Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Questions on differentiation from first principles, and continuity and differentiability.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Calculate confidence interval for the mean, sample variance n>30

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Given a number evaluate simple power, negative power, to one half.

This exercise will help you solve equations of type ax-b = c.

Simplifying algebraic expressions

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Practical questions

Find the dot product and the angle between two vectors

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Find the angle between two vectors

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

Small, simple question.

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

Multiplication and division of upper and lower bounds.

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

Convert a height given in feet and inches into cm and then metres.

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

This question assesses the student's ability to use some given information involving two different units of measurement to rewrite the information as a compound measure.

This question assesses the students ability to calculate and convert between different types of compound units, including rates of pay, speed and unit pricing.

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.

Converting between giga, mega, kilo, base, milli and micro, nano. Metres, grams and litres.

Is this number divisible by 2? Half the time the number is, half the time it isn't. Steps give the divisibility test.