Basic Maths Student Handout

7/28/2019 Basic Maths Student Handout

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Kaplan Masterclass

Basic Maths



Introduction

• Symbols

• Using your calculator

• Order of operations

• Rearranging equations

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• Ratios

• Percentages

• Simultaneous equations



Symbols

Σ = Sum of

^ = to the power of (e.g. 102 is 10^2)

√ = square root

≥ = greater than or equal to

3

≤ = less than or equal tox = average of x

σ = Standard deviation



Using your calculator

• Find the following buttons-Square: x2

-e.g. 42 =

-Raising to any power: xy

or yx

or ^ or x□

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-e.g. 54 =

- Square rooting: √□or √

-e.g. √25 =



Using your calculator

• Find the following buttons-Calculating any root: x√ or □√□

-e.g. 4√81 =

- Log: Log

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-e.g. Log 2 =

- Decimal to a fraction: SD

-e.g. 0.85 =



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



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. =



Order of operations rules

• Brackets

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

• Divide or

• Multiply,

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• Add or

• Subtract



Order of operations illustration

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

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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?



Order of operations example

e.g.

PV = x x 1

(1 + i)n

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




x y xy x2 y2

([n∑x2 – (∑x)2 ] [n∑y2 – (∑y)2 ])

n∑xy – ∑x∑y=r

2 8 16 4 64

3 11 33 9 121

4 14 56 16 196

9 33 105 29 381

∑x ∑y ∑xy ∑x2 ∑y2



Order of operation illustration

([n∑x2 – (∑x)2 ] [n∑y2 – (∑y)2 ])

n∑xy – ∑x∑y=r

∑x = 9 ∑y = 33 ∑xy = 105 ∑x2 = 29 ∑y2 = 381



Rearranging equations rules

• Write out the equation (from a formula sheet or frommemory)

• Replace any letters with numbers that are given in theinformation

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• en rearrang ng, you mus o e same ng o osides of the equation



Rearranging equations illustration

e.g.

P0 = D0

Dividend yield

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Where P0 = £20 million & D0 = £1 million,

what is the dividend yield?



Rearranging equations illustration

e.g.Y = a + bx

100,000 = a + 4 x 2,000

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What is the value of a?



Rearranging equations example

e.g.Y = a + bx

5,000 = 100 + b x 50

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What is the value of b?



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



Percentages quickly

• The quick way-DON’T use the ‘%’ button on the calculator

- INSTEAD convert the % given into a decimal by moving the decimal 2places to the left then use that number in the calculator

- Don’t waste time writing down separate numbers

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Percentages quickly example

e.g.

5% =

15% =

One half of a percent =

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125% =

3.894% =



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?




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?



Percentage changes formulae

• Two ways of calculating percentage change:

New – Old or New

Old Old

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Percentage changes illustration

e.g. What is the percentage change if sales moved from£5m 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%



Mark up example

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

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Mark up example

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

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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

37

pro o



Margins Formulae

• Equation approach:

Sales = Cost

(1 - P%)

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• Format approach:Sales 100%

Costs 75%

Profit 25 %



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 x and y

Step 1:Multiply one or both equations so that the number of either x’s or y’s is equal

Step 2:’ ’

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Step 3:Rearrange the resulting equation to find the value of either x or y

Step 4:

Substitute the value calculated in step 3 into one of the original equations



Simultaneous equations illustration

e.g. Solve the following to find x and y.

5x + 2y = 34

x + 3y = 25

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Simultaneous equations illustration


5x + 2y = 18

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6x + 3y = 24



How does it help?

Speed Knowledge

Calculations

Made Simple

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Confidence

Improved chance of success

O f



Order of operations questions

e.g.

6 x (5 + 3) =

45

5 x 22 =

2 + 5 x 3 =

O d f ti ti



Order of operations question

e.g.y = axb where b = log r

log 2

46

What is the value for y?When a = 10

x = 4

r = 90%

R i ti ti



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



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



Simultaneous equations question


8x + 4y = 64

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7x + 2y = 50

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Basic Maths Student Handout