Hannah Aldous

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

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.

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

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

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

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

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

The amount of money a person gets on their birthday follows an arithmetic sequence.

Calculate the amount on a given birthday, then calculate the sum up to that point.

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

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 a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

Each part is broken into steps, with the formula given.

Given the common difference and first term of an arithmetic sequence, work out the index of the nth term of the sequence.

Framed as a word problem with ticket numbers in an ice cream shop.

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Apply and combine logarithm laws in a given equation to find the value of $x$.