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

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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.

Solving quadratic equations using a formula,

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

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.

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

This question is to test if you know how to use your calculator correctly.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

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

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

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

Use the quotient rule to differentiate various functions.

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Questions which rely on knowledge of standard integrals.

Solve a system of linear equations using Gaussian elimination.

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5 questions on using substitution to find indefinite integrals.

Solve a pair of linear equations by writing an equivalent matrix equation.