# 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)**