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Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

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Integrate Paris Law equation to estimate life to failure.

This is a diagnostic test - we use it to determine where extra mathematical help is needed for the class as a whole and where you get to see specific areas where you may need to work on your mathematical skills. The diagnostic test DOES NOT count in any way towards your first year grade.

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Matrix by scalar and matrix by matrix multiplication exercises.

Exercises in solving simultaneous equations with 2 variables.

Exercises on inverting 2x2 and 3x3 matrices.

Semi-worked example of inverting a 3x3 matrix using cofactor, adjoint and determinant.

Addition and Subtraction by hand questions, whole numbers and decimals. Fully worked solutions in feedback.

Subtraction questions, whole and decimal, to be carried out by hand. Full worked solutions given in feedback.

Addition calculations to be carried out by hand, full worked solutions in feedback.

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

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Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Fill in a frequency table for grouped data, then estimate the mean and identify the modal class.

Exercises covering matrix addition and subtraction

This is a set of questions for students to practice identifying parabolas, hyperbolas and exponentials.

There are also a few questions asking students to draw graphs, and to evaluate the curves at specific points.

10 questions are selected from a larger pool. 

In the first question students are asked to identify the type of a graph.

In the second question students are asked to identify the type of an equation.

Then next 6 questions are basic questions about evaluating points on a curve or matching curves and equations.

The last 2 questions are applications - e.g. compound interest, displayed as an equation, a table or a graph.

Practise solving simultaneous linear equations graphically and algebraically.