Cambridge & Pearson Edexcel Past Paper Questions

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.

The polynomial p(x) = ax³-9x²+bx-6, where a and b are constants, has a factor of x-2. The polynomial has a remainder of 66 when divided by x-3.

The first 3 terms in the expansion of (a+x)²(1-x/3)⁵, in ascending powers of x, can be written in the form 27+ bx + cx², where a, b and c are integ...

The functions f and g are defined as follows. f(x) = x² + 4x for x ∈ R g(x) = 1+e²x for x∈R

(a) (i) Find how many different 5-digit numbers can be formed using the digits 1, 3, 5, 6, 8 and 9. No digit may be used more than once in any 5-di...

(a) In this question, all lengths are in metres and time, t, is in seconds. [Figure 7.1] The diagram shows the displacement-time graph for a runner...

DO NOT USE A CALCULATOR IN THIS QUESTION. A curve has equation y = (2-√3)x²+x-1. The x-coordinate of a point A on the curve is (√3+1)/(2-√3)

(a) (i) Write 6xy+3y+4x+2 in the form (ax+b)(cy+d), where a, b, c and d are positive integers. (ii) Hence solve the equation 6 sin θ cos θ+3 cos θ+...

In this question all lengths are in centimetres. [Figure 10.1] The diagram shows a shaded shape. The arc AB is the major arc of a circle, centre O,...

Write (pqr)-23 / (p2r) q³ in the form paqor, where a, b and c are constants.

On the axes, sketch the graph of y = |4-3x|, stating the intercepts with the coordinate axes.

The diagram shows the quadrilateral OABC such that OA = a, OB = b and OC = c. The lines OB and AC intersect at the point P, such that AP : PC = 3:2...

A curve is such that d²y/dx² = (3x+2)^(-1/3). The curve has gradient 4 at the point (2, 6.2). Find the equation of the curve.

Given that logₐp + logₐ5 - logₐ4 = logₐ20, find the value of p.

DO NOT USE A CALCULATOR IN THIS QUESTION. A curve has equation y = (3+√5)x²-8√5x+60.

A six-character password is to be made from the following eight characters. Digits: 1, 3, 5, 8, 9 Symbols: *, $, # No character may be used more th...

Variables x and y are such that y = Ax^b, where A and b are constants. When lgy is plotted against lgx, a straight line graph passing through the p...

The first three terms of an arithmetic progression are –4, 8, 20. Find the smallest number of terms for which the sum of this arithmetic progressio...

Solve the equation sinα cosec²α + cosα sec²α = 0 for -π < α < π, where α is in radians.

The normal to the curve y = ln(x²+2)/(2x-3) at the point where x = 2 meets the y-axis at the point P. Find the coordinates of P.

Write the expression x²-6x+1 in the form (x+a)² + b, where a and b are constants.

Variables x and y are such that, when lny is plotted against lnx, a straight line graph passing through the points (6, 5) and (8, 9) is obtained. S...

Solve the inequality |4x-1|> 9.

The graph of y=a+2tanbx, where a and b are constants, passes through the point (0, -4) and has period 480°.

The curves y = x² and y² = 27x intersect at O(0, 0) and at the point A. Find the equation of the perpendicular bisector of the line OA.

Variables x and y are such that y = e2 + x cos 2x, where x is in radians. Use differentiation to find the approximate change in y as x increases fr...

Find the exact values of the constant k for which the line y=2x+1 is a tangent to the curve y = 4x² +kx+k-2.

In this question, a, b, c and d are positive constants.

A curve is such that d²y/dx² = sin(6x-π/2). Given that dy/dx = 1/2 at the point (π/4, 13π/12) on the curve, find the equation of the curve.

Relative to an origin O, the position vectors of the points A, B, C and D are OA = (6, -3), OB = (10, 3), OC = (x, y) and OD = (12, 7)

The 2nd, 8th and 44th terms of an arithmetic progression form the first three terms of a geometric progression. In the arithmetic progression, the ...

The diagram shows part of the curve y = (9-x)(x-3) and the line y = k−3, where k > 3. The line through the maximum point of the curve, parallel to ...

Using the binomial theorem, expand (1+e2x)4, simplifying each term.

On the axes, sketch the graph of y = 3 (x-3)(x-1)(x+2) stating the intercepts with the coordinate axes.

Find the values of the constant k for which (2k-1)x² +6x+k+1 = 0 has real roots.