Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Given the graph of the line determine the equation of the line.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

Multiplication of $2 \times 2$ matrices.

Introduction to counting with permutations and combinations

Simple counting exercise, with combinations

Simple counting exercise, with combinations

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

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

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Question on drug calculations

Question on drug calculations

Question on drug calculations

Question on drug calculations

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250