9709 AS & A Level Mathematics: past papers

Complete the square, the condition for no real roots, and an exact solution.

Complete the square, then find an inverse and a composite function.

Complete the square to find a vertex, then the area between a parabola and a line.

Minimum point of a quadratic, then its image after a stretch and a translation.

Complete the square, then use the discriminant for a quadratic with no real roots.

Complete the square, solve with it, and sketch the turning point.

Complete the square, the condition for no real roots, and an exact solution.

Solve an equation that is quadratic in a power of x.

Complete the square, solve with it, and sketch the turning point.

Complete the square, the condition for no real roots, and an exact solution.

Condition for a line and a curve not to meet.

Where a curve meets a line, and the condition for them not to meet.

Complete the square, then use the discriminant for a quadratic with no real roots.

Range of a constant for no real roots, and a quadratic in cos θ.

Where a parabola meets a line, and the condition for a tangent.

Trigonometric equation as a quadratic, and the discriminant to show no solutions.

Find where a curve and a straight line meet.

Condition for a line and a curve not to meet.

Where a curve meets a line, and the condition for them not to meet.

Where two curves meet, then the area of the region between them.

Where a parabola meets a line, and the condition for a tangent.

Composite functions, transformations of a curve and constants from a range.

Composite functions, range, whether an inverse exists, and a composite equation.

Inverse function, its domain and range, and a composite function equation.

Show a function is increasing, decide if its inverse exists, and a composite function.

Complete the square, then find an inverse and a composite function.

Composite functions, transformations of a curve and constants from a range.

Sketch a transformed graph, find an inverse and solve a composite function equation.

Composite functions, range, whether an inverse exists, and a composite equation.

Inverse function, its domain and range, and a composite function equation.

Composite and inverse functions with an unknown constant and domain restrictions.

Inverse and composite functions, when no inverse exists, and a tangent triangle area.

Show a function is increasing, decide if its inverse exists, and a composite function.

Complete the square, then find an inverse and a composite function.

Sketch a transformed graph, find an inverse and solve a composite function equation.

Composite functions, range, whether an inverse exists, and a composite equation.

Inverse function, its domain and range, and a composite function equation.

Inverse function: find it, sketch it and describe transformations of a sine graph.

Composite and inverse functions with an unknown constant and domain restrictions.

Inverse and composite functions, when no inverse exists, and a tangent triangle area.

Inverse function: find it, sketch it and describe transformations of a sine graph.

Describe combined transformations and write the equation after a stretch and reflection.

Describe two transformations, in order, that map one graph onto another.

Composite functions, transformations of a curve and constants from a range.

Sketch a transformed graph, find an inverse and solve a composite function equation.

Describe a sequence of graph transformations in the right order.

Minimum point of a quadratic, then its image after a stretch and a translation.

Inverse function: find it, sketch it and describe transformations of a sine graph.

Sketch a stretched and translated graph and write its equation.

Rates of change on a curve, then the perpendicular bisector of a chord.

Perpendicular lines, a circle through three points, and a tangent.

Perpendicular bisector of a segment and a circle centred on a point.

Circle from a diameter, the tangent at a point and where two tangents meet.

Points on a circle, the angle at the centre and the area of a segment.

Circle centre in terms of the radius, the radius from a distance, and the gradient of a tangent.

Circle in centre–radius form, the normal at a point and unknown constants.

Values of a constant for which a line touches a circle, then a perpendicular diameter.

Perpendicular lines, a circle through three points, and a tangent.

Circle and tangent: find a constant, the normal and parallel tangents.

Perpendicular bisector of a segment and a circle centred on a point.

Circle through two points: find the centre, then a tangent.

Circle from a diameter, the tangent at a point and where two tangents meet.

Circle centre in terms of the radius, the radius from a distance, and the gradient of a tangent.

Circle in centre–radius form, the normal at a point and unknown constants.

Values of a constant for which a line touches a circle, then a perpendicular diameter.

Perpendicular lines, a circle through three points, and a tangent.

Circle and tangent: find a constant, the normal and parallel tangents.

Circle through two points: find the centre, then a tangent.

Circle geometry to show a length ratio, then the exact area of a shaded region.

