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