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• 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.

• Question

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

• 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

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

• 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.

• Question

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

• Question

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

• Question

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

• Question

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

Small, simple question.

• Question

Substitute values into formulae for the area or volume of various geometric objects.

• Units of measurement