Download Algebra2.1#2

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