basic maths student handout.pdf

8/14/2019 Basic Maths Student Handout.pdf

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Kaplan Masterclass

Basic Maths


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Introduction

Symbols

Using your calculator

Order of operations

Rearranging equations

2

Ratios

Percentages

Simultaneous equations


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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


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Find the following buttons-Square:2

-e.g. 42 =

-Raising to any power:

or

or ^ or

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-e.g. 54 =

- Square rooting: or

-e.g. 25 =


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Find the following buttons-Calculating any root: x or

-e.g. 481 =

- Log: Log

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-e.g. Log 2 =

- Decimal to a fraction: SD

-e.g. 0.85 =


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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:

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TRY TO AVOID RETYPING IN A

NUMBER UNLESS UNAVOIDABLE


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Rounding example

e.g.-To the nearest thousand

-e.g. 123,456 to the nearest thousand =

-e.g. 987,654 to the nearest thousand =

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-To a specific number of decimal places

-e.g. 3.14159265 (pi) to 2d.p. =

-e.g. 3.14159265 (pi) to 4d.p. =


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Order of operations rules

Brackets

Order (i.e. raising to the power of)

Divide or

Multiply,

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Add or

Subtract


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Order of operations illustration

e.g. 7 + (6 x 52 +3) = ?

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Order of operations illustration

e.g.

IRR = L + NPVL x ( H - L )

(NPVL NPVH)

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Where L = 5, NPVL = 40,000, H = 10 & NPVH = 5,000,what is the IRR?


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Order of operations example

e.g.

PV = x 1

(1 + i)n

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Where x = 10,000 and i = 10%, what is the value of PV?


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Order of operation illustration

=

9 33 = 105 = 29 381


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Rearranging equations illustration

e.g.

P0 = D0Dividend yield

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Where P0 = 20 million & D0 = 1 million,

what is the dividend yield?


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Rearranging equations illustration

e.g. = a + b

100,000 = a + 4 x 2,000

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What is the value of a?


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Rearranging equations example

e.g. = a + b

5,000 = 100 + b x 50

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What is the value of b?


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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

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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?

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Ratio example

e.g. how much would each shareholder get if the profitswere 250,000 and they were to be split 2:3?

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Percentages

A percentage is a way of expressing a number as afraction of 100

Per cent (%) = per hundred

45% = 45 / 100 = 0.45

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To convert fraction/decimal to a % multiply by 100 To convert % to a fraction or decimal divide by 100


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Percentages quickly example

e.g.

5% =

15% =

One half of a percent =

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125% =

3.894% =


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Percentages quickly illustration

e.g. A sales value of 150,000 will increase by 5% nextyear to what?

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e.g. 40,000 with a 3% increase?

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e.g. 40,000 with a 23.75% increase?


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e.g. A sales value of 150,000 will decrease by 10% nextyear to what?

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e.g. 40,000 with a 30% decrease?

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e.g. 40,000 with a 6.40% decrease?


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Percentage changes illustration

e.g. What is the percentage change if sales moved from5m to 8m?

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Percentage changes examples


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Percentage changes illustration


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Percentage changes examples


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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

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Mark ups formulae

Equation approach:

Sales = Cost x (1 + P%)

Format approach:

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Sales 125%Costs 100%

Profit 25%


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Mark up example

e.g. calculate the sales price for a product with a 30%mark up that costs 40.

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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

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pro o


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Margin example

e.g. calculate the sales price for a product with a 30%margin that costs 42.

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Margin example

e.g. calculate the profit for a product with a 20% marginand a sale value of 90.

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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:

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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


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Simultaneous equations illustration

e.g. Solve the following to find and

5 + 2 = 34

+ 3 = 25

42


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Simultaneous equations illustration


5 + 2 = 18

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6 + 3 = 24


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O f


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Order of operations questions

e.g.

6 x (5 + 3) =

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5 x 22 =

2 + 5 x 3 =

O d f ti ti


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Order of operations question

e.g. ab where b = log r

log 2

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What is the value for?When a = 10

= 4

r = 90%

R i ti ti


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Rearranging equations question

F = O(1+g)n

e.g. What is the growth rate (g) if the original figure is

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10,000 (O), the final figure is 13,310 (F), and thenumber of years of growth is 3 (n)?

R ti ti


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Ratio question

e.g. how much would each shareholder get if the profitswere 360,000 and they were to be split 2:3:4?

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Si lt ti ti


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Simultaneous equations question


8 + 4 = 64

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7 + 2 = 50

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