# CPA | CIFA – QUANTITATIVE ANALYSIS REVISED STUDY NOTES

### MASOMO MSINGI PUBLISHERS APP – Click to download and access all our soft copy materials

Below is sample of QUANTITATIVE ANALYSIS STUDY NOTES as per July 2021 syllabus

You can buy using our APP or in HARD COPY

For enquiries: Call, Text or WhatsApp 0728 776 317

# TOPIC 1

### FUNCTIONS

Functions are often representatives of real phenomena or events. Functions therefore are models. Obtaining a function to act as a model is commonly the key to understanding business in many areas.

Functions may be represented by formulae. There are a number of common ways in which functions are presented and used. We shall consider functions given by formulae, since this provides a natural context for explaining how a function works.

1. Functions of one variable

If you get a job that pays Ksh 200 per hour, the amount of money M that you earn depends on the number of hours (h) that you work, and the relationship is given by a simple function:

The formula M=200h shows that the money M that you earn depends on the number of hours worked. We say that M is a function of h.

In this context, h is a variable whose value we may not know until the end of the week. Once the value of h is known, the formula M=200h can be used to calculate the value of M. To emphasise that M is a function of h, it is common to write M=M(h),so that M(h)=700h.

Example 1

if you work 30 hours, then the function M(30) is the money you would earn. To calculate the amount earned, you need to replace the formula by 30. Thus, M = M(30) = 700×30 = sh. 21,000.

Note:

• It is important to remember that h is measured in hours and M is measured given is Kenya shillings. The function/formula is not useful unless you state in words the units you are using.
• We would also use different letters or symbols for the variables. Whatever letter/symbol used, it is critical that you explain in word what they mean.

We normally write functions as f(x) and read as “function f of x”. We could use other letters such as g, p, H or h and write the function of x as g(x), p(x), H(x) or h(x).

Given f(x) = 3x +5, the value of this function f(x) when x=0 is written as f(0). The values are obtained by substituting.

Example 2

1. a) Given f(x) = 3x + 5, find i) f(0), ii) f(2) and iii) f(-2).
2. b) Given that h(x) =2×2 +5x +3, find i) h(0). ii) h(-2) and iii) h(3).
3. c) Given that G(t) = 2 +3t – 5t2 +t3, find i) g(-1) and g(2).
4. d) If h(x) = 5 – 2x, find the value of x for which the function is zero.

Solution:

1. a) i) f(0) =3(0) + 5 = 0 + 5 = 5
2. ii) f(2) =3(2)+5 = 6 + 5=11

iii) f(-2) = 3(-2) + 5 = -6 +5 = -1

1. b) i) h(0) = 2(0)2+ 5(0)+3 = 3
2. ii) h(-2) = 2(-2)2 + 5(-2) +3 =1

iii)  h(3) = 2(3)2+ 5(3)+3 = 36

1. c) i) G(-1) = 2+3(-1)-5(-1)2-2(-1)3 = -4
2. ii) G(2) = 2+3(2) – 5(2)2 – 2(2)3 = -28

1. d) h(x) = 5-2x = 0

-2x = – 5 x = 2.5

Example 2. 3

1. a) If f(x) = 5x -3. find f(x+2).
2. b) If y = g(x) = 3x – 7. find g(y) in terms of x.

### MASOMO MSINGI PUBLISHERS APP – Click to download and access all our soft copy materials

(Visited 735 times, 1 visits today) 