Rearrange formula

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.

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.

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.

This tests the student's ability to understand the components of formula.

Apply formulas to calculate the areas of various shapes.

Given the formula for BMI, students are asked to determine a patient's BMI given their height in cm (as people usually do) and their mass in kg.

This is a very simple question with no randomisation.

Students are asked to identify an inverse relationship equation.

Students are given a formula and asked to evaluate it for a given input value, which is randomised.

Given a parcel's width, height and length, calculate its volume and surface area. Additionally, classify its size based on a formula inspired by a real delivery company (as mad as it sounds!).

The student must give units with each measurement.

Substitute values into formulae for the area or volume of various geometric objects.

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

A question testing the application of the Area of a Triangle formula when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

rebelmaths

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Apply formulas to calculate the areas of various shapes.

Substitute values into formulae for the area or volume of various geometric objects.

Identify parts of statistical formulas, and answer questions about how changing one variable affects the statistic.

Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$. Which are unbiased and efficient?

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$