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Non-moderated Mathematics Achievement Standard 2.1 Manipulate Algebraic Expressions And Solve Equations Time allowed: 50 minutes 1. Expand and simplify (k+1)(k+2)(k-3) 2. Simplify 3. Factorise 4. Write as the log of a single number 3log2 – log4 5. Solve 5(7 x -9) = 12 x + 5 6. Solve 6x = x +2 7. Solve 3x = 2 8. A mathematician says “the number of hours I work each week is one more than double my hourly rate.” If she earns $155 per week. This gives the formula: x (2 x + 1) = 155 where x is the hourly rate. Find how much she earns per hour to 2dp. 9. Butter is twice as expensive as margarine per kg. A company buys 3 times as much butter as margarine and a weekly order costs $52. If the order included 5kg of butter, what is the price per kg of butter. 10. Solve log327 = x + 2 11. The cost of land is believed to be given by Aekt Dollars, where t is the number of years after purchase, and A and k are constants. After 3 years the value of the land was $112,486 and after 7 years the value of the land was $131,593. Find the value of the land after 10 years. 4ab ÷ 8a 5 b (i) 16 - h2 (ii) 3k2 + 18k + 24 ASSESSMENT SCHEDULE 2.1 Manipulate Algebraic Expressions and Solve Equations. Achievement Criteria Manipulate algebraic expressions. Question ACHIEVEMENT ACHIEVEMENT WITH MERIT Solve problems involving equations. Judgement Sufficiency 1 k2 -7k - 6 ACHIEVEMENT: 2 4b2 25 3 out of 4 correct from number one to four 3 (i) Solve equations. Evidence (4-h)(4+h) and (ii) 3(k+4)(k+2) 4 log2 5 x = 50 (2.17 2dp) 6 x = 2 or -1 3 2 7 0.63 (2dp) 8 $8.56 9 $2.60 p/kg 10 x=1 2 out of 3 correct from numbers five to seven Replacement evidence: ACHIEVEMENT WITH MERIT: 2 out of 3 correct Replacement evidence: ACHIEVEMENT WITH EXCELLENCE Achievement Criteria Question Choose algebraic techniques and strategies to solve problems. 11 Evidence k = 0.03922 A = 100,000 C (ten years) = 148,023 Judgement Error of rounding acceptable. Correct if find k and A only Sufficiency ACHIEVEMENT WITH EXCELLENCE: Must have question 11