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• Question

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other.

• Question

Fill in a frequency table for grouped data, then estimate the mean and identify the modal class.

• Question

Given some numbers in standard index form, convert to decimal form.

• Question

Given a table of data, calculate the mean, mode and median, and complete a frequency table.

• Question

Multiply two numbers in standard form, then divide two numbers in standard form.

• Laws of Indices
Question

This question aims to test understanding and ability to use the laws of indices.

• Question

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

• Expansion of brackets
Question

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

• Exam (3 questions)

Apply formulas to calculate the areas of various shapes.

• Question

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

• Exam (2 questions)

Questions on adding, subtracting, multiplying and dividing numbers in standard form.

• Decimals to fractions
Question

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

• Question

Add two numbers in standard form, then subtract two numbers in standard form.

• Question

Convert a variety of numbers from decimal to standard index form.

• Question

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

• Question

This question aims to assess the student's understanding of the difference between biased and unbiased events and also to assess the student's understanding of the fact that the experimental probability tends towards the theoretical probability as the number of trials increases.

• Question

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

• Weight and Mass
Exam (4 questions)

Work with measurements of weight, mass and density.

• Question

Calculate outcomes for different configurations of rolling two dice.

• Volume
Exam (3 questions)

Questions involving the calculation of the volumes of shapes.

• Question

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

• Question

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

• Question

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

• Question

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

• Logarithms
Exam (4 questions)

Questions on manipulating logarithms.

• Question

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

• Question

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

• Question

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

• Question

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

• Question

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions.