Cambridge & Pearson Edexcel Past Paper Questions

The diagram shows the curve with equation y = 9/(5x+4)^1/2 and the line y = 6-3x. The line and the curve intersect at the point P which has y-coord...

Prove the identity tanθ+7 / tan²θ−3 = sinθcosθ+7cos²θ / 1−4cos²θ

The diagram shows the circle with equation x²+y² – 14x+8y+36 = 0 and the line y=-2. The line intersects the circle at the points A and B. The centr...

The equation of a curve is such that d²y/dx² = 24/x³ . It is given that the curve has a stationary point at (-2, 19).

The first, second and third terms of an arithmetic progression are 4k, k² and 8k respectively, where k is a non-zero constant.

Express x² +4x+2 in the form (x+a)² + b, where a and b are integers.

Given that y = 6x cos(x²+1), find an expression for dy/dx.

Use logarithms to solve the inequality 4^x < 0.05. Give your answer in the form x < a, where the value of a is correct to 3 significant figures.

Sketch, on a single diagram, the graphs of y = 3e^-2x and y = secx for values of x such that 0 < x < π/2.

The diagram shows the curve with equation y = 6e^2x – e^3x. The shaded region is bounded by the axes and the curve.

The polynomial p(x) is defined by p(x) = ax³ + bx² - ax-24, where a and b are constants. It is given that (2x-3) is a factor of p(x) and that the r...

The parametric equations of a curve are x = (2t+1)/(3t+4), y = 2ln(3t+4), where t > -4/3.

Prove that sin² 2x+4 cos²x cos2x=4cos⁴x.

Show that ∫ from 2 to 11 (8 / (4x+1)) dx = ln a, where a is an integer to be found.

Sketch on the same diagram the graphs of y = |2x-9| and y=4x-5.

Find the coordinates of the stationary points of the curve with equation y = 8x / (2x+3) - 6x+5.

The diagram shows parts of the curves with equations y = 4e⁻²ˣ and y = 1+0.5 sin3x. Point P is a point of intersection of the curves, and the shade...

The polynomial p(x) is defined by p(x) = ax⁴ + bx³ +13x²-35x+15, where a and b are constants. It is given that (2x−1) and (x-3) are factors of p(x).

A curve has equation (x²-3)lny+6x = 14.

Express 4 cosθsin(θ+30°) in the form Rcos (2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.

Show that ∫₂¹¹ (8 / (4x+1)) dx = ln a, where a is an integer to be found.

Find the coordinates of the stationary points of the curve with equation y = 8x/(2x+3) - 6x + 5.

Express 4 cosθsin(θ+30°) in the form Rcos(2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.

Sketch the graph of y = |2x-3|.

It is given that 2 lnp+ln(p-1)-½ln(q+1) = 3. Find q in terms of p.

Find the complex numbers z for which z+5i / z-5 is real and |z|= √17. Give your answers in the form z = x+iy, where x and y are real.

The parametric equations of a curve are x = etant, y = 3 tan²t. Find the equation of the tangent to the curve at the point (e, 3). Give your answer...

The polynomial 3x³ +pax²+7a²x+qa³ is denoted by f(x), where p, q and a are constants and a ≠ 0. When f(x) is divided by (x+2a) the remainder is -22...

It is given that z₁ = 3e^(i π/4), z₂ = (1/2)e^(i π/2) and w = 2e^(-i π/2).

Express 5 sin(x+π/6)-4 cosx in the form Rsin(x-α), where R > 0 and 0 < α < π/2. State the exact value of R and give the value of α correct to 3 dec...

With respect to the origin O, the points A and B have position vectors 2i+4k and 5i+j+6k respectively. The line l₁ passes through the points A and B.

The constant a is such that ∫(from 2 to a) 6x ln x dx = 4.

Find the quotient and remainder when x³ + 5x² – 2x – 15 is divided by x² -3.

The diagram shows the curve y = cos x √sin 2x for 0 ≤ x ≤ π/2. The curve has a maximum point at M, where x = a. [Figure 11.1]

Solve the equation ex+2e-xex-3 = 4. Give your answer correct to 3 decimal places.

Expand (6-x)(1-2x)¯½ in ascending powers of x, up to and including the term in x², simplifying the coefficients.

Solve the equation 3 cotx-4 cot2x = 3 for 0° ≤ x ≤ 180°.

The square roots of -1-4√5 i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in ...

By sketching a suitable pair of graphs, show that the equation |x-2|= 2sinx has only one root in the interval 0 < x < π.

Express 7 sinθ+24 cosθ in the form Rcos(θ-α), where R > 0 and 0 < α < ½π. Give the value of α correct to 4 decimal places.

The variables x and θ satisfy the differential equation dx/dθ sin 2θ = (4x+3) cos 2θ, and x = 0 when θ = ¹⁄₁₂π. Solve the differential equation and...

With respect to the origin O, the points A, B and C have position vectors given by OA = [1, -4, 2] OB = [-2, 1, 3] OC = [2, 3, 5] (a) Find a vecto...

Find the quotient and remainder when x² is divided by 1 + 4x².

The diagram shows the graph of y = 5 sin 2x cos²x for 0 < x ≤ ½π and its maximum point M. [Figure X.X] (a) Find the exact x-coordinate of M. (b) By...

Sketch the graph of y = |3x-2a|, where a is a positive constant.

Solve the equation 2 ln (2x+3) - ln(2x + 5) = ln(3x).

Find the exact value of ∫(from -π/4 to π/4) 3 cos² 5x dx.

It is given that z₁ = r₁e^(iθ₁) and z₂ = r₂e^(iθ₂). Show that (z₁z₂)* = z₁*z₂*.

The equation of a curve is xy+y²e^x = 4.

Find the complex numbers z for which (z+4)/(z+4i) is real and |z|= √10. Give your answers in the form z = x+iy, where x and y are real.