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.
The diagram shows the curve y = 4 + 3x - x² intersecting the positive x-axis at the point A. The line y = mx + 8 is a tangent to the curve at the p...
Solve 1 + √2 sin(x+50°) = 0 for -180° ≤ x ≤ 180°.
Find the equation of the curve which has a gradient of 4 at the point (0, -3) and is such that d²y/dx² = 5 + e^(2x).
On the axes below, sketch the graph of y = |6-3x|, showing the coordinates of the points where the graph meets the coordinate axes.
y = x³ ln(2x+1) Find the value of dy/dx when x = 0.3. You must show all your working.
The 7th term in the expansion of (a+bx)¹² in ascending powers of x is 924x⁶. It is given that a and b are positive constants.
Find d/dx (5x²-125)³.
The vector v has a magnitude of 39 units and is in the same direction as (-12 / 5). Write v in the form (a / b) where a and b are constants.
A = ( (a 3) / (4 a+4) ) Find the values of the constant a for which A⁻¹ does not exist.
The polynomial p(x) = ax³ + bx² + cx - 9 is divisible by x + 3. It is given that p'(0) = 36 and p''(0) = 86.
The diagram shows part of the curve y = a+4cosbx, where a and b are positive constants. The curve meets the y-axis at the point (0,6) and the x-axi...
The diagram shows the sector OPQ of a circle, centre O, radius r cm, where angle POQ = θ radians. The perimeter of the sector is 10cm. [Figure X.X]
The line y = 2x+5 intersects the curve y+xy = 5 at the points A and B. Find the coordinates of the point where the perpendicular bisector of the li...
Solve the inequality (x-3)(x+4) > x+13.
E [Figure: Venn Diagram with F and C circles, overlapping] There are 105 boys in a year group at a school. Some boys play football (F) and some pla...
A curve has equation y = x³ / sin 2x . Find
Solve 2^(3x-1) = 6,
Solve the simultaneous equations 8^(p+1)/4^q = 2^11, 3^(2p+5)/27^q = 9^(3q)
A 5-character code is to be formed from the 13 characters shown below. Each character may be used once only in any code. Letters: A, B, C, D, E, F ...
Solve the quadratic equation (1-√3)x² + x + (1+√3) = 0, giving your answer in the form a+b√3, where a and b are constants.
Show that 1/(1-sinx) - 1/(1+sinx) = 2tanxsecx.
y [Figure: Graph showing y = 2√x curve from O, a tangent/normal line AB. Point A(4,4) is on the curve. Point B is on the x-axis.] The diagram shows...
Two lines are tangents to the curve y = 12-4x-x². The equation of each tangent is of the form y = 2k+1-kx, where k is a constant.
The functions f and g are defined for real values of x ≥ 1 by f(x) = 4x-3, g(x) = (2x+1)/(3x-1).
A plane that can travel at 260km/h in still air heads due North. A wind with speed 40 km/h from a bearing of 310° blows the plane off course. Find ...
(i) On the axes below, sketch the graph of y = 2cos3x-1 for -90° ≤x≤ 90°. [Figure 1.1]
When lgy² is plotted against x, a straight line is obtained passing through the points (5, 12) and (3, 20). Find y in terms of x, giving your answe...
The first three terms in the expansion of (1-x/7)^14 (1-2x)^4 can be written as 1 + ax+bx². Find the value of each of the constants a and b.
(i) On the axes below, sketch the graph of y = |2x²-9x-5| showing the coordinates of the points where the graph meets the axes. [Figure 4.1]
(a) It is given that f : x ↦ √x for x ≥ 0, g : x ↦ x + 5 for x ≥ 0. Identify each of the following functions with one of f⁻¹, g⁻¹, fg, gf, f², g². ...
(a) Write √(p(qp²/r)²) / (p⁻¹(³√qr)) in the form p^a q^b r^c, where a, b and c are constants. (b) Solve log₇x + 2logₓ7 = 3.
It is given that y = (1+e^(x²))(x+5).
(a) Five teams took part in a competition in which each team played each of the other 4 teams. The following table represents the results after all...
A solid circular cylinder has a base radius of r cm and a height of h cm. The cylinder has a volume of 1200π cm³ and a total surface area of S cm².
The diagram shows a circle centre O, radius 10cm. The points A, B and C lie on the circumference of the circle such that AB = BC = 18 cm. [Figure 1...
A curve is such that d²y/dx² = 2(3x-1)^(-3/2). Given that the curve has a gradient of 6 at the point (3, 11), find the equation of the curve.
On each of the Venn diagrams below, shade the region indicated.
Given that y = 2 sin 3x + cos 3x, show that d²y/dx² + dy/dx + 3y = k sin 3x, where k is a constant to be determined.
A 5-digit code is formed using the following characters. Letters a c e i o u Numbers 1 2 3 4 5 6 Symbols @ * # No character can be repeated in a co...
Find the values of k for which the line y = kx+3 does not meet the curve y = x²+5x+12.
At the point where x = 1 on the curve y = k/(x+1)², the normal has a gradient of 1/3.
Show that tan x / (1 + sec x) + (1 + sec x) / tan x = 2 / sin x
The cubic equation x³ +ax²+bx-40 = 0 has three positive integer roots. Two of the roots are 2 and 4. Find the other root and the value of each of t...
A particle A travels with a speed of 6.5 ms⁻¹ in the direction -5i – 12j. Find the velocity, vA, of A.
The diagram shows the points A (−3, 5) and B (5, −1). The mid-point of AB is M and the line PM is perpendicular to AB. The point P has coordinates ...
Given that y = ln x / x², find dy/dx.
Do not use a calculator in this question. Solve the quadratic equation (√5-3)x² + 3x + (√5 +3) = 0, giving your answers in the form a+b√5, where a ...
The curve y = 2x²+k+4 intersects the straight line y = (k+4)x at two distinct points. Find the possible values of k.
[Figure 2.1] The diagram shows the graph of y = f(x), where f(x) is a cubic polynomial.
Write down the amplitude of 2 cos x/3 - 1.