Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

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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.

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Another transposition question, which requires (basic) factorisation.

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Open and answer

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.