Perimeter and area of a region made from a sector and a triangle.

Perimeter and area of a shape made of sectors; find the radius and angle.

A shape made of sectors: show a length, find an area, and find a radius from the perimeter.

Perimeter of a shape built from circular arcs, and an exact area.

Arc length and areas of sectors and segments in radians.

Perimeter and areas of sectors and triangles in a cross-section.

Arc length to find an angle, then the area of a triangle.

Circle geometry to show a length ratio, then the exact area of a shaded region.

Points on a circle, the angle at the centre and the area of a segment.

Perimeter and area of a region made from a sector and a triangle.

Perimeter and area of a shape made of sectors; find the radius and angle.

A shape made of sectors: show a length, find an area, and find a radius from the perimeter.

Perimeter of a shape built from circular arcs, and an exact area.

Arc length and areas of sectors and segments in radians.

Perimeter and areas of sectors and triangles in a cross-section.

Arc length to find an angle, then the area of a triangle.

Exact value from an equation with inverse tan and inverse cos.

Sketch a trigonometric graph with a linear term, count solutions and solve an equation.

Range and sketch of a trigonometric curve, then count solutions of an equation.

Find the constants of a sine curve from its graph and count solutions of related equations.

Exact value from an equation with inverse tan and inverse cos.

Prove a trigonometric identity, then use it to solve an equation.

Prove a trigonometric identity, then solve an equation in an interval.

Rewrite a trigonometric equation in terms of sine, then solve it.

Prove a trigonometric identity and use it to solve an equation.

Prove a trigonometric identity and use it to solve an equation.

Prove a trigonometric identity, then solve the related equation.

Sketch a trigonometric graph with a linear term, count solutions and solve an equation.

Prove a trigonometric identity, then use it to solve an equation.

Prove a trigonometric identity, then solve an equation in an interval.

Rewrite a trigonometric equation in terms of sine, then solve it.

Prove a trigonometric identity and use it to solve an equation.

Prove a trigonometric identity and use it to solve an equation.

Range of a constant for no real roots, and a quadratic in cos θ.

Prove a trigonometric identity, then solve the related equation.

Trigonometric equation as a quadratic, and the discriminant to show no solutions.

Constant term in a binomial expansion.

Find a constant from a given coefficient in a binomial expansion.

Full binomial expansion, then use it to find one coefficient of a product.

The term independent of x in binomial expansions.

Equate binomial coefficients from two expansions to find a constant.

Binomial expansion: find a constant so one coefficient is a multiple of another.

Binomial expansion: compare coefficients to find an unknown constant.

Match binomial coefficients to find a positive constant.

Linked geometric and arithmetic progressions, a sum to infinity and a partial sum.

Arithmetic and geometric progressions: find a constant, partial sums and a sum to infinity.

Sum the terms of an arithmetic progression that lie in a given range.

Sum of an arithmetic progression and a relationship between partial sums.

Arithmetic and geometric progressions with trigonometric terms, including a sum to infinity.

Sum of the first 50 terms of an arithmetic progression.

Arithmetic progression: find a constant, then the sum of 30 terms.

Linked geometric and arithmetic progressions, a sum to infinity and a partial sum.

Arithmetic and geometric progressions: find a constant, partial sums and a sum to infinity.

Common ratio of a geometric progression and a sum to infinity after removing terms.

Arithmetic and geometric progressions with trigonometric terms, including a sum to infinity.

Geometric progression with trigonometric terms: find an angle, then a sum.

Geometric progressions: first term from the second term and the sum to infinity.

A term of a geometric progression.

Sum to infinity of a geometric progression from two of its terms.

Linked geometric and arithmetic progressions, a sum to infinity and a partial sum.

Arithmetic and geometric progressions: find a constant, partial sums and a sum to infinity.

Common ratio of a geometric progression and a sum to infinity after removing terms.

Arithmetic and geometric progressions with trigonometric terms, including a sum to infinity.

Geometric progressions: first term from the second term and the sum to infinity.

Sum to infinity of a geometric progression from two of its terms.

Find a constant from a gradient condition, then integrate to find the curve.

Gradient at a point, then the minimum point of a curve.

