Number and Algebra: Equations and expressions, Level 6
AO1: Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns. This means students will create equations to model everyday situations, e.g. express a taxi charge as a linear equation (flagfall and kilometre rate) or the exponential relationship between the number of repeated folds (in thirds) of a paper strip and the number of sections formed. This includes forming pairs of simultaneous linear equations. Students should be able to form equations from tables of values, using differences between terms, constant first order for linear relations, constant second order differences for quadratic relations and constant ratio for simple exponentials. They should use algebraic manipulation skills to simplify expressions, including rational expressions involving exponents, e.g. 9n4 / 6n3. Students should apply their manipulations skills to solve linear and quadratic equations by applying inverse operations with an appreciation of equality and connect their solutions to corresponding situations of inequality, e.g. If (6x - 8)/4 = 10 has the solution x = 8 then (6x - 8) /4 < 10 has the solution x < 8. They should be able to solve quadratic equations by factorising and have the disposition and capability to check all of their algebraic solutions by substituting values. Solving simple exponential equations should be done by inspection at this level, e.g. 3x = 81 by recognising 34 = 81 so x = 4. Pairs of simultaneous equations may be solved by substitution, elimination and by intercept of graphs.
