Given a number evaluate simple power, negative power, to one half.

Given a number evaluate simple power, negative power, to one half.

Several quadratics are given and students are asked to complete the square.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Find the unit vector parallel to a given vector.

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

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

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

rebelmaths

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

rebelmaths

Calculate the number of moles in a given mass of a substance given the molecular weight.

Calculating mass of a substance given molecular weight and number of moles.

Practice at a longer calculation to work out how much glucose is needed to make a solution of a given concentration.

Practice calculating number of moles of a substance given the concentration and volume of a solution.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Given the graph of the line determine the equation of the line.

A copy of Amy Chadwicks block question, with adaptions to provide a diagram for the student.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

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

rebelmaths

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

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.

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

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Given the probabilities that each of four out of five friends will win a round of mini-golf, work out the probability that the fifth friend won't win, then use that to find the probability that they will win.