Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

Finding surface area and volume, given formulae.

Another transposition question.

rebalmaths

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.

Find i using compound interest formula A=P(1+i)^n

rebelmaths

Substitute given values into formulas.

Solving quadratic equations using a formula,

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.

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

rebelmaths

Given an equation or a worded formula determine if it is a function or not

Manipulation of algebraic fractions

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.

Using the reduction formulas for products of powers or sin and cosine

Given the original formula the student enters the transformed formula.

READY TO USE

No description given

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

rebelmaths

Match the question with the correct formula.

rebelmaths

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

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.

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

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

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

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.

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.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

rebelmaths

Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.

Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.

Both parts use custom marking algorithms.

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

Given th original formula the student enters the transformed formula

READY TO USE

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