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Educator and Tagging Information:
Learning Area:
Maths
Resource Name:
Maths
Assessment Exemplar Number:
M8.88
Item:
88
Phase:
Senior
Grade:
8
Learning Outcome(s) and Assessment Standard(s):
Learning Outcome 2: Patterns, Functions and Algebra
Assessment Standard: We know this when the learner
8.2.5 Solves equations by inspection, trial-and improvement or algebraic processes (additive and
multiplicative inverses), checking the solution by substitution.
8.2.8 Uses conventions of algebraic notation and the commutative, associative and distributive laws
to: classify terms as like or unlike, and to justify the classification; collect like terms; multiply or
divide an algebraic expression with one, two or three terms by a monomial; simplify algebraic
expressions given in bracket notation, involving one or two sets of brackets and two kinds of
operations; compare different representations of algebraic expressions involving one or more
operations, selecting those which are equivalent, and justifying own choice; write algebraic
expressions, formulae or equations in simpler or more useful equivalent forms in context.
8.2.9 Interprets and uses the following basic algebraic vocabulary in context: term, expression,
coefficient, exponent (or index), base, constant, variable, equation, formula (or rule).
Learning Space:
Assessment
Hyperlinks:
To be completed later.
Number of questions for exemplar:
2
Rating:
Easy questions:
Question 1 and 2
Medium questions:
Difficult questions:
Assessment Task
Questions:
1.
2.
In each of the following, solve for x:
a)
120  3x  69
b)
5x2 15x  0
c)
3x   2x  5  4x  3  2  2x 1
d)
x2  2x  3
5
x3
e)
 x  1 x  3  x2  2  34
f)
2  3x  4x 12
g)
2  x  3  4
For each of the following, simplify each expression:
a)
b)
c)
    x  
 x3

6
3
2 2

1
x2
2  3  2    3  2 
5   2  4
2 x(3 pq  4qr  6 pr )
3xp
Solution
1.
a)
120  3 x  69
3 x  69  120
3 x  51
51
3
 x  17
x 
b)
5 x 2  15 x  0
 5 x ( x  3)  0
 x  3  0 or 5 x  0
 x  3 or x  0
c)
3 x   2 x  5   4 x  3  2  2 x  1
 3x  2 x  5  4 x  3  4 x  2
 x  5  1
 x  1  5
 x  6
d)
x2  2 x  3
5 ;
x  3
x3
x2  2 x  3
 ( x  3) 
 5  ( x  3)
x3
 x 2  2 x  3  5( x  3)
 x 2  2 x  3  5 x  15
 x 2  2 x  3  5 x  15  0
 x 2  3x  18  0
 ( x  6)( x  3)  0
 x  6 or
x  3
n.a. since x 3
e)
 x  1 x  3  x 2  2  34
 x 2  x  3x  3  x 2  2  34
 x 2  4 x  3  x 2  2  34
 4 x  1  34
 4 x  33
x 
33 
3

 or 8 or 8.75 
4
4

f)
)
2  3 x  4 x  12
 2  12  4 x  3 x
14  7 x
 7 x  14
x  2
g)
2 x3 4
2  x  3  4
2  3  x  4  3
5  x  1
2.
a)
    x  
 x3

6
3
2 2

1
x2
1
  x 54  x12   2
x
1
  x 66   2
x
64
x
3
  x18  x 4  
1
x2
b)
2  3  2    3  2 
5   2  4
((2  3)  ( 2  2))  (3  2)
5  (2  4)
(6  ( 4))  (5)

5  (2)
(6  4)  5

5 2
2  5

5 2
7

7
 1

or
2  3  2    3  2 
5   2  4
2(1)  (5)
5  (2)
2  5

5 2
7

7
 1

c)
2 x(3 pq  4qr  6 pr ) 2(3 pq  4qr  6 pr )

3xp
3p
Textbooks are full of these types of problems and in this item bank collection questions like these
are deliberately kept at a minimum.
Appendix of Assignment Tools
Solving equations
Solving the inequality
Fractions
Variable
Simplifying algebraic expressions