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Educator and Tagging Information: Learning Area: Maths Resource Name: Maths Assessment Exemplar Number: M8.82 Item: 82 Phase: Senior Grade: 8 Learning Outcome(s) and Assessment Standard(s): Learning Outcome 2: Patterns, Functions and Algebra Assessment Standard: We know this when the learner 8.2.3 Represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using: verbal descriptions; flow diagrams; tables; formulae and equations. 8.2.5 Solves equations by inspection, trial-and improvement or algebraic processes (additive and multiplicative inverses), checking the solution by substitution. 8.2.9 Interprets and uses the following basic algebraic vocabulary in context: term, expression, coefficient, exponent (or index), base, constant, variable, equation, formula (or rule). Learning Space: Assessment Hyperlinks: To be completed later. Number of questions for exemplar: 1 Rating: Easy questions: Medium questions: Question 1 Difficult questions: Assessment Task Questions: 1. a) If x is any even number on the interval (8; 4] , write down three ordered pairs x; y that satisfy the equation 3 2 x 2y 5 . b) For which integral values of x and y will xy 6 and y x 1 share the same values? c) Give one set of positive integral values of x and y for which y x 3 ? Solution 1. 3 x 2y 5 2 a) Any three of the following will be correct (6;7), (4; 5.5), (2; 4), 0; 2.5), (2; 1), (4;1 b) The integral value that gives a product of 6: x y x y y x 1? 1 6 6 1–6=-5 2 3 6 2 – 3 = -1 3 2 6 3–2=1 6 1 6 6–1=5 -1 -6 6 -1 – (-6) = -1+6 = 5 -2 -3 6 -2 – (-3) = -2+3 = 1 -3 -2 6 -3 – (-2) = -1 -6 -1 6 -6 – (-1) = -5 So the two answers that are possible x = 3 and y = 2 and also x = -3 and y = -2. c) y x 3 will be when x; y 6;1 as it will equal 5 at this point. The equation can be solved by inspection or we can solve it algebraically. The algebraic solution will resemble the solution to a simultaneous equation. y x 1 x 1 x 6 x2 x 6 0 x 3 x 2 0 x 2 or x 3 Then : y 3 or y 2 Interpreting what the inequality is telling us is a necessary and important skill for later application in algebra. Appendix of Assignment Tools Points on functions Equations Inequality