Gradient of a chord, then the gradient at a point as a limit.

Differentiate and find and classify a stationary point.

Differentiate a square-root function, find a stationary point and a normal.

Find a curve from its second derivative, classify stationary points and find a normal.

Areas bounded by a curve and the axes, and by a curve, a tangent and an axis.

Normal to a curve, find f(x) by integration, and whether f is increasing.

Normal to a curve from its gradient function, then the curve by integration.

Differentiate a square-root function, find a stationary point and a normal.

Inverse and composite functions, when no inverse exists, and a tangent triangle area.

Locate a maximum point, then the exact area under the curve.

Show a function is increasing, decide if its inverse exists, and a composite function.

Rate of change along a curve, then a constant from a minimum point.

Find a curve from its second derivative, classify stationary points and find a normal.

Gradient at a point, then the minimum point of a curve.

Classify a stationary point with the second derivative, then find the curve by integration.

Normal to a curve, find f(x) by integration, and whether f is increasing.

Turning point and intercept of a curve, then the area between the curve and a line.

Where a function is decreasing from its derivative, then find the function from a point.

Stationary points, their nature, and where the function is increasing.

Differentiate a square-root function, find a stationary point and a normal.

Integrate a derivative to find the curve, then its stationary point and where it increases.

Minimum point, area between curves, and a rate of change.

Differentiate and find and classify a stationary point.

Rate of change along a curve, then a constant from a minimum point.

Rates of change on a curve, then the perpendicular bisector of a chord.

Minimum point, area between curves, and a rate of change.

Find a constant from a gradient condition, then integrate to find the curve.

Find a curve from its second derivative, classify stationary points and find a normal.

Classify a stationary point with the second derivative, then find the curve by integration.

Normal to a curve, find f(x) by integration, and whether f is increasing.

Where a function is decreasing from its derivative, then find the function from a point.

Normal to a curve from its gradient function, then the curve by integration.

Find a curve from its derivative, a power of a linear bracket, and a point on it.

Integrate a derivative to find the curve, then its stationary point and where it increases.

Integrate a derivative and use a point to find the curve.

Find a curve from its derivative, a power of a linear bracket, and a point on it.

Locate a maximum point, then the exact area under the curve.

Area between a curve and a line by integration.

Areas bounded by a curve and the axes, and by a curve, a tangent and an axis.

Complete the square to find a vertex, then the area between a parabola and a line.

Turning point and intercept of a curve, then the area between the curve and a line.

Where two curves meet, then the area of the region between them.

Area under a curve with fractional powers, by integration.

Minimum point, area between curves, and a rate of change.

Exact area between a square-root curve and a line.

Sketch two graphs, then solve an inequality.

Solve a modulus inequality, then the largest integer satisfying a related one.

Sketch two graphs, then solve an inequality.

Solve an inequality involving the modulus.

Divide a polynomial by a quadratic, then find exact real roots of a related equation.

Use the factor theorem to find coefficients, factorise, then solve an equation in cot.

Factor and remainder theorems, then a cosec equation.

Polynomial division, then a definite integral of the form a + b ln 2.

Solve a logarithmic equation exactly.

Use logarithms to rearrange an exponential equation.

Show a value cannot occur on a logarithmic curve, then find the equation of a tangent.

Use logarithms to rearrange an exponential equation.

Solve an exponential equation using logarithms.

Solve a logarithmic equation exactly.

Constants from a straight-line graph of ln y against x.

Solve an equation in tan and sec over a given range.

Use the factor theorem to find coefficients, factorise, then solve an equation in cot.

Factor and remainder theorems, then a cosec equation.

Solve an equation in sec and tan.

Write a trigonometric expression in R cos(θ ± α) form, then solve an equation.

Prove an identity, an exact value, and integrate a trigonometric product.

Prove a trigonometric identity, solve an equation and integrate.

Write a trigonometric expression in R cos(θ ± α) form, then solve an equation.

Write an expression in R-form and solve a related equation.

Show a value cannot occur on a logarithmic curve, then find the equation of a tangent.

Gradient of an exponential curve at a point.

Gradient of an exponential curve, an intercept and an area.

