Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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.

Practice finding parallel and perpendicular lines to a given line.

rebelmaths

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Find roots and the area under a parabola

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each .

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

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

Find a% of b using a calculator. Suggested method to use decimal equivalent.

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

rebelmaths

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

Tests the ability to find the gradient and intercept of a straight line graph.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

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

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

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

rebelmaths

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.

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 $d\times a+f \neq 0$.

5 questions on using substitution to find indefinite integrals.

5 questions on using substitution to find indefinite integrals.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

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

rebelmaths

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Find the first four non-zero terms in the Maclaurin series for $e^{ax}$.

Find the first three non-zero terms in the Maclaurin series for $\cos(x)$.

Find the first three non-zero terms in the Maclaurin series for $\sin(x)$.

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.