Cambridge Past Paper Questions
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Let f(x) = (8x² + 9x + 8) / ((1-x)(2x + 3)²).
It is given that ∫(1 to a) x² ln x dx = 2, where a > 1.
Two planes p and q have equations x + y + 3z = 8 and 2x – 2y + z = 3 respectively.
Let f(x) = (4x² + 9x - 8) / ((x + 2)(2x−1)).
The diagram shows the curve y = (1 + x²)e⁻½ˣ for x ≥ 0. The shaded region R is enclosed by the curve, the x-axis and the lines x = 0 and x = 2. [Fi...
A block of mass 3 kg is initially at rest on a smooth horizontal floor. A force of 12 N, acting at an angle of 25° above the horizontal, is applied...
A tractor of mass 3700 kg is travelling along a straight horizontal road at a constant speed of 12 m s⁻¹. The total resistance to motion is 1150 N.
A roller-coaster car (including passengers) has a mass of 840 kg. The roller-coaster ride includes a section where the car climbs a straight ramp o...
The diagram shows the velocity-time graph of a particle which moves in a straight line. The graph consists of 5 straight line segments. The particl...
A particle starts from a point O and moves in a straight line. The velocity of the particle at time t s after leaving O is v m s⁻¹, where v = 1.5 +...
Coplanar forces, of magnitudes F N, 3F N, G N and 50 N, act at a point P, as shown in the diagram. [Figure 6.1]
Two particles A and B of masses 0.9 kg and 0.4 kg respectively are attached to the ends of a light inextensible string. The string passes over a fi...
A particle of mass 0.2 kg is resting in equilibrium on a rough plane inclined at 20° to the horizontal.
A block of mass 15 kg hangs in equilibrium below a horizontal ceiling attached to two strings as shown in the diagram. One of the strings is inclin...
A car travels along a straight road with constant acceleration. It passes through points A, B and C. The car passes point A with velocity 14 m s⁻¹....
A particle P is projected vertically upwards from horizontal ground with speed 12 m s⁻¹.
A cyclist is riding up a straight hill inclined at an angle α to the horizontal, where sin α = 0.04. The total mass of the bicycle and rider is 80 ...
Two particles P and Q, each of mass m kg, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley whi...
A particle starts from rest and moves in a straight line. The velocity of the particle at time t s after the start is v m s⁻¹, where v = −0.01t³ + ...
Three coplanar forces of magnitudes FN, 20 N and 30 N act at a point P, as shown in the diagram. The resultant of the three forces acts in a direct...
A lorry of mass 7850 kg travels on a straight hill which is inclined at an angle of 3° to the horizontal. There is a constant resistance to motion ...
A particle is released from rest and slides down a line of greatest slope of a rough plane which is inclined at 25° to the horizontal. The coeffici...
Two particles A and B have masses 0.35 kg and 0.45 kg respectively. The particles are attached to the ends of a light inextensible string which pas...
A particle starts from a fixed origin with velocity 0.4 m s⁻¹ and moves in a straight line. The acceleration a m s⁻² of the particle t s after it l...
The diagram shows the velocity-time graphs for two particles, P and Q, which are moving in the same straight line. The graph for P consists of four...
A particle P of mass 0.2 kg rests on a rough plane inclined at 30° to the horizontal. The coefficient of friction between the particle and the plan...
A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4kg is in contact with the inner surface of the cylinder. The...
A small ball is projected from a point 1.5 m above horizontal ground. At a point 9 m above the ground the ball is travelling at 45° above the horiz...
One end of a light inextensible string of length 0.4 m is attached to a fixed point A which is above a smooth horizontal surface. A particle P of m...
A particle P is projected with speed 25 m s⁻¹ at an angle of 30° above the horizontal from a point O on horizontal ground. At time t s after projec...
One end of a light elastic string of natural length 0.8 m and modulus of elasticity 24 N is attached to a fixed point O. The other end of the strin...
A solid object consists of a uniform hemisphere of radius 0.4m attached to a uniform cylinder of radius 0.4 m so that the circumferences of their c...
A particle P of mass 0.2 kg is released from rest at a point O on a rough plane inclined at 60° to the horizontal, and travels down a line of great...
A particle P of mass 0.2kg is released from rest at a point O on a smooth horizontal surface. A horizontal force of magnitude te⁻ᵛ N directed away ...
A uniform solid cone has height 0.6 m and base radius 0.2 m. A uniform hollow cylinder, open at both ends, has the same dimensions. An object is ma...
A particle P of mass 0.4 kg is released from rest at a point O on a smooth plane inclined at 30° to the horizontal. P moves down the line of greate...
A light elastic string has natural length 2 m and modulus of elasticity 39 N. The ends of the string are attached to fixed points A and B which are...
OAB is a uniform lamina in the shape of a quadrant of a circle with centre O and radius 0.8 m which has its centre of mass at G. The lamina is smoo...
One end of a light elastic string of natural length 0.4 m and modulus of elasticity 8 N is attached to a fixed point O on a smooth horizontal plane...
A small ball B is projected from a point O which is h m above a horizontal plane. At time 2s after projection B has speed 18 m s⁻¹ and is moving in...
A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4 kg is in contact with the inner surface of the cylinder. Th...
A solid object consists of a uniform hemisphere of radius 0.4 m attached to a uniform cylinder of radius 0.4 m so that the circumferences of their ...
The discrete random variable X has the following probability distribution. x | 1 | 2 | 3 | 6 P(X = x) | 0.15 | p | 0.4 | q Given that E(X) = 3.05, ...
The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summa...
An experiment consists of throwing a biased die 30 times and noting the number of 4s obtained. This experiment was repeated many times and the aver...
The ages of a group of 12 people at an Art class have mean 48.7 years and standard deviation 7.65 years. The ages of a group of 7 people at another...
Over a period of time Julian finds that on long-distance flights he flies economy class on 82% of flights. On the rest of the flights he flies firs...
The weight, in grams, of pineapples is denoted by the random variable X which has a normal distribution with mean 500 and standard deviation 91.5. ...
Andy counts the number of emails, x, he receives each day and notes that, over a period of n days, Σ(x – 10) = 27 and the mean number of emails is ...