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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.