Find the coordinates of the stationary points of a curve.

Gradient of an exponential curve at a point.

Stationary point of a logarithmic function, located and found by iteration.

Exact gradient at an intercept and the exact maximum point.

Implicit differentiation, a gradient, and showing there is no vertical tangent.

Normal to a parametric curve.

Parametric differentiation: where the gradient is 1.

Maximum points on a trigonometric curve, then an exact area.

Find the coordinates of the stationary points of a curve.

Show a value cannot occur on a logarithmic curve, then find the equation of a tangent.

Exact gradient at an intercept and the exact maximum point.

Maximum points on a trigonometric curve, then an exact area.

Set up an iteration for where two curves meet, use it, then find an area between the curves.

A function value and an integral.

Gradient of an exponential curve, an intercept and an area.

Prove a trigonometric identity, solve an equation and integrate.

Prove an identity, an exact value, and integrate a trigonometric product.

Show an integral result with exponentials, locate a constant and find it by iteration.

Show the value of an integral that gives a logarithm, and find a whole-number constant.

Trapezium rule, exact area with a logarithm, and over- or under-estimate.

Polynomial division, then a definite integral of the form a + b ln 2.

Exact area under a reciprocal-type curve.

Trapezium rule, exact area with a logarithm, and over- or under-estimate.

Show an integral result with exponentials, locate a constant and find it by iteration.

Sketch graphs, form an equation for where they meet and solve it by iteration.

Stationary point of a logarithmic function, located and found by iteration.

Sketch graphs, locate a root and iterate.

Show an integral result with exponentials, locate a constant and find it by iteration.

Set up an iteration for where two curves meet, use it, then find an area between the curves.

Sketch graphs, form an equation for where they meet and solve it by iteration.

Stationary point of a logarithmic function, located and found by iteration.

Sketch graphs, locate a root and iterate.

Sketch a modulus graph and solve an inequality.

Sketch a modulus graph and solve a modulus inequality.

Sketch a modulus graph and solve an inequality.

Sketch a modulus graph and solve an inequality.

Sketch a modulus graph and solve a modulus inequality.

Sketch a modulus graph and solve an inequality.

Solve an inequality involving the modulus.

Factor theorem with a repeated factor, finding unknown coefficients.

Polynomial division, then an exact definite integral.

Coefficients from the factor and remainder theorems, then factorise and solve an inequality.

Find two coefficients of a cubic from the factor and remainder theorems.

Factor theorem to find a constant, then a cubic inequality.

Find two coefficients of a cubic from divisibility and a remainder.

Partial fractions, then an exact integral in logarithmic form.

Partial fractions, then a definite integral with a logarithmic answer.

Stationary point, then an integral by substitution and partial fractions.

Split a rational expression into partial fractions.

Partial fractions and a definite integral to a given exact result.

Partial fractions, then integrate to a single logarithm.

Partial fractions, then integrate between limits.

Expand an algebraic expression as a series up to x² and state where it is valid.

Binomial expansion for a rational power, up to x².

Solve a logarithmic equation exactly.

Solve an exponential equation to 3 significant figures.

Solve an equation involving exponentials, giving the answer to 3 decimal places.

Solve an exponential or logarithmic equation to 3 decimal places.

Solve an exponential equation with different bases.

Solve an equation with exponentials and logarithms to 3 decimal places.

Solve a logarithmic equation to 4 decimal places.

Solve a logarithmic equation exactly.

Find constants from a straight-line graph of ln y against x.

Show a relationship becomes a straight line using logarithms and find its equation.

Solve a trigonometric equation involving cotangent for angles between 0° and 180°.

Turn a tan equation into a quadratic in tan x and solve it.

Turn a trigonometric equation into a quadratic in tan x and solve it.

Turn a tan equation into a quadratic in tan x and solve it.

Prove a triple-angle identity and use it to solve an equation.

Prove a trigonometric identity, then use it for an exact integral.

Solve a trigonometric equation involving cotangent for angles between 0° and 180°.

Turn a trigonometric equation into a quadratic in tan x and solve it.

Prove a trigonometric identity and use it to evaluate an integral.

