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.
Solve `6 sin²x - 13 cosx = 1` for `0° ≤ x ≤ 360°`.
Find the unit vector in the direction of `5i – 15j`.
The velocity, v ms⁻¹, of a particle travelling in a straight line, t seconds after passing through a fixed point O, is given by v = 4/(t+1)³.
(a) The functions f and g are defined by `f(x) = 5x-2` for `x > 1`, `g(x) = 4x²-9` for `x > 0`. (b) The function h is defined by `h(x) = √(x²-1)` f...
The diagram shows the graph of a cubic curve y = f(x). [Figure X.X]
Write down the period of 2 cos x/3 - 1.
The radius, r cm, of a circle is increasing at the rate of 5 cms⁻¹. Find, in terms of π, the rate at which the area of the circle is increasing whe...
DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4√7)x²+(4-2√7)x-1 = 0, giving your answer in the form a+b√7...
Find the equation of the tangent to the curve y = ln(3x²-1) / (x+2) at the point where x = 1. Give your answer in the form y = mx+c, where m and c ...
The line y = 5x+6 meets the curve xy = 8 at the points A and B.
The diagram shows an isosceles triangle OAB such that OA = OB and angle AOB = θ radians. The points C and D lie on OA and OB respectively. CD is an...
Show that 3/(2x-3) + 3/(2x+3) can be written as 12x / (4x²-9).
An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.
Show that 1/(sec θ - 1) - 1/(sec θ + 1) = 2 cot² θ.
A curve is such that d²y/dx² = 5 cos 2x. This curve has a gradient of 3/4 at the point (-π/12, 5π/4). Find the equation of this curve.
On the axes below, sketch the graph of y=|(x-2)(x+1)(x+2)| showing the coordinates of the points where the curve meets the axes.
The volume, V, of a sphere of radius r is given by V = 4/3 πr². The radius, r cm, of a sphere is increasing at the rate of 0.5 cms⁻¹. Find, in term...
Find the first 3 terms in the expansion of (4-x/16)⁶ in ascending powers of x. Give each term in its simplest form.
Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.
f: x → (2x+3)² for x > 0 Find the range of f.
The diagram shows the straight line 2x+y=-5 and part of the curve xy+3 = 0. The straight line intersects the x-axis at the point A and intersects t...
Given that y = (x²-1)√5x+2, show that dy/dx = (Ax²+Bx+C) / (2√5x+2) where A, B and C are integers.
The diagram shows a triangle OAB such that OA = a and OB = b. The point P lies on OA such that OP = 3/4 OA. The point Q is the mid-point of AB. The...
A particle P moves in a straight line such that its displacement, xm, from a fixed point O at time ts is given by x = 10 sin2t-5. Find the speed of...
Solve tan 3x = -1 for -π/2 ≤ x ≤ π/2 radians, giving your answers in terms of π.
Variables x and y are such that, when √y is plotted against 1/x, a straight line graph passing through the points (0.5, 9) and (3, 34) is obtained....
Write 9x²-12x+5 in the form p(x-q)² +r, where p, q and r are constants.
DO NOT USE A CALCULATOR IN THIS QUESTION. p(x) = 15x³ +22x² - 15x+2
In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. F...
The vectors a and b are such that a = αi+j and b = 12i+βj.
Find the values of k for which the line y = kx-7 and the curve y = 3x² +8x+5 do not intersect.
Solve the simultaneous equations 10^(x+2y) = 5, 10^(3x+4y) = 50, giving x and y in exact simplified form.
Expand (2-x)⁵, simplifying each coefficient.
A particle travels in a straight line. As it passes through a fixed point O, the particle is travelling at a velocity of 3 ms⁻¹. The particle conti...
The diagram shows part of the graphs of y = 4x^(1/2) and y = (x-3)². The graph of y = (x-3)² meets the x-axis at the point A(a, 0) and the two grap...
The function f is defined by f(x) = ln(2x+1) for x ≥ 0.
Find the x-coordinates of the stationary points of the curve y = e^(3x)(2x+3)⁶.
Variables x and y are such that y = sinx+e^*. Use differentiation to find the approximate change in y as x increases from π/4 to π/4+h, where h is ...
DO NOT USE A CALCULATOR IN THIS QUESTION. The point (1 - √5, p) lies on the curve y = (10+2√5) / x². Find the exact value of p, simplifying your an...
Find the values of k for which the line y=x-3 intersects the curve y = k²x² +5kx+1 at two distinct points.
The three roots of p(x) = 0, where p(x) = 2x³ + ax² + bx + c are x = 1/2, x = n and x = −n, where a, b, c and n are integers. The y-intercept of th...
Solutions to this question by accurate drawing will not be accepted. The points A and B are (4, 3) and (12, −7) respectively.
Find the equation of the tangent to the curve 2y = tan2x+7 at the point where x = π/8. Give your answer in the form ax-y = π/b+c, where a, b and c ...
Giving your answer in its simplest form, find the exact value of
Solve 3 cot²x-14 cosecx-2 = 0 for 0° < x < 360°.
Solve the equation 9^(5x) / 27^(x-2) = 243.
10 (a) The first 5 terms of a sequence are given below. 4 -2 1 -0.5 0.25
The circles with centres C₁ and C₂ have equal radii of length r cm. The line C₁C₂ is a radius of both circles. The two circles intersect at A and B...
(a) On the axes, sketch the graph of y = 5(x+1)(3x-2)(x-2), stating the intercepts with the coordinate axes. [Figure 1.1] (b) Hence find the values...
Find ∫₃⁵(1/(x-1)-1/((x-1)²)) dx, giving your answer in the form a+lnb, where a and b are rational numbers.