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Educator and Tagging Information:
Learning Area:
Maths
Resource Name:
Maths
Assessment Exemplar Number:
M8.82
Item:
82
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
8.2.3 Represents and uses relationships between variables in order to determine input and/or output
values in a variety of ways using: verbal descriptions; flow diagrams; tables; formulae and
equations.
8.2.5 Solves equations by inspection, trial-and improvement or algebraic processes (additive and
multiplicative inverses), checking the solution by substitution.
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:
1
Rating:
Easy questions:
Medium questions:
Question 1
Difficult questions:
Assessment Task
Questions:
1.
a)
If x is any even number on the interval (8; 4] , write down three ordered pairs  x; y 
that satisfy the equation
3
2
x  2y  5 .
b)
For which integral values of x and y will xy  6 and y  x  1 share the same values?
c)
Give one set of positive integral values of x and y for which y  x  3 ?
Solution
1.
3 x  2y 5
2
a)
Any three of the following will be correct
(6;7), (4;  5.5), (2;  4), 0;  2.5), (2;  1), (4;1
b)
The integral value that gives a product of 6:
x y x y
y  x  1?
1 6 6
1–6=-5
2 3 6
2 – 3 = -1
3 2 6
3–2=1
6 1 6
6–1=5
-1 -6 6
-1 – (-6) = -1+6 = 5
-2 -3 6
-2 – (-3) = -2+3 = 1
-3 -2 6
-3 – (-2) = -1
-6 -1 6
-6 – (-1) = -5
So the two answers that are possible x = 3 and y = 2 and also x = -3 and y = -2.
c)
y  x  3 will be when  x; y    6;1 as it will equal 5 at this point.
The equation can be solved by inspection or we can solve it algebraically.
The algebraic solution will resemble the solution to a simultaneous equation.
y  x 1
  x  1 x  6
 x2  x  6  0
  x  3 x  2   0
 x  2 or x  3
Then : y  3 or y  2
Interpreting what the inequality is telling us is a necessary and important skill for later application
in algebra.
Appendix of Assignment Tools
Points on functions
Equations
Inequality