Prove a triple-angle identity and use it to solve an equation.

Solve a trigonometric equation involving a half angle.

Write a combination of cos and sin in R-form, then solve a double-angle equation.

Solve an equation with cos 2θ and cos θ.

Write a trigonometric combination as R cos(θ − α), then solve an equation with it.

Write a combination of cos and sin in R-form, then solve a double-angle equation.

Differentiate a secant expression, then solve a differential equation.

Show a derivative result, then solve a separable differential equation.

Stationary point of a curve made of a trigonometric product.

Stationary point on a trigonometric curve.

Implicit differentiation, then where the normal is parallel to the y-axis.

Gradient of an implicitly defined curve at a point.

Gradient of an implicitly defined curve at a point.

Implicit differentiation and points where the tangent has a given direction.

Implicit differentiation and points with a horizontal tangent.

Parametric differentiation and the normal at a given parameter.

Gradient of a parametric curve at a point.

Implicit differentiation, then where the normal is parallel to the y-axis.

Exact position of a maximum point, then an enclosed area using a substitution.

Equation for a turning point, check a root lies in an interval, then iterate.

Stationary point, then an integral by substitution and partial fractions.

Find a maximum point, then evaluate an integral.

Maximum point of a trigonometric curve and the exact area under it.

Maximum point of a curve and an area by substitution.

Stationary point of a curve made of a trigonometric product.

Stationary point on a trigonometric curve.

Evaluate an exact definite integral.

Prove a trigonometric identity, then use it for an exact integral.

Exact value of a definite integral of a product of trigonometric functions.

Prove a trigonometric identity and use it to evaluate an integral.

Partial fractions, then an exact integral in logarithmic form.

Polynomial division, then an exact definite integral.

Partial fractions, then a definite integral with a logarithmic answer.

Evaluate an exact definite integral.

Partial fractions and a definite integral to a given exact result.

Partial fractions, then integrate to a single logarithm.

Partial fractions, then integrate between limits.

Exact value of a definite integral.

Exact position of a maximum point, then an enclosed area using a substitution.

Stationary point, then an integral by substitution and partial fractions.

Maximum point of a curve and an area by substitution.

An exact value from a sine curve, then an area by substitution.

Exact value of a definite integral.

Exact value of a definite integral of a product of trigonometric functions.

Find a maximum point, then evaluate an integral.

Maximum point of a trigonometric curve and the exact area under it.

Locate a root graphically and by a sign change, then use an iterative formula.

Show a single root graphically, locate it by calculation, then use an iterative formula.

Equation for a turning point, check a root lies in an interval, then iterate.

Sketch graphs to show there is one root, and check an iteration converges.

Locate a root, show an iteration converges to it, and use the iteration.

Locate a root by sketch and sign change, then iterate.

Locate a root and use fixed-point iteration.

Set up an equation for an angle from a segment area and use iteration.

Show there is one root by sketching, then iterate.

Locate a root graphically and by a sign change, then use an iterative formula.

Show a single root graphically, locate it by calculation, then use an iterative formula.

Equation for a turning point, check a root lies in an interval, then iterate.

Locate a root, show an iteration converges to it, and use the iteration.

Locate a root by sketch and sign change, then iterate.

Locate a root and use fixed-point iteration.

Set up an equation for an angle from a segment area and use iteration.

Show there is one root by sketching, then iterate.

Sketch graphs to show there is one root, and check an iteration converges.

Vectors: a midpoint, the angle between two vectors and the area of a triangle.

Position vectors in a trapezium, where diagonals meet, and an angle by scalar product.

Angle between vectors by scalar product, then a triangle’s area in 3D.

Vectors: a midpoint, the angle between two vectors and the area of a triangle.

Vector equation of a line, an angle by scalar product and the exact area of a triangle.

Show two lines are skew and find the obtuse angle between them.

Position vectors in a trapezium, where diagonals meet, and an angle by scalar product.

Angle between two lines, then a perpendicular distance from a point to a line.

Angle between vectors by scalar product, then a triangle’s area in 3D.

Two lines in 3D: when they meet, perpendicularity and the point of intersection.

Vector equation of a line, an angle by scalar product and the exact area of a triangle.

