Download 1 - SMC-Math

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
x4
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
x3
(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