Transition to university

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

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

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

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

Multiplication and division of upper and lower bounds.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

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

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

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

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

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.

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

Calculate outcomes for different configurations of rolling two dice. 

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

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

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

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

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

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.

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

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

Identify the centre of enlargement and the scale factor in a transformation of an image A to an image B

Determine the way in which an image A has been reflected onto an image B.

Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Substitute given values into formulas.

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.