Exam-style Questions: Advanced Algebra
1. The function f is given by:
Given that:
where A, B and C are constants,
(i) find the values of B and C,
(ii) show that A = 0.
(Marks available: 4 marks)
Answer outline and marking scheme for question: 1
Give yourself marks for mentioning any of the points below:
(max 3 marks)
(max 1 mark)
(Marks available: 4)
2. The function f is defined for the domain by:
a) Deduce that f is a decreasing function for all.
(Marks available: 2)
Answer outline and marking scheme for question: 2
a) The function f(x) is decreasing if f '(x) is negative. Therefore we need to show that f '(x) is less than zero, shown below:
rearranging this and changing back to square roots gives:
rearranging further gives:
which is always true for all.
(2 marks)
(Marks available: 2)
3. A function is given by:
find the value of the constants A and B.
(Marks available: 3)
Answer outline and marking scheme for question: 3
Give yourself marks for mentioning any of the points below:
Adding the two fractions on the right hand side gives:
As the denominators are now the same the numerators must match as well.
Therefore:
Selecting x = -1, will eliminate the constant B.
This gives:
-2 -1 = A (-3 + 2 )
-3 = -A
A = 3
Selecting x = 2/3 to this will eliminate the constant A.
This gives:
-2/3 x 2 -1 = B (-2/3 +1)
-4/3 -1 = B (1/3)
-7/3 = 1/3 B
-7 = B
B = -7
Therefore:
(Marks available: 3)
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