Vector equations of two lines, where they meet, and a point at a given distance.

Two lines in 3D: when they meet, perpendicularity and the point of intersection.

Show two lines are skew and find the obtuse angle between them.

Position vectors in a trapezium, where diagonals meet, and an angle by scalar product.

Vector equations of two lines, where they meet, and a point at a given distance.

Show two lines do not meet and find the foot of a perpendicular in 3D.

Two lines in 3D: when they meet, perpendicularity and the point of intersection.

Angle between two lines, then a perpendicular distance from a point to a line.

Show two lines do not meet and find the foot of a perpendicular in 3D.

Form and solve a differential equation for a tank filling and draining.

Form and solve a differential equation for a balloon’s radius.

Solve a first-order differential equation from an initial condition.

Solve a differential equation with an initial condition.

Differentiate a secant expression, then solve a differential equation.

Solve a separable differential equation with a condition and find a limit.

Solve a separable differential equation and describe the long-term behaviour.

Show a derivative result, then solve a separable differential equation.

Solve a separable differential equation with an initial condition.

Solve a first-order differential equation from an initial condition.

Form and solve a differential equation for a balloon’s radius.

Solve a separable differential equation and describe the long-term behaviour.

Solve a separable differential equation with an initial condition.

Form and solve a differential equation for a tank filling and draining.

Form and solve a differential equation for a balloon’s radius.

Find the exact square roots of a complex number by forming a quartic.

Exact square roots of a complex number by forming a quartic.

Square roots of a complex number.

Complex products, modulus–argument form and a geometric result.

Equate real and imaginary parts to form and solve an equation.

Simplify a complex expression and find its argument.

Argand diagram: where a line meets a circle, and the greatest argument in a region.

Argument of a complex quotient, and the geometric transformation to its conjugate.

Complex products, modulus–argument form and a geometric result.

Simplify a complex expression and find its argument.

Solve a complex quadratic, then modulus, argument and an equilateral triangle.

Complex products, modulus–argument form and a geometric result.

Find the exact square roots of a complex number by forming a quartic.

Exact square roots of a complex number by forming a quartic.

Square roots of a complex number.

Equate real and imaginary parts to form and solve an equation.

Solve a complex quadratic, then modulus, argument and an equilateral triangle.

Use a complex root of a cubic, then sketch a locus and find the greatest argument.

Argand diagram: where a line meets a circle, and the greatest argument in a region.

Shade a region of the Argand diagram given by a modulus and an argument inequality.

Describe a region of the Argand diagram with inequalities and find its greatest modulus.

Shade a region on an Argand diagram and find the greatest argument.

Sketch a circular locus and find the least modulus.

Use a complex root of a cubic, then sketch a locus and find the greatest argument.

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.

Back-to-back stem-and-leaf, median and IQR, and combined mean and standard deviation.

Median and IQR from a stem-and-leaf diagram, box plots, and mean or median.

Back-to-back stem-and-leaf, median and IQR, and comparing spread.

Back-to-back stem-and-leaf: median, IQR, box plots and choosing an average.

Back-to-back stem-and-leaf: median, IQR, box plots and a comparison.

Draw a histogram and estimate the mean of grouped data.

Read a cumulative frequency graph, then estimate the mean and standard deviation of grouped data.

Draw a cumulative frequency graph, estimate from it and estimate a grouped mean.

Draw a histogram and estimate a standard deviation from grouped data.

Draw a histogram and estimate the mean of grouped data.

Read a cumulative frequency graph, then estimate the mean and standard deviation of grouped data.

Draw a cumulative frequency graph, estimate from it and estimate a grouped mean.

Draw a histogram and estimate a standard deviation from grouped data.

Back-to-back stem-and-leaf, median and IQR, and combined mean and standard deviation.

Use summary statistics with coding to find the number of values.

Arrangements of letters with restrictions, and choosing two different letters.

Arrangements and selections of letters from a word with repeated letters and restrictions.

Arrangements and selections of books with restrictions.

Arrangements of letters with a restriction on a gap.

Arrangements with repeated letters and restrictions, and a probability.

Selections with restrictions and arrangements with grouping or separation.

