Simplifying and sharing in a ratio, direct and inverse proportion, compound measures such as speed and density, and compound interest with growth and decay.
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1.How do you simplify a ratio?
Divide every part by their highest common factor.
2.Simplify the ratio 12 : 18.
Divide both by 6 to get 2 : 3.
3.How do you share an amount in a given ratio?
Add the parts to find the total number of shares, divide the amount by that total, then multiply by each part.
4.Share 60 in the ratio 2 : 3.
Total 5 shares, so one share is 12. The amounts are 24 and 36.
5.How do you write a ratio as a fraction of the whole?
Each part goes over the total number of parts. In 2 : 3, the first part is 2 fifths of the total.
6.How do you write a ratio in the form 1 : n?
Divide both sides by the first number.
7.What is direct proportion?
When one quantity increases, the other increases by the same factor, and their ratio stays constant.
8.What does a direct proportion graph look like?
A straight line through the origin.
9.What is inverse proportion?
When one quantity increases, the other decreases by the same factor, so their product stays constant.
10.What does an inverse proportion graph look like?
A curve, since y is proportional to 1 over x.
11.If 5 pens cost 3, what do 8 pens cost?
One pen costs 0.6, so 8 pens cost 4.8.
12.What is a compound measure?
One made from two other measures, such as speed, density or pressure.
13.State the equation for speed.
speed = distance divided by time
14.State the equation for density.
density = mass divided by volume
15.State the equation for pressure.
pressure = force divided by area
16.A car travels 150 km in 2 hours. Find its average speed.
150 divided by 2 = 75 km per hour.
17.How do you convert a speed from km/h to m/s?
Multiply by 1000 to convert km to m, then divide by 3600 to convert hours to seconds.
18.What is simple interest?
Interest calculated on the original amount only, so the same amount is added each time period.
19.What is compound interest?
Interest calculated on the new total each period, so the amount added grows each time.
20.State the compound interest formula.
final amount = starting amount x (multiplier) to the power of the number of periods
21.Find the value of 1000 after 3 years at 5 per cent compound interest.
1000 x 1.05 cubed = 1157.63 to the nearest penny.
22.What is depreciation?
A decrease in value over time, calculated in the same way as compound interest but with a multiplier below 1.
23.A car worth 12000 depreciates 20 per cent a year. Find its value after 2 years.
12000 x 0.8 squared = 7680.
24.How do you decide the better buy between two package sizes?
Work out the cost per unit for each, or the amount per unit of money, and compare.
25.Why does compound interest grow faster than simple interest?
Each period the interest is worked out on a larger amount, so the increase itself keeps increasing.
26.How do you convert between currencies?
Multiply by the exchange rate to convert one way, and divide by it to convert back.
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