No description given

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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 $\neg q \to \neg p$.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Multiplication of $2 \times 2$ matrices.

Understanding order of operations on a calculator and using power and root keys.

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)

Converting binary number to decimal.

Given a number evaluate simple power, negative power, to one half.

Permutation of n objects; choosing e.g. 3 from 5.

A box contains $m$ white balls and $n$ black balls. A ball is drawn out of the box at random. What is the probability that the ball is black/white?

Shows how to define variables to stop degenerate examples.

Solve $p - t < \text{or}> q$

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

Understanding of intersection and union symbols.

Understanding order of operations on a calculator and using power and root keys.

rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths

Another transposition question, which requires (basic) factorisation.

rebelmaths

15 questions based on module so far. 

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

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

A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.

No description given

Practice finding parallel and perpendicular lines to a given line.

rebelmaths

Practice dividing polynomials using the long division method.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.