Download N H 2 5 7 7. NCEA. LEVEL 1.1. ALGEBRA. 13 - SMC-Math

NH 2577
N.C.E.A. LEVEL 1.1
ALGEBRA. 13.
THE FLORIST.
4 CREDITS.
You are advised to spend 30 minutes answering these questions.
You should show ALL working.
1.
2.
Solve these equations:
a)
3 ( k  5 )  21
b)
8t – 7 = 3t + 9
c)
7d(d – 3) = 0
a)
Expand and simplify
(4x – 5)(x + 3)
b)
Simplify
6r 7
15r 2
c)
A sphere with a surface area A has its radius r given by the formula r =
A
.
4
Find r when A = 48.
4i 2i
5
7
3.
Simplify
4.
There are five consecutive odd integers. The sum of the first two integers is thirty-seven less than the
sum of the last three integers. Use this information to write an equation.
Solve your equation to find the five integers.
5.
A florist sells roses for $ 12.50 a bunch and daffodils for $ 4.50 a bunch. Benjamin ordered R bunches
of roses and D bunches of daffodils. Altogether he ordered a total of 30 bunches and spent $ 207.
Solve the pair of simultaneous equations below to find the number of bunches of roses and the number
of bunches of daffodils Benjamin bought.
R + D = 30
12.5R + 4.5D = 207
6.
A two digit number has its tens digit five more than two times the units (ones) digit.
The number is one less than nine times the sum of its digits. What is the number ?
Show all your working.
Set out your working logically.
Use correct mathematical statements.
NH 2577
ASSESSMENT SCHEDULE : ALGEBRA : THE FLORIST : 90147
Achievement
Achievement Criteria
Solve equations.
No
1(a) k = 2
1(b) t = 16
Evidence
Code
Judgement
A1 No alternative
A1 Or equivalent
5
Use straight forward
algebraic methods.
1(c) d = 0 or d = 3
A1
2(a) 4x2 + 7x - 15
2(b) 2r 5
A2
A2
Both solutions
needed
No alternative
Or equivalent
A2
M
Or equivalent
Or equivalent
Sufficiency
Achievement:
2 x A1
2 x A2
Replacement
evidence: Q3, 4,
5, 6
Achievement with
Excellence
Achievement with Merit
5
Use algebraic
methods and solve
equations in context.
2(c) r = 1.95
2i
4i
7
5
18 i
3
x x =
4
7
35
5
5
7
[(x + (x + 2)]
= [(x + 4) + (x + 6) + (x + 8)] -37
M
Integers are 21, 23, 25, 27, 29
Use algebraic
strategies to
investigate and solve
problems.
5
R=9
D = 21
M
6
Let xy be the number
x = 2y + 5
10x + y = 9(x + y) -1
x = 2y + 5
x = 8y -1
x=7
y=1
Number is 71
M
Achievement
with Merit:
CAO is M(or
EITHER
A1)
Achievement plus
A2 solved with 2 x M
algebraic
working
OR
CAO is M(or
3xM
A1)
A2 solved with Replacement
algebraic
evidence: Q6
working
CAO is M(or
Achievement
A1)
with
A2 solved with Excellence:
algebraic
Merit plus
working
E