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Finding lengths of sides of triangles

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Finding the numerators & denominators of 4 equivalent fractions.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Find the determinant of a $3 \times 3$ matrix.

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

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

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

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

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Students are given a graph of a cubic, and are asked to find the equation for it.

Students enter equation and turning point

Finding lengths of sides of triangles

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Solve a quadratic equation by completing the square. The roots are not pretty!

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Practice finding parallel and perpendicular lines to a given line.

rebelmaths

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

Modular arithmetic. Find the following numbers modulo the given number $n$. Three examples to do.

Solve a quadratic equation by completing the square. The roots are not pretty!

Given sequences with missing terms, find the common difference between terms.

Draws a right angled triangle based on a length and an angle.

Draws a right angled triangle based on a length and an angle.

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.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

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.