basic maths student handout.pdf
TRANSCRIPT
-
8/14/2019 Basic Maths Student Handout.pdf
1/49
Kaplan Masterclass
Basic Maths
-
8/14/2019 Basic Maths Student Handout.pdf
2/49
Introduction
Symbols
Using your calculator
Order of operations
Rearranging equations
2
Ratios
Percentages
Simultaneous equations
-
8/14/2019 Basic Maths Student Handout.pdf
3/49
Symbols
= Sum of
^ = to the power of (e.g. 102 is 10^2)
= square root
= greater than or equal to
3
= less than or equal to = average of
= Standard deviation
-
8/14/2019 Basic Maths Student Handout.pdf
4/49
Using your calculator
Find the following buttons-Square:2
-e.g. 42 =
-Raising to any power:
or
or ^ or
4
-e.g. 54 =
- Square rooting: or
-e.g. 25 =
-
8/14/2019 Basic Maths Student Handout.pdf
5/49
Using your calculator
Find the following buttons-Calculating any root: x or
-e.g. 481 =
- Log: Log
5
-e.g. Log 2 =
- Decimal to a fraction: SD
-e.g. 0.85 =
-
8/14/2019 Basic Maths Student Handout.pdf
6/49
Using your calculator cont.
Functions to speed up calculations- Bringing up the last answer: Ans
- Storing a number: STO
-Recalling a number: RCL
-Amending a number:
6
TRY TO AVOID RETYPING IN A
NUMBER UNLESS UNAVOIDABLE
-
8/14/2019 Basic Maths Student Handout.pdf
7/49
Rounding example
e.g.-To the nearest thousand
-e.g. 123,456 to the nearest thousand =
-e.g. 987,654 to the nearest thousand =
7
-To a specific number of decimal places
-e.g. 3.14159265 (pi) to 2d.p. =
-e.g. 3.14159265 (pi) to 4d.p. =
-
8/14/2019 Basic Maths Student Handout.pdf
8/49
Order of operations rules
Brackets
Order (i.e. raising to the power of)
Divide or
Multiply,
8
Add or
Subtract
-
8/14/2019 Basic Maths Student Handout.pdf
9/49
Order of operations illustration
e.g. 7 + (6 x 52 +3) = ?
9
-
8/14/2019 Basic Maths Student Handout.pdf
10/49
Order of operations illustration
e.g.
IRR = L + NPVL x ( H - L )
(NPVL NPVH)
10
Where L = 5, NPVL = 40,000, H = 10 & NPVH = 5,000,what is the IRR?
-
8/14/2019 Basic Maths Student Handout.pdf
11/49
Order of operations example
e.g.
PV = x 1
(1 + i)n
11
Where x = 10,000 and i = 10%, what is the value of PV?
-
8/14/2019 Basic Maths Student Handout.pdf
12/49
-
8/14/2019 Basic Maths Student Handout.pdf
13/49
Order of operation illustration
=
9 33 = 105 = 29 381
-
8/14/2019 Basic Maths Student Handout.pdf
14/49
-
8/14/2019 Basic Maths Student Handout.pdf
15/49
Rearranging equations illustration
e.g.
P0 = D0Dividend yield
15
Where P0 = 20 million & D0 = 1 million,
what is the dividend yield?
-
8/14/2019 Basic Maths Student Handout.pdf
16/49
Rearranging equations illustration
e.g. = a + b
100,000 = a + 4 x 2,000
16
What is the value of a?
-
8/14/2019 Basic Maths Student Handout.pdf
17/49
Rearranging equations example
e.g. = a + b
5,000 = 100 + b x 50
17
What is the value of b?
-
8/14/2019 Basic Maths Student Handout.pdf
18/49
Ratios
A ratio is an expression that compares quantitiesrelative to each other
Ratios are given in the format a:b:c
A ratio can be used to show how something is to be spit
18
-
8/14/2019 Basic Maths Student Handout.pdf
19/49
Ratio illustration
e.g. a partnership of 3 partners have an agreement toshare profits of 14,000 in the proportions 1:2:4.
How much will each of the partners get?
19
-
8/14/2019 Basic Maths Student Handout.pdf
20/49
Ratio example
e.g. how much would each shareholder get if the profitswere 250,000 and they were to be split 2:3?
20
-
8/14/2019 Basic Maths Student Handout.pdf
21/49
Percentages
A percentage is a way of expressing a number as afraction of 100
Per cent (%) = per hundred
45% = 45 / 100 = 0.45
21
To convert fraction/decimal to a % multiply by 100 To convert % to a fraction or decimal divide by 100
-
8/14/2019 Basic Maths Student Handout.pdf
22/49
-
8/14/2019 Basic Maths Student Handout.pdf
23/49
Percentages quickly example
e.g.
