position vectors of the points A and B, relative to an origin O, are 4i – 21j and 22i – 30j respectively. The point C lies on AB such that AB =...
Calculators must not be used in this question. The diagram shows a trapezium ABCD in which AD = 7cm and AB = (4+ √5)cm. AX is perpendicular to DC w...
The shaded region in the diagram is a segment of a circle with centre O and radius r cm. Angle AOB = π/3 radians.
Differentiate, with respect to x,