A block lies on rough horizontal ground. The coefficient of friction is given and students find the maximum value of friction $F_{\text{MAX}} = \mu R$. This is then used to determine the magnitude of force that must be exceeded to achieve movement when the force is applied horizontally and at two different angles to the horizontal.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

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.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

Given three vectors with integer components, find the corresponding magnitude and direction.

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Differentiation question with customised feedback to catch some common errors and corresponding partial marks.

malrules

Partial differentiation question with customised feedback to catch some common errors.

Simple ratio question with custom marking and partial credit possible

The marking checks for some common errors and awards partial credit and appropriate feedback. The errors that give different levels of partial credit include: forgetting to add one to the denominator, forgetting to change to a percentage.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

This is a homework assignment. Students may complete this assignment during a maths lesson with the support from the teacher. 

• Passing mark 60%
• Difficulty level 3 Moderat/Average (C+, B-, B Level).

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Match the question with the correct formula.

rebelmaths

Two column vectors are given, with one entry unknown. Given that the vectors are perpendicular, question is to determine the unknown entry.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Slightly harder introductory exercises about the power set.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Finding the stationary points of a rational function with specific features.

Finding the stationary points of a cubic with two turning points

This question tests the student's ability to find remainders using the remainder theorem. 

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

rebelmaths

A sample of what can be done with the differentiation extension, and the corresponding custom part type.

Kruskal-Wallis test with ties.

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

Percentage Error

rebelmaths