Basic Maths Student Handout
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Transcript of Basic Maths Student Handout
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Kaplan Masterclass
Basic Maths
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Introduction
• Symbols
• Using your calculator
• Order of operations
• Rearranging equations
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• Ratios
• Percentages
• Simultaneous equations
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Symbols
Σ = Sum of
^ = to the power of (e.g. 102 is 10^2)
√ = square root
≥ = greater than or equal to
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≤ = less than or equal tox = average of x
σ = Standard deviation
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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 =
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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 =
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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 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 operations illustration
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
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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
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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
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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?
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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?
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Rearranging equations example
e.g.Y = a + bx
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
• 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% =
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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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Percentages quickly example
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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Percentages quickly example
e.g. A sales value of £150,000 will decrease by 10% nextyear to what?
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Percentages quickly example
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 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
e.g. What is the percentage change if sales moved from£12m to £15m?
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Percentage changes illustration
e.g. What is the percentage change if sales moved from£8m to £5m?
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Percentage changes examples
e.g. What is the percentage change if sales moved from£20m to £18m?
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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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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
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pro o
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Margins Formulae
• Equation approach:
Sales = Cost
(1 - P%)
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• Format approach:Sales 100%
Costs 75%
Profit 25 %
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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.
40
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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
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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
e.g. Solve the following to find x and y.
5x + 2y = 18
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6x + 3y = 24
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How does it help?
Speed Knowledge
Calculations
Made Simple
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Confidence
Improved chance of success
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.y = axb where b = log r
log 2
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What is the value for y?When a = 10
x = 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
e.g. Solve the following to find x and y.
8x + 4y = 64
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7x + 2y = 50