교육자를 위해: Percentage change, interest and growth or decay(Mathematics, Ratio, proportion and rates of change)을(를) 위한 바로 쓸 수 있는 수업 슬라이드, 복습 노트 — 수업에 사용하거나, 학습자들이 실시간 게임으로 즐기는 인터랙티브 클래스 활동으로 진행하세요.
Percentage change = \frac{\text{change}}{\text{original}} \times 100. A price rising from £40 to £46 is \frac{6}{40} \times 100 = 15\% increase.
Use multipliers: increase by 15% → ×1.15; decrease by 20% → ×0.8. Multiplier = 1 ± (percentage as a decimal).
Reverse percentages
To find the original, divide by the multiplier. A coat is £68 after a 15% reduction: 68 \div 0.85 = £80.
Do not just add 15% to the new price.
Simple and compound interest
With unchanged principal P, fixed annual percentage rate R and time T in years, simple interest is PRT/100. £500 at 4% for 3 years earns £60.
For annual compound interest A = P(1 + r)ⁿ, r is the annual decimal rate and n is whole years. £500 × 1.04³ ≈ £562.43.
Same £500 principal and 4% annual rate
Growth and decay
Exponential growth/decay uses the same multiplier idea: a population growing at 5% a year multiplies by 1.05 each year; depreciation of 12% a year multiplies by 0.88.
After n periods: final = original × multipliern.
Repeated percentage changes
Multiply the multipliers: +10% then −10% is 1.1 \times 0.9 = 0.99, an overall 1% decrease, not no change.
슬라이드
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4.A TV costs £400 and is reduced by 15% in a sale. What is the sale price?
Easy
A£340
B£60
C£385
D£460
5.A price rises from £40 to £46. What is the percentage increase?
Easy
A6%
B15%
C13%
D86%
6.A value falls from £250 to £200. What is the percentage decrease?
Easy
A20%
B25%
C50%
D80%
7.£500 is invested at 4% simple interest for 3 years. How much interest is earned?
Easy
A£60
B£62.43
C£20
D£120
8.A coat costs £68 after a 15% reduction. What was the original price?
Medium
A£80
B£78.20
C£58
D£85
더 많은 문제
9.After a 20% increase a rent is £600. What was the original rent?
Medium
A£480
B£500
C£720
D£520
10.£500 is invested at 4% compound interest for 3 years. What is the final amount (nearest penny)?
Medium
A£562.43
B£560.00
C£600.00
D£562.00
11.A car worth £12 000 depreciates at 15% a year. What is it worth after 2 years?
Medium
A£8 670
B£8 400
C£9 000
D£10 200
12.A population of 2000 grows by 5% a year. What is it after 3 years (nearest whole)?
Medium
A2315
B2300
C2400
D2100
13.Increase £200 by 10% and then decrease the result by 10%. What is the final amount?
Medium
A£200
B£198
C£202
D£220
14.What is the single multiplier for +10% then −10%?
Medium
A1
B0.99
C1.01
D0.9
15.In one week a price is reduced by 10% and the next by 20%. What is the single multiplier?
Medium
A0.7
B0.72
C0.68
D0.3
16.A sum of £2000 earns compound interest of 3% a year. After how many years does it first exceed £2200?
Medium
A4
B3
C5
D2
17.A house increased in value by 12% to £280 000. What was its value before?
Medium
A£250 000
B£246 400
C£313 600
D£268 000
18.A value decreases by 8% each year. After 5 years it is £6 000. About how much was it originally?
Medium
A£9 100
B£8 400
C£7 200
D£10 000
19.For the same positive principal and no fees or withdrawals, which gives more money after 2 years: 5% annual simple interest or 5% interest compounded annually?
Medium
Acompound
Bsimple
Cequal
Dcannot tell
20.What is 15% as a decimal multiplier for an increase?
Easy
A1.15
B0.15
C0.85
D15
21.What does \frac{\text{change}}{\text{original}} \times 100 calculate?
Easy
Apercentage change
Bpercentage of
Cratio
Dmean
22.A bike costs £120 including 20% VAT. What is the price without VAT?
Medium
A£100
B£96
C£144
D£110
23.Compound interest uses which multiplier for 6% growth?
Easy
A1.06
B0.06
C0.94
D6
24.The multiplier for a 30% decrease is 0.7.
Easy
True or false?
25.A 10% increase followed by a 10% decrease leaves a value unchanged.
Easy
True or false?
26.A reverse percentage problem with a nonzero multiplier is solved by dividing the new value by that multiplier.
Easy
True or false?
27.At a fixed annual simple-interest rate on an unchanged original principal, the interest added each year is the same.
Easy
True or false?
28.Compound interest on £100 at 10% for 2 years gives £120.
Medium
True or false?
29.Which multipliers are correct?
Medium
A20% increase: 1.2
B20% decrease: 0.8
C5% increase: 1.5
D5% decrease: 0.95
E12% increase: 1.012
30.Which give £121 from £100?
Medium
A10% compound for 2 years
B10% simple for 2 years
C100 \times 1.1 \times 1.1
D100 \times 1.21
E100 \times 1.2
31.A car costs £15 000 and loses 20% of its value each year. Calculate its value after 3 years.
Medium
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