Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

sin vertically shifted Working 1_11_16

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Using $\cos^2\theta+\sin^2\theta=1$ to evaluate expressions.

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax

Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.

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This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers.

Calculating rates and scaling rates. Drops per mL and drops per minute questions unit rate to equivalent rate.

Calculate probability using P(A) = 1-P(not A)

Using geogebra to draw lines tangent to a curve and calculate their gradient.

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

The subtraction algortihm using the borrow and pay back method with integers.

A single question which asks you to round to the nearest ten, hundred or thousand. 

These question are designed to be completed without using a calculator.

Quiz for expanding brackets and factorising

Given n-1 angles inside a polygon, students have to calculate the value of the last internal angle.

Students explore the relationship between length and area of a rectangle.

The perimeter of the rectangle is randomised. Students are given 11 different lengths, and asked to compute rectangle width and area for each. They are then asked to graph the function, identify it as a parabola, and estimate the maximum value.