In order to do well in the admission test, it is important that you are able to perform algebraic manipulation quickly and accurately. The algebra required can be much more complicated than you might be used to, but it is essential that you hold your nerve and work through it logically, looking for ways to simplify your working as you go.

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You may need to combine techniques that you normally use on their own, or apply these techniques to more complicated expressions and equations. For example, you may have to rearrange or solve equations and inequalities, which may also include surds, indices, or other functions. 

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You should be very confident with quadratic equations and understand how the coefficients affect the shape of the graph and the number of roots, and what this means for the discriminant. You should be able to solve quadratic equations (including disguised quadratics where another variable is used in place of ‘x’ ) by factorising, completing the square or using the quadratic formula - all without a calculator!  

 

You must be able to set up equations and inequalities from information given in the question, and then be confident in solving these. This may involve both linear and quadratic expressions, and may also include simultaneous equations. Remember that you can use the discriminant of any quadratic to determine the number of solutions, and this can be particularly helpful if you are trying to find a unique solution of simultaneous equations.

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You should be able to factorise higher order polynomials (cubics, quartics etc) by inspection, or by long division, using the Factor Theorem to help identify factors, and deduce the number and position of any roots and intercepts. (Some differentiation may also be useful here to identify the position of the turning points.)

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Finally you should be familiar with the square root function and the modulus function, and be able to work with these in combination with any of the previously mentioned techniques.