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

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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

4 questions on using partial fractions to solve indefinite integrals.

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

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

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

Several questions on rounding number and using approximations to estimate. Several real-world examples.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

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

Questions on manipulating logarithms.

An introduction to using the quotient rule

An introduction to using the quotient rule

An introduction to using the quotient rule

An introduction to using the quotient rule

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Solving three simultaneous congruences using the Chinese Remainder Theorem:

\[\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*} \] where $\operatorname{gcd}(n_1,n_2,n_3)=1$

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Simplify logarithmic expressions using rules on logarithms.

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

An introduction to using the quotient rule

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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

Solving arithmetic progressions using simultaneous equations

Integration using partial fractions

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Solving arithmetic progressions using simultaneous equations

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

Find the leading coefficient of a degree 3 polynomial using a difference table.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.