5% =
15% =
One half of a percent =
23
125% =
3.894% =
-
8/14/2019 Basic Maths Student Handout.pdf
24/49
Percentages quickly illustration
e.g. A sales value of 150,000 will increase by 5% nextyear to what?
24
-
8/14/2019 Basic Maths Student Handout.pdf
25/49
Percentages quickly example
e.g. 40,000 with a 3% increase?
25
e.g. 40,000 with a 23.75% increase?
-
8/14/2019 Basic Maths Student Handout.pdf
26/49
Percentages quickly example
e.g. A sales value of 150,000 will decrease by 10% nextyear to what?
26
-
8/14/2019 Basic Maths Student Handout.pdf
27/49
Percentages quickly example
e.g. 40,000 with a 30% decrease?
27
e.g. 40,000 with a 6.40% decrease?
-
8/14/2019 Basic Maths Student Handout.pdf
28/49
-
8/14/2019 Basic Maths Student Handout.pdf
29/49
Percentage changes illustration
e.g. What is the percentage change if sales moved from5m to 8m?
29
-
8/14/2019 Basic Maths Student Handout.pdf
30/49
Percentage changes examples
e.g. What is the percentage change if sales moved from12m to 15m?
30
-
8/14/2019 Basic Maths Student Handout.pdf
31/49
Percentage changes illustration
e.g. What is the percentage change if sales moved from8m to 5m?
31
-
8/14/2019 Basic Maths Student Handout.pdf
32/49
Percentage changes examples
e.g. What is the percentage change if sales moved from20m to 18m?
32
-
8/14/2019 Basic Maths Student Handout.pdf
33/49
Mark ups
A mark up is where the profit is expressed as apercentage of the cost
e.g. a 25% mark up on 100 cost would mean a profit of
33
-
8/14/2019 Basic Maths Student Handout.pdf
34/49
Mark ups formulae
Equation approach:
Sales = Cost x (1 + P%)
Format approach:
34
Sales 125%Costs 100%
Profit 25%
-
8/14/2019 Basic Maths Student Handout.pdf
35/49
Mark up example
e.g. calculate the sales price for a product with a 30%mark up that costs 40.
35
-
8/14/2019 Basic Maths Student Handout.pdf
36/49
-
8/14/2019 Basic Maths Student Handout.pdf
37/49
Margin
A margin is where the profit is expressed as apercentage of the sales price
e.g. a 25% margin on 100 sales price would mean a
37
pro o
-
8/14/2019 Basic Maths Student Handout.pdf
38/49
-
8/14/2019 Basic Maths Student Handout.pdf
39/49
Margin example
e.g. calculate the sales price for a product with a 30%margin that costs 42.
39
-
8/14/2019 Basic Maths Student Handout.pdf
40/49
Margin example
e.g. calculate the profit for a product with a 20% marginand a sale value of 90.
40
-
8/14/2019 Basic Maths Student Handout.pdf
41/49
Simultaneous equations rules
Two linear equations both containing unknown values of and
Step 1:Multiply one or both equations so that the number of eithers ors is equal
Step 2:
41
Step 3:Rearrange the resulting equation to find the value of either or
Step 4:
Substitute the value calculated in step 3 into one of the original equations
-
8/14/2019 Basic Maths Student Handout.pdf
42/49
Simultaneous equations illustration
e.g. Solve the following to find and
5 + 2 = 34
+ 3 = 25
42
-
8/14/2019 Basic Maths Student Handout.pdf
43/49
Simultaneous equations illustration
e.g. Solve the following to find and
5 + 2 = 18
43
6 + 3 = 24
-
8/14/2019 Basic Maths Student Handout.pdf
44/49
O f
-
8/14/2019 Basic Maths Student Handout.pdf
45/49
Order of operations questions
e.g.
6 x (5 + 3) =
45
5 x 22 =
2 + 5 x 3 =
O d f ti ti
-
8/14/2019 Basic Maths Student Handout.pdf
46/49
Order of operations question
e.g. ab where b = log r
log 2
46
What is the value for?When a = 10
= 4
r = 90%
R i ti ti
-
8/14/2019 Basic Maths Student Handout.pdf
47/49
Rearranging equations question
F = O(1+g)n
e.g. What is the growth rate (g) if the original figure is
47
10,000 (O), the final figure is 13,310 (F), and thenumber of years of growth is 3 (n)?
R ti ti
-
8/14/2019 Basic Maths Student Handout.pdf
48/49
Ratio question
e.g. how much would each shareholder get if the profitswere 360,000 and they were to be split 2:3:4?
48
Si lt ti ti
-
8/14/2019 Basic Maths Student Handout.pdf
49/49
Simultaneous equations question
e.g. Solve the following to find and
8 + 4 = 64
49
7 + 2 = 50