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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.

Finding x and y values for straight line graphs

Finding x and y values for straight line graphs

Finding the cost including VAT

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

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

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Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

Finding surface area and volume, given formulae.

Given the original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

No description given

Finding lengths of sides of triangles

Finding the numerators & denominators of 4 equivalent fractions.

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Finding lengths of sides of triangles

Practice finding parallel and perpendicular lines to a given line.

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This question asks the student to find the inversed composite function finding the inverses of two functions then composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Question assessing the students understanding of linear sequences.

Students are assessed on their ability to find the common difference and first term in a linear sequence and then find the nth term of the sequence using the arithmetic formula.

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

Finding values which satisfy an inequality.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

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.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Using differentiation to find the tangent and normal to a line at a given point