Math NUMBER - calculators allowed!

GST

15%

Example is practise test Q1

1a 1400000 or 1.4 million 2SF (numbers) 1b = 0.15 x500 = 75 500 +75 575mL 1 c 2.4/1.2 = 2 tonnes. 1d 1.51x1011 151000000000 1e (1)Investment Space=$20 Carrot=0.45x200x1.15 =$103.50 Total cost=$123.50 (2) Super quality=2/5x200x1.24 =$99.20 Left=3/5x200=120kg Only sold=120x0.75=90kg Cost=90x$0.90=$81.00 Total sold=$180.20 Profit=$180.20-$103.50-$20 =$56.70

Q2

2a (5.8 × 106 ) ÷ 44500 = 130.337 = 1.30 x102 sheets No alternative. 2b $2688 2c Cost × 1.5 × 1.15 = Cost × 1.725 Half way Correct solution 2d 5.382 x 108 2e Investment after 5 years = $550,000 × 1.09555 = $867,810 Total with subsidy = $867,810 ×5/3 = $1,446,350 Cost without GST = $1,500,000 ÷ 1.15 = $1,304,347 Therefore there is enough money $867,810 2f 400734=340690(1+x)3 1.18=(1+x)3 X =0.06

Q3

3 a $22.18 × 1.15 = $25.51 5 boxes means =$25.51 × 5 = $127.54 3 b $25.80 3 c $2565/1.2=$2137.50 $2137.50/1.15=$1858.70 If two calculations only Two calculations and comparison values. 3 d $65190.48 Correct solution 3 e $499x3=$1497(parents Abby) 0.75x$499=$374.25 0.10x$499=$49.90 Total flight=$1921 $1921+69x+185x=6000 X=16.06 16days Total flight calculated Equation formed correctly 3f Cost plus import tax: 5.95 x 1.05 = $6.25 Profit added: 6.25 x 1.60 = $10.00 Adding GST : 10 x 1.15 = $11.50 Adding on Trade me fee : 11.5 x 1.10 = $12.65 Minimum price $12.65 $10.00 or $12,65 correct Correct solution but not fully explained Correct solution and fully explained.

Finding the whole original quantity

eg: 40% of class has blue eyes and that is 14 people, find the number of the peers in the class 40% of X=14 0.4x X=14 X= 14/0.4 X= 35

Adding and subtracting fractions with not same denominator

- always make sure the denominators are the same eg:1/2 + 1/3 - D are not equal, so find common multiple number =6 1x3/2x3 (3 because 2,4,6) + 1x2/3x2 = 3/6+2/6 = 5/6

improper fraction to mixed number

1 divide numerator by denominator put remainder over d eg: 2 2/5 = r 1/2 5/2 -> 2 1/2

Decimal to Fraction

Create top then bottom then simplify eg: first write decimal over 1 multiply top and bottom by 10 for every number after the decimal point - 0.75x100/1x100 (10 for on number, 100 for 2 etc...) 75 is 2 numbers so 100 75/ 100 simplify : 3/4 (or simply put it in numerator w bigger number)

Percentages to Decimal

Divide by 100

Fraction to Percentage

Divide numerator and denominator then multiply by 100 then add % sign

Fraction to Decimal

Divide numerator with denominator

Calculation for GST 2.0

GST /0.15 > price before GST x 1.15 > inc GST reverse: inc GST /1.15 > price before GST x0.15 > GST

simple interest

I= PRT/100 I= interest R= rate P= principal T= time

multiplier (increase)

M= 1+y/100 (y- percentage) original > x (1+y/100) = final same as opposite side just divide

Decimal to Percentages

Multiply (times) by 100

Percentage change

actual change/original value x 100% eg: % change when 200 is increased to 250 50/200x100 = 25%

Percentage to Fraction

convert percentage to to decimal (/100) then Create top then bottom then simplify (decimal to fraction)

Multiplying fractions

eg: 2/5 x 3/4 times numerator and times both denominator = 6/20 simplify! = 3/10

To find a percent of something

eg: 20% of 50 20/100x50 - percent divided by 100 times the amount

finding a fraction of a total given

eg: 2:3 2+3= 5 5 is denominator 2/5: 3/5

Adding fractions and subtracting with same denominator

eg: 4/5 + 3/5 = add up numerators = 7/5 - do same for subtract

divide fractions

eg: 4/5 / 2/3 = convert division sign to times simplify = 12/10 = 1 1/5

Standard form

eg: 543000 5.43000 moved 6 to the right = 5.43x10by the power of 6 (would written small and above) if moved to the left like 0.00004.891 point is after first number moved to the left 5 times make sure it is negative! = 4.981x10(-5)

Rounding to decimal places

eg: I want 2dp - after point answer= 8.245 look at 3rd digit and see if it is 5+ or under. if 1,2,3,4 leave 2nd number, if 5 or higher add it up.

Significant numbers

eg: I want 2sf - 2 numbers 1.24 - same as decimal places but number instead. so 1.2 and 4 is lower than 5 so, leave 2. = 1.2

ratios

eg: find common number then divide both sides by the same number - units should be the same eg: 3km : 500m 3000m :500m if ratios have decimals: multiply both sides by powers of 10 to get rid of point if have fractions: make bottoms same then multiply

Splitting a ratio

eg: split 40 in 3:5 3+5=8 - denominator 3/8 and 5/8 divide fraction then multiply by the number it wants you to do it by. 3/8 x 40 = 15 5/8 x 40 = 25 15+25=40

mixed number

eg:2 3/5 2 sets of 5s

compound interest (decrease)

final = P(1+r/100)n N= number of years original > x (1-r/100) > final same as opposite but divide

FDP

fraction or decimal x 100 = percentage percentage divided by 100 gives you fraction or decimal

mixed to improper

multiply denominator with big number = x x + numerator = imp denominator always stays the same

Calculation for GST

price before GST x1.15 > price including GST price including GST /1.15 > price before GST