9709 AS & A Level Mathematics: past papers

Resultant of four coplanar forces, then a coefficient of friction for a ring on a wire.

Three coplanar forces in equilibrium: an unknown angle and force.

Four coplanar forces in equilibrium: find an angle and a force.

Magnitude and direction of the resultant of coplanar forces.

Mass of a particle and tension in a string held in equilibrium by a perpendicular force.

Three coplanar forces in equilibrium: an unknown angle and force.

Two suspended particles joined by a string: tensions and an angle.

Four coplanar forces in equilibrium: find an angle and a force.

Smooth ring on a string pulled sideways: tension and mass.

Coplanar forces in equilibrium: show an equation and find a force and an angle.

Particle held by two strings: a tension and an angle.

Resultant of four coplanar forces, then a coefficient of friction for a ring on a wire.

Particles connected over pulleys: tensions, friction and the distance moved after a string breaks.

Block pushed on a rough slope: time of motion and limiting friction.

Particles over a pulley with friction on a slope: tension, acceleration and further distance.

Range of a force keeping a particle in equilibrium on a rough slope.

Coefficient of friction, then the distance covered in one particular second.

Least horizontal force keeping a particle on a rough slope.

Particles over a pulley with rough then smooth sections: acceleration, speed and time.

Limiting friction on a slope, then motion up the slope under a force.

Limiting equilibrium of a block on a rough slope pulled by a string.

Work–energy for a block pulled down a rough slope by an angled force.

Energy methods for motion up and back down a rough inclined plane.

Range of a force keeping a particle in equilibrium on a rough slope.

Least horizontal force keeping a particle on a rough slope.

Limiting equilibrium of a block on a rough slope pulled by a string.

Distance and acceleration from a displacement–time graph.

Sketch a velocity–time graph and use constant acceleration to find a time from a total distance.

Motion in stages with constant acceleration and deceleration.

Coefficient of friction, then the distance covered in one particular second.

Two particles with constant acceleration on parallel tracks, and displacement–time sketches.

Two particles moving vertically meet and coalesce: meeting height and speed at the ground.

Two particles moving vertically, their speeds before colliding, and a speed at the ground.

Vertical motion, an impulse in a collision, and the time between two landings.

Particles over a pulley: tension, acceleration and greatest height after one lands.

Distance and acceleration from a displacement–time graph.

Sketch a velocity–time graph and use constant acceleration to find a time from a total distance.

Velocity–time graph: find the top speed and the total time from the distance.

Two particles with constant acceleration on parallel tracks, and displacement–time sketches.

Velocity–time relations: a sudden change in acceleration and total distance.

Distance travelled under variable acceleration until it becomes zero.

Maximum velocity from a velocity function, then the displacement at that time.

Velocity as a function of time: unknown constants and distance over an interval.

Piecewise acceleration: velocity, a velocity expression and distance travelled.

Velocity as a function of time: sign of acceleration and when displacement is zero.

Velocity given by a cubic: when acceleration is zero, and total distance.

Velocity as a function of time: constants, acceleration, rest and return speed.

Variable acceleration: constants, velocity, distance and stopping time.

Velocity–time relations: a sudden change in acceleration and total distance.

Collisions on a smooth plane, including particles that coalesce.

Two particles moving vertically, their speeds before colliding, and a speed at the ground.

Vertical motion, an impulse in a collision, and the time between two landings.

Collision on a smooth table: unknown speed and kinetic energy lost.

Speeds after a collision and the kinetic energy lost.

Two particles moving vertically meet and coalesce: meeting height and speed at the ground.

Kinetic energy lost when two particles collide and coalesce.

Particles that collide and coalesce: momentum, energy lost and timing.

Collision on a smooth table: unknown speed and kinetic energy lost.

Speeds after a collision and the kinetic energy lost.

Collisions on a smooth plane, including particles that coalesce.

Particles that collide and coalesce: momentum, energy lost and timing.

Successive collisions: find a mass, then the time to a further collision.

Engine power from Newton’s second law, then distance using work done.

Newton's second law for a locomotive and coach on a slope: acceleration and tension.

Block pushed on a rough slope: time of motion and limiting friction.

Power of a car uphill and on the level, with resistance proportional to v².

Limiting friction on a slope, then motion up the slope under a force.

Connected blocks on a slope with resistance: acceleration, tension and time.

Newton's second law for a locomotive and coach on a slope: acceleration and tension.

Particles connected over pulleys: tensions, friction and the distance moved after a string breaks.

Particles connected over a smooth pulley: tension, acceleration and starting height.

Particles over a pulley with friction on a slope: tension, acceleration and further distance.

Particles connected over a pulley on a rough slope: acceleration, then speed by energy.

Towed vehicles: acceleration and tension, then a slope angle at constant power.

Particles over a pulley with rough then smooth sections: acceleration, speed and time.

Connected blocks on a slope with resistance: acceleration, tension and time.

Particles over a pulley: tension, acceleration and greatest height after one lands.

Constant speed from distance and time, then work done by an angled force and power.

Power and resistance for an aeroplane at constant speed, and average power.

Work done by a cyclist against resistance while speeding up.

Speed of a block pulled up a rough slope at an angle, by energy.

Work done against air resistance by a falling particle.

Acceleration on a road, average power by energy, and steady speed at that power.

Work–energy for a block pulled down a rough slope by an angled force.

Energy methods for motion up and back down a rough inclined plane.

Work–energy principle for a block sliding down a rough slope.

Work done by a cyclist against resistance while speeding up.

Particles connected over a pulley on a rough slope: acceleration, then speed by energy.

Work–energy: resistive work on a block sliding down a slope.

Speed of a block pulled up a rough slope at an angle, by energy.

Work done against air resistance by a falling particle.

An athlete’s power on the level, then an energy method on a slope.

Work and energy for a cyclist against resistance to find the mass.

Work, energy and power for a car on a hill, then steady speed on the level.

Acceleration on a road, average power by energy, and steady speed at that power.

Constant speed from distance and time, then work done by an angled force and power.

Power and resistance for an aeroplane at constant speed, and average power.

Power, resistance and acceleration of a cyclist, then steady speed uphill.

Power of a car uphill and on the level, with resistance proportional to v².

Towed vehicles: acceleration and tension, then a slope angle at constant power.

An athlete’s power on the level, then an energy method on a slope.

Engine power from Newton’s second law, then distance using work done.

Work, energy and power for a car on a hill, then steady speed on the level.