Unit notes and practice questions
Everything here is for unit 5 of the Grade 12 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 12 Mathematics page. Open one at a time.
When you use it
Use this relation to solve for an unknown value when two ratios are set equal, where b and d are non-zero.
Watch out
Multiply the extremes together and the means together. Multiplying terms belonging to the same ratio produces a false result.
Drafted from Grade 12 Mathematics, pages 303-413, then checked twice before it went up
| Variation Type | Proportionality | Constant Form | Constant Property |
|---|---|---|---|
| Direct variation | Ratio remains constant | ||
| Inverse variation | Product remains constant |
When you use it
Use this reference to set up the correct variation formula based on whether two quantities vary directly or inversely.
Watch out
For inverse variation, the product of the two variables remains constant, not their quotient.
Drafted from Grade 12 Mathematics, pages 303-413, then checked twice before it went up
When you use it
Use this formula to calculate the relative increase or decrease of a quantity compared to its starting level.
Watch out
Always divide by the original amount in the denominator, never the final amount. A negative result represents a rate of decrease.
Drafted from Grade 12 Mathematics, pages 303-413, then checked twice before it went up
When you use it
Review this whenever forming a ratio or a rate from physical quantities given in different measurement units.
Watch out
Never divide numbers before converting both quantities into identical units. For instance, comparing 6 Birr to 50 cents requires converting 6 Birr to 600 cents first, giving 600 to 50.
Drafted from Grade 12 Mathematics, pages 303-413, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
Ashamo borrows Birr 18,500 at a simple interest rate of 9.5% per year for 2 years. How much interest will he pay?
Answer: B Birr 3515
Why
Use the simple interest formula I = Prt. Here P = 18,500, r = 9.5% = 0.095 and t = 2 years. So I = 18500 x 0.095 x 2 = 3515. The interest is Birr 3515. Birr 22015 is the total amount to repay, not the interest.
Question 2
Find the amount of turnover tax on a Birr 400,000 sale when the turnover tax rate is 2%.
Answer: C Birr 8000
Why
Use Percentage = base x rate. The base is Birr 400,000 and the rate is 0.02. So 400,000 x 0.02 = 8000. The tax is Birr 8,000.
Question 3
Allocate Birr 1500 in the continued ratio 2:3:7. How much does each share receive?
Answer: A Birr 250, Birr 375 and Birr 875
Why
First add the parts: 2 + 3 + 7 = 12. Then find the value of one part: 1500 / 12 = 125. Multiply each part by 125: 2 x 125 = 250, 3 x 125 = 375 and 7 x 125 = 875.
Question 4
Adane scored 12 goals in 4 Ethiopian premier league games. What is his average rate of goals per game?
Answer: B 3 goals per game
Why
A rate is a quotient of two quantities. Divide the goals by the games: 12 / 4 = 3. Adane scored an average of 3 goals per game.
Question 5
On a house construction plan, 1 cm on the paper represents 25 meters on the ground. What distance on the ground is represented by 3.20 cm on the paper?
Answer: C 80 m
Why
First convert 25 m to 2500 cm. Set up the proportion 1 cm / 2500 cm = 3.20 cm / x. Then x = 2500 x 3.20 = 8000 cm. Since 8000 cm = 80 m, the answer is 80 m.
Question 6
A boutique bought a T-shirt for Birr 546. It wants a markup of 30% on the selling price (retail). What is the selling price?
Answer: C Birr 780
Why
Cost is 100% - 30% = 70% of the selling price. So 546 = 0.70 x selling price. Selling price = 546 / 0.70 = Birr 780.
Question 7
During festive shopping, edible oil is sold at a 20% discount of Birr 175.00 per liter. What was the original (regular) price?
Answer: B Birr 875
Why
The discount is 20% of the regular price, and the discount is Birr 175. So 0.20 x regular price = 175. Regular price = 175 / 0.20 = Birr 875. The selling price is then Birr 700.
Question 8
Under constant temperature, the volume of a gas is inversely proportional to its pressure. The volume is 4 m3 at a pressure of 1 kilopascal. What is the pressure when the volume is 3 m3 at the same temperature?
Answer: B 1.33 kilopascal
Why
For inverse proportion, P1 x V1 = P2 x V2. So 1 x 4 = x x 3, which gives x = 4/3 = 1.33. The volume decreased, so the pressure increased to 1.33 kilopascal.
Question 9
Tekletsadik borrowed Birr 1500 from his brother-in-law and agreed to pay back Birr 1650 one year later. What rate of simple interest is he paying?
Answer: B 10%
Why
The interest is 1650 - 1500 = Birr 150. Use r = I / (P x t) = 150 / (1500 x 1) = 0.1. So the rate is 0.1, or 10%.
Question 10
A bank pays 9.5% nominal interest compounded monthly. What is the equivalent annual (effective) rate, rounded to two decimal places?
Answer: C 9.92%
Why
Find the value of Birr 100 after one year at 9.5% compounded monthly: A = 100(1 + 0.095/12)12 = Birr 109.92. The effective rate r satisfies 1 + r = 1.0992. So r = 0.0992, which is 9.92%.
The app holds 12 questions on this unit, marked as you go. These are the first 10.
Unit 5 runs from page 303 to page 413 of the Ministry of Education edition.
Ministry of Education edition, English, 426 pages
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