Xiaodan Leng

Solve a random oblique triangle for sides and angles.

Solve a random oblique triangle for sides and angles.

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

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.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

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