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NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 1 of 3 SAMPLE ASSESSMENT SCHEDULE Mathematics and Statistics 91028 (1.3): Investigate relationships between tables, equations or graphs. Assessment Criteria Achievement Merit Investigate relationships between tables, equations and graphs. Excellence Investigate relationships between tables, equations and graphs, using relational thinking. Investigate relationships between tables, equations and graphs, using extended abstract thinking. Evidence Statement One Expected Coverage Achievement Merit Excellence Investigates relationships between tables, equations and graphs by: Investigates relationships between tables, equations and graphs, using relational thinking, by: Investigates relationships between tables, equations and graphs, using extended abstract thinking, by: THREE of: TWO of: TWO of: T 4n 1 (ii) Graph drawn from equation or table. drawing a correct graph with n as a continuous variable drawing a correct graph with n=1 to 10 as a continuous variable drawing a correct graph up from n=1 to 10 as a discrete variable with no y intercept. (iii) Rule given using the context to find the solution of 324 forming a quadratic model with minor errors. forming a correct generalisation forming the correct symbolic representation of a relationship forming and using the correct symbolic representation of a relationship demonstrating an understanding of one important concept (perhaps vaguely expressed). demonstrating an understanding of both important concepts but with incomplete description(s). (a)(i) S 2n 3n 2 (b) (i) T 5n (ii) T (6) 30 (iii) The gradient is steeper having increased from 4 to 5, and both graphs begin at the point (1,5) linking table to equation demonstrating an understanding of both important concepts with clear and complete descriptions. NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 2 of 3 Two (a) (i) Expected coverage P 20x 50 Or equivalent Achievement Merit Excellence Investigates relationships between tables, equations and graphs by: Investigates relationships between tables, equations and graphs, using relational thinking, by: Investigates relationships between tables, equations and graphs, using extended abstract thinking, by: TWO of: TWO of: TWO of: linking the graph to the equation correctly or solving one of the problems correctly linking the graph to the equation correctly linking the graph to the equation correctly using the graph to find a solution to one problem (ii) Cost of 2kg bag is $10 (accept $5 per kg) (iii) $150 profit over 10 kg implies $30 for 2kg bag (accept $15 per kg) (iv) The y intercept becomes -45 instead of -50. But gradient remains the same (as they are sold at the same price) demonstrating an understanding of one important concept (perhaps vaguely expressed) demonstrating an understanding of both important concepts but with incomplete description(s) demonstrating an understanding of both important concepts with clear and complete descriptions (v) Gradient is reduced after 6 kg of sausages have been sold. Extra profit per extra kg sold drops from $20 to $10 Price per kg drops from$20 to $10 (halves) Overall profit reduced from $15 per kg at original price to $11 per kg now. ($110÷10, per kg) demonstrating an understanding of the change gradient (perhaps vaguely expressed). demonstrating an understanding of the change in gradient with specific values quoted but not connected to the context. demonstrating an understanding of the change gradient with specific values quoted and clearly connected to the context. using the graph to find solutions to both problems NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 3 of 3 Three (a) (i) Expected coverage x intercepts 1 and -2 y intercept 2 (ii) y = -(x-1)(x+2) y = -(x+0.5)2+2.25 y = -x2 – x + 2 (iii) y = -x2 + 5x + 1 y = -(x+2.5)2+7.25 new y-intercept =1 Achievement Merit Excellence Investigates relationships between tables, equations and graphs by: Investigates relationships between tables, equations and graphs, using relational thinking, by: Investigates relationships between tables, equations and graphs, using extended abstract thinking, by: THREE of: TWO of: TWO of: giving either the intercepts or the equation. giving a complete solution sketching the new graph and quoting the new y-intercept correctly developing the equation of the new graph but not giving the yintercept sketching the graph to give the correct shape, with the vertex clearly shown to reach above 6 (b) (i) Correct graph drawn with smooth curves sketching the graph to give the correct shape, even if the vertex is not clearly shown to reach above 6 (ii) For maximum value x = 2.5 y = 6.25 quoting a maximum value consistent with the graph drawn above 4 x x 5 stating the length of the support as 3m, with no algebraic or graphical justification. (iii) x2 5x 4 0 x 1 or 4 length of support =3 stating and solving either consistently an incorrect equation (of comparable complexity), or incorrectly solving the correct equation. developing the equation of the new graph and giving the y-intercept as 1 stating and solving completely the equation connecting the y-value of 4 with the length of the support being 3m. Judgement Statement Achievement Achievement with Merit Achievement with Excellence Minimum of: 2A Minimum of: 2M Minimum of: 2E