Arrangements of letters with grouping and spacing, a probability, and selections.

Arrangements with restrictions, selections and splitting into groups.

Arrangements of letters with restrictions, and choosing two different letters.

Arrangements and selections of letters from a word with repeated letters and restrictions.

Arrangements and selections of books with restrictions.

Arrangements of letters with a restriction on a gap.

Arrangements with repeated letters and restrictions, and a probability.

Arrangements with restrictions and a probability of a selection.

Selections with restrictions and arrangements with grouping or separation.

Arrangements of letters with grouping and spacing, a probability, and selections.

Arrangements with restrictions, selections and splitting into groups.

Arrangements of letters with restrictions, and choosing two different letters.

Arrangements and selections of letters from a word with repeated letters and restrictions.

Arrangements and selections of books with restrictions.

Selecting groups of students with restrictions.

Arrangements with restrictions and a probability of a selection.

Selections with restrictions and arrangements with grouping or separation.

Arrangements of letters with grouping and spacing, a probability, and selections.

Arrangements with restrictions, selections and splitting into groups.

Two-way table: conditional probability, independence and a binomial probability.

Two groups: find an unknown from a ratio, then the probability two cards match.

Conditional probability when drawing marbles with and without replacement.

Choosing toy cars without replacement: same-colour and mixed-colour probabilities.

A biased coin and a choice of marbles, with a conditional probability.

Tree diagram, matching colours and a conditional probability.

Rain on successive days with dependence: several probabilities.

Geometric probabilities, a conditional probability and a binomial “at least”.

Probabilities by type of journey, and a conditional probability.

Fair and biased coins: a conditional probability and a probability distribution.

Choosing without replacement, and a conditional probability.

Probability that the first success comes on or before a given trial.

Two-way table: conditional probability, independence and a binomial probability.

Probability distribution from selections without replacement, and its variance.

Probability distribution for the number of tails from three biased coins.

Distribution of heads from three biased coins, then the variance.

Probability distribution of a coin-and-dice variable and its variance.

Probability distribution, expectation and variance of the total of two coins.

Probability distribution from a formula with an unknown constant, then mean and variance.

Fair and biased coins: a conditional probability and a probability distribution.

Distribution of the sum of two rolls of a non-standard die, mean and variance.

Probability distribution from selections without replacement, and its variance.

Distribution of heads from three biased coins, then the variance.

Probability distribution of a coin-and-dice variable and its variance.

Probability distribution, expectation and variance of the total of two coins.

Unknown probabilities from the expectation, then the variance.

Probability distribution from a formula with an unknown constant, then mean and variance.

Distribution of the sum of two rolls of a non-standard die, mean and variance.

Binomial probabilities and a normal approximation for birthdays.

Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.

Binomial probabilities and a normal approximation.

Two-way table: conditional probability, independence and a binomial probability.

Binomial probabilities and the normal approximation to the binomial.

Geometric probability, then a binomial probability over a range.

Geometric probabilities, a conditional probability and a binomial “at least”.

Binomial and normal approximation, with a justification.

Binomial probability for a small sample, normal approximation for a large one.

Geometric distribution: first head on, or after, a given throw.

Probability that the first success comes on or before a given trial.

Normal probabilities, a standard deviation from a percentage, and the first day an event happens.

Geometric distribution and the normal approximation to a binomial.

Geometric probabilities for repeated attempts.

Geometric probability, then a binomial probability over a range.

Geometric probabilities, a conditional probability and a binomial “at least”.

Geometric probabilities for repeated throws.

Normal distribution: expected numbers in a range and a standard deviation from a percentage.

Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.

Normal probabilities, a standard deviation from a percentage, and the first day an event happens.

Normal distribution: expected count below a value and a standard deviation from a tail.

Normal distribution: a percentage above a value and a boundary value.

Normal probabilities and a value from a tail probability.

Normal probabilities, an unknown standard deviation and the normal approximation.

Normal distribution: expected count and probability within half a standard deviation.

Normal probabilities and an unknown standard deviation.

Normal distribution: expected numbers in a range and a standard deviation from a percentage.

Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.

Normal probabilities, a standard deviation from a percentage, and the first day an event happens.

