Cambridge & Pearson Edexcel Past Paper Questions

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.

Let f(x) = (3a-5x) / ((3a+2x)(2a-x)), where a is a positive constant.

Prove the identity cot²θ - tan²θ ≡ 4 cot 2θ cosec 2θ.

With respect to the origin O, the points A, B and C have position vectors given by OA = i+2j, OB = i+3j-2k and OC = 2i-j+3k. The line l passes thro...

The variables x and y satisfy the differential equation sin 4y dy/dx = x sin 2y sin 3x. It is given that y = π/6 when x = π/2.

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

A block of mass 12kg is being pulled by a rope up a rough plane. The plane is inclined at an angle of 20° above the horizontal. The rope pulling th...

Three coplanar forces of magnitudes PN, 5N and 10N act at a point O, as shown in the diagram. The resultant of the three forces has magnitude QN an...

The diagram shows the velocity-time graph of the motion of a cyclist. The graph consists of three straight line segments. The cyclist passes a poin...

A lorry of mass 18000 kg is travelling along a straight road.

When a particle P of mass mkg has speed ums⁻¹, its momentum is 4Ns and its kinetic energy is 16J.

Two particles, P and Q, of masses 0.3 kg and 0.6kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...

A particle X moves along a straight track, starting from a point O at time t = 0. The displacement of X from O at time ts is sm, where s = 3t³/² - 6t.

A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25 N inclined at 20° above the horizontal. The crate ...

Two particles P and Q, of masses 0.2kg and 0.1kg respectively, are free to move in a straight line on a smooth horizontal plane. P is projected tow...

A particle P of mass mkg is attached to one end of a light inextensible string of length 2.6 m. The other end of the string is attached to a fixed ...

A car is travelling along a straight horizontal road. The car passes through a point A, on the road travelling at a speed of 15ms⁻¹, and then accel...

One end of a light inextensible string is attached to a particle A of mass 3 kg. The other end of the string is attached to a particle B of mass 4k...

A particle P moves in a straight line and passes through the point A at time t = 0. The velocity vms⁻¹ of P at time t seconds is given by v = (2t+1...

A particle P of mass 3 kg is projected with a speed of 8 ms⁻¹ up a line of greatest slope of a rough plane inclined at 30° to the horizontal. P is ...

Two particles P and Q, of masses 0.1kg and 0.3kg respectively, are at rest on a smooth horizontal plane. P is projected directly towards Q with spe...

A van of mass 4500kg is towing a trailer of mass 350kg along a straight horizontal road. The van and trailer are connected by a light rigid tow-bar...

The diagram shows a velocity-time graph which models the motion of a particle. The graph consists of 3 straight line segments. The velocity of the ...

Three blocks P, Q and R, of masses 25kg, 20kg and mkg respectively, are held in equilibrium by three light inextensible strings OP, OQ and OR. The ...

A van of mass 2500kg travelling at speed vms⁻¹ experiences a resistance force of kv² N. The constant power of the van's engine is 62.5 kW.

The diagram shows the vertical cross-section ABC of a rough waterslide. The section AB is a straight line of length 5m inclined at an angle of θ to...

A particle X moves in a straight line. The displacement of X from O at time ts after leaving O is sm, where s = 0.3t² +0.6t for 0≤t≤4.

The masses of the bags of rice made by a company are normally distributed with mean μkg and standard deviation 0.14kg. The probability that the mas...

Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.