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NH 849 N.C.E.A. LEVEL 1.1 ALGEBRA. 6. THE VEGETABLE GARDEN. 4 CREDITS. You are advised to spend 30 minutes answering the questions in this booklet. You should show ALL working. 1. Solve each of the following equations a) 9x 4 3x 8 b) 3 1 x4 2 2 c) ( x 2 )( 2 x 3 ) 0 8( x 1 ) 3( x 3 ) 2. Expand and simplify the expression 3. Factorise fully 4x 2 9 4. Simplify ( 4 x 3 )2 2 5. Kelly buys some fertiliser for her vegetable garden. A formula for the amount of fertiliser (grams) needed is given on the side of the pack. where 20 P g 2 F W W = Number of litres of water ; g = area of garden in m2 ; P = Number of plants in the garden a) Use has the formula to work out how much fertilizer Kelly will 9 L of water for 12 m2 of garden, which has six plants. b) Show how Kelly should rearrange the formula to make g the subject. need if she 6. Kelly is worried about the number of weeds growing in her garden. She decides to count the number of new weeds each week in a new patch of garden. In the first week she counts 3 weeds. In the second week she counts 8 weeds. In the third week she sees 15 new weeds. Kelly suspects that there is a quadratic pattern in the number of new weeds each week. Number of new weeds 1st week 2nd week 3rd week 3 8 15 Complete the table to help find the rule, 7. 4th week 5th week nth week “ W = “, for the number of new weeds, W, for the nth week. Kelly decides to plant broccoli and cauliflower in her vegetable garden. Each broccoli plant cost 50 cents while each cauliflower plant cost 30 cents. In total she spends $6.30 to buy 17 plants. Solve the pair of simultaneous equations to find the number of broccoli plants and the number of cauliflower plants she bought. 30c 50b 630 c b 17 8. Kelly decides to build 2 new rectangular garden beds between the shed and the fence. The garden beds must have the same dimensions and be 10m2 each. She has bought 18m of plastic edging for the new beds. She will not need to put edging on the sides of the garden beds that are against the fence and shed. Fence Garden Beds Shed Write at least ONE equation to model this situation. Use the model to find the dimensions of the garden beds. NH 849 The Vegetable Garden Achievement Criteria Use straightforward algebraic methods. Question Code Evidence Judgment Sufficiency One (a) A1 x 2 (b) A1 x3 (c) A1 3 x 2, x 2 No Alternative Both solutions needed Two A2 5x 1 No Alternative Three A2 Four A2 8x 6 Accept 23x6 Five (a) A2 29.3g (1 dp) Accept approx 30 g Units not needed g FW 20 P Correct algebraic statements must be used. ACHIEVEM ENT plus Accept other variables. 2 of Code M or 3 code M No Alternative No Alternative (2 x 3)( 2 x 3) No Alternative 2 of Code A1 AND 3 of Code A2 Solve equations. Achievement with Merit Five (b) Use algebraic methods and solve equations in context Six M/A2 M/A2 x2 2x Seven or x( x 2) M/A1 b=6 c=11 Achievement with Excellence Let x= width of bed Let y = length of bed 4 x 2 y 18 Use algebraic strategies to investigate and solve problems x y 10 0 2 x 9 x 10 2 Eight 0 (2 x 5)( x 2) x 2.5 & x 2 A1/M E 2 possible answers: when width is 2.5m length is 4m when width is 2m length is 5m. At least 1 correct equation must be given to model the situation At least one correct algebraic statement must be used to get the solution. Both pairs of numbers must be given. MERIT plus Code E