Normal distribution: expected count below a value and a standard deviation from a tail.

Normal distribution: a percentage above a value and a boundary value.

Normal probabilities and a value from a tail probability.

Normal probabilities, an unknown standard deviation and the normal approximation.

Normal probabilities and an unknown standard deviation.

Binomial probabilities and a normal approximation for birthdays.

Normal approximation to a binomial probability.

Binomial probabilities and a normal approximation.

Geometric distribution and the normal approximation to a binomial.

Binomial probabilities and the normal approximation to the binomial.

Normal approximation to a binomial.

Normal probabilities, an unknown standard deviation and the normal approximation.

Binomial and normal approximation, with a justification.

Binomial probability for a small sample, normal approximation for a large one.

Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.

Poisson probability in terms of e, and the value of n making two probabilities equal.

Poisson probabilities, sums and a normal approximation.

Poisson mean and variance, when Poisson approximates binomial, and a tail probability.

Poisson conditions, probabilities over different periods, and a Poisson total.

Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.

Poisson probabilities, sums and a normal approximation.

Sums of independent Poisson variables and a conditional probability.

Poisson conditions, probabilities over different periods, and a Poisson total.

Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.

Approximate binomial and Poisson probabilities with suitable distributions.

Poisson approximation to a binomial probability.

Poisson probabilities, sums and a normal approximation.

Normal approximation to a Poisson probability, with justification.

Poisson mean and variance, when Poisson approximates binomial, and a tail probability.

Standard deviations of combinations of normal and Poisson variables.

Difference and weighted sum of normal variables.

Standard deviations of combinations of normal and Poisson variables.

Use a dice to choose at random, then the probability that a difference of two normal times exceeds a value.

Probabilities for combinations of two independent normal variables.

Sums of independent Poisson variables and a conditional probability.

Difference and weighted sum of normal variables.

Find a constant in a probability density function, then use the median for a probability.

Probability density function: find a constant, a parameter from the mean, and the median.

Continuous distribution: constants and the median.

Probability density function: a constant, the median and E(X).

Linear density function: constant, expectation and a limit from the median.

Probability density function: find a constant, a parameter from the mean, and the median.

Probability density function: a constant, the median and E(X).

Linear density function: constant, expectation and a limit from the median.

Find a constant in a probability density function, then use the median for a probability.

Probability density function: find a constant, a parameter from the mean, and the median.

Continuous distribution: constants and the median.

Probability density function: a constant, the median and E(X).

Linear density function: constant, expectation and a limit from the median.

Use a dice to choose at random, then the probability that a difference of two normal times exceeds a value.

Find a sample mean from data using an unbiased estimate of variance.

Random sampling, unbiased estimates of mean and variance.

Unbiased estimates from summary data, then a test of a mean at 1%.

Standard deviation from a confidence interval, the Central Limit Theorem and repeated intervals.

Read a confidence interval for a mean and estimate the standard deviation.

Distribution of the sample mean: a probability, then a boundary value.

Standard deviation from a confidence interval, the Central Limit Theorem and repeated intervals.

Work back from the width of a confidence interval to possible sample proportions.

Read a confidence interval for a mean and estimate the standard deviation.

Confidence level from a confidence interval for a proportion.

Confidence interval for a proportion.

Binomial test for a proportion, and why a Poisson approximation does not suit.

Binomial test on the chance of rolling a six, then Type I and Type II error probabilities.

Binomial hypothesis test at 10%, and whether the model suits the context.

Type I error from a binomial test and a Type II error.

Test for a normal mean, with Type I and Type II error probabilities.

Test a normal mean, state an assumption and find the smallest significant sample mean.

Type I error, a large-sample test of a mean, and a Type II claim.

One-tailed test of a mean, then the probability of a Type II error.

Unbiased estimates from summary data, then a test of a mean at 1%.

Test for a normal mean, with Type I and Type II error probabilities.

Binomial test on the chance of rolling a six, then Type I and Type II error probabilities.

Type I error, a large-sample test of a mean, and a Type II claim.

One-tailed test of a mean, then the probability of a Type II error.

Type I error from a binomial test and a Type II error.