This document outlines common mistakes made when solving algebra, geometry, and other math problems. It provides tips on correctly solving problems involving factors, expressions vs equations, simultaneous linear equations using substitution, Pythagorean theorem, and calculating volume and surface area. Key advice includes showing steps, changing subjects of formulas correctly, rejecting answers appropriately, including units, and not oversimplifying numbers.

1. Careless Mistakes The most common mistakes 8 + 19 = 26 (27) 106 2= 58 (53) 7 x 6 = 58 (42) Changing of signs Reading of questions . .

2. Congruence and Similarity Changing the subject of a formula = a = (b) b = a x a c b d c d d c

3. Algebra Factorisation = Over-factorisation -x 2 y – xy + 6 = 6 – xy (x+1) In simplifying into eqns Include “(shown)” Equation and Expression Form an expression (x + y) km Form an equation x + y = 7 Incorrect rejection = 0 (do not reject) is not possible. (rejected) 16d 4d 4abc abc 0 a a 0

4. Simultaneous Linear Equations Write out the equations [ ? (1) ] Change subject [ From (1) : ? ] Substitution [ Sub. x = ? into only (2) ] Complete Equation Reject accordingly [ if necessary ] Substitution [ Sub. y = ? into (1) or (2) ]

6. Volume and Surface Area Open cones and pyramids Bases are not counted in the calculation of surface area. Do not simplify explicit numbers ( like surds and calculations with ) unless asked to. Remember to include units.