Students should be able to square negative numbers. Students should be able to substitute into formulae. Students should be able to plot points on a coordinate grid. Students should be able to expand single brackets and collect terms. ‘like’ KEYWORDS Quadratic, function, solve, expand, factorise, simplify, expression, graph, curve, factor, coefficient, bracket 16a. Quadratic equations: expanding and factorising Teaching time (A4, A11, A18) 4–6 hours OBJECTIVES By the end of the sub-unit, students should be able to: Define a expression; ‘quadratic’ Multiply together two algebraic expressions with brackets; Square a linear expression, e.g. (x + 1)2; x2 bx c; Factorise quadratic expressions of the form + + Factorise a quadratic expression using the difference of two squares; Solve quadratic equations by factorising; quadratic equations that require rearranging; Find the of a quadratic function algebraically. POSSIBLE SUCCESS CRITERIA Solve 3x2 + 4 = 100. Expand (x + 2)(x + 6). Factorise x2 + 7x + 10. x2 Solve + 7x + 10 = 0. (x 3)(x + 4)= 0. – COMMON MISCONCEPTIONS x x2. can sometimes be with ‘collected’ NOTES a This unit can be extended by including quadratics where 1. ≠ x2 x Emphasise the fact that and are different of term illustrate this with numbers. – 16b. Quadratic equations: graphs Teaching time (A11, A12, A18) 3–5 hours
Students should be able to square negative numbers. Students should be able to substitute into formulae. Students should be able to plot points on a coordinate grid. Students should be able to expand single brackets and collect ‘like’ terms. KEYWORDS Quadratic, function, solve, expand, factorise, simplify, expression, graph, curve, factor, coefficient, bracket 16a. Quadratic equations: expanding and factorising (A4, A11, A18) Teaching time 4–6 hours OBJECTIVES By the end of the sub-unit, students should be able to: Define a ‘quadratic’ expression; Multiply together two algebraic expressions with brackets; Square a linear expression, e.g. (x + 1)2; Factorise quadratic expressions of the form x2 + bx + c; Factorise a quadratic expression using the difference of two squares; Solve quadratic equations by factorising; quadratic equations that require rearranging; Find the of a quadratic function algebraically. POSSIBLE SUCCESS CRITERIA Solve 3x2 + 4 = 100. Expand (x + 2)(x + 6). Factorise x2 + 7x + 10. Solve x2 + 7x + 10 = 0. (x – 3)(x + 4)= 0. COMMON MISCONCEPTIONS x can sometimes be ‘collected’ with x2. NOTES This unit can be extended by including quadratics where a ≠ 1. Emphasise the fact that x2 and x are different of term – illustrate this with numbers. 16b. Quadratic equations: graphs (A11, A12, A18) Teaching time 3–5 hours
Edexcel-3-year-Scheme-of-Work.docx