Questions on rearranging expressions, expanding brackets and collecting like terms.

Some questions of relevance to consumers.

Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.

Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.

Find the original price before a discount by dividing the new price by the percentage discount.

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

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

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. 

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. 

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

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r digits are picked at random (with replacement) from the set $\{0,\;1,\;2,\ldots,\;n\}$. Probabilities that 1) all $\lt k$, 2) largest is $k$?

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A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version I. Graph is quadratic

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal

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

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

Calculation of the length and alternative form of the parameteric representation of a curve.

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

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The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Students seem to freak out when their answer is not written exactly the same as the answer provided. This question tries to enforce that $(x-y)=-(y-x)$ and $\frac{a-b}{c-d}=\frac{b-a}{d-c}$

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

35 simple subtraction questions are given with a 2 minute time limit.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.