Graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, the value of various integrals are to be deduced.

Graphs are given with areas underneath them shaded. The student is asked to select or enter the correct integral which calculates its area.

The student will be given 2 integers between -9 and +9 to add together.

Student is given two whole numbers to add, they have to give the sum.

The numbers are in the range -9 to 9.

The thicknesses of two sedimentary layers are given. The student has to add the thicknesses and give the answer to 2 siginificant figures.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

A quartic graph is given. The question is to determine whether the gradient is positive or negative at various values of x. Non-calculator. Advice is given.

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point. Non-calculator. Advice is given.

A parabolic graph is given. The question is to determine the equation of the graph. Non-calculator. Advice is given.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line. Non-calculator. Detail advice is given.

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.

Find a regression equation.

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.

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

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Find the equation of the straight line perpendicular to the given line that passes through the given point $(a,b)$.

Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a certain point.

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

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

Integration by susbtitution, no hint given

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

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Substitute given values into formulas.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Substitute given values into formulas.

Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a certain point.

Solve for x and y on a given triangle and calculate the area

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

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