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Direct and Inverse Variations — Flashcards

ICSE · Class 8 · Mathematics

26 flashcards for Direct and Inverse Variations (ICSE Class 8 Mathematics) to test yourself on key terms and facts.

61 questions26 flashcards5 formulas & key relations5 concepts

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26 Flashcards·
Direct variationInverse variationDirect variation testDirect variation missing valuesDirect variation application
Card 1Direct variation

Solve: If 7 bags weigh 560 kg, what will 14 bags weigh?

Answer

Step 1: Find the weight of 1 bag. 560 ÷ 7 = 80 kg Step 2: Find the weight of 14 bags. 14 × 80 = 1120 kg Answer: 14 bags weigh 1120 kg. This is direct variation because more bags give more weight.

Card 2Inverse variation

Solve: If 7 men can do a work in 560 days, how many days will 14 men take?

Answer

Step 1: More men mean fewer days, so this is inverse variation. Step 2: Use the inverse relation. 7 × 560 = 14 × d Step 3: Solve for d. d = (7 × 560) ÷ 14 = 280 days Answer: 14 men will take 280 days.

Card 3Direct variation test

Check whether x and y are in direct variation: x = 6, 10, 14, 18, 24 and y = 18, 30, 42, 54, 72

Answer

Step 1: Find the ratio x/y for each pair. 6/18 = 1/3 10/30 = 1/3 14/42 = 1/3 18/54 = 1/3 24/72 = 1/3 Step 2: All ratios are equal. Answer: x and y are in direct variation.

Card 4Direct variation test

Check whether x and y are in direct variation: x = 30, 20, 24, 16 and y = 36, 30, 30, 20

Answer

Step 1: Find the ratio x/y for each pair. 30/36 = 5/6 20/30 = 2/3 24/30 = 4/5 16/20 = 4/5 Step 2: The ratios are not all the same. Answer: x and y are not in direct variation.

Card 5Direct variation missing values

If p and q are in direct variation, find x, y, and z: p = 6, x, y, 30 and q = 72, 60, 96, z

Answer

Step 1: In direct variation, p/q is constant. 6/72 = x/60 = y/96 = 30/z Step 2: Solve each missing value. x = (6/72) × 60 = 5 y = (6/72) × 96 = 8 z = 30 × (72/6) = 360 Answer: x = 5, y = 8, z = 360.

Card 6Direct variation missing values

If x and y vary directly, find a, b, and c: x = 5, a, b, 42 and y = 10, 16, 48, c

Answer

Step 1: Use the constant ratio. 5/10 = a/16 = b/48 = 42/c Step 2: Solve. a = 8 b = 24 c = 84 Answer: a = 8, b = 24, c = 84.

Card 7Direct variation application

Solve: A 525 cm pole casts a 300 cm shadow. Find the shadow of a 280 cm pole at the same time.

Answer

Step 1: Heights and shadows vary directly. Step 2: Use the constant ratio. 280/160 = 525/x Step 3: Solve for x. x = (160 × 525) ÷ 280 = 300 cm Answer: The shadow is 300 cm.

Card 8Direct variation application

Solve: A pole casting a 250 cm shadow has height 437.5 cm. Is this reasonable under direct variation with the pole-shadow relation?

Answer

Step 1: Use the direct variation ratio from the pole-shadow relation. 280/160 = y/250 Step 2: Solve for y. y = (280/160) × 250 = 437.5 cm Step 3: Check. A longer shadow gives a taller pole, which matc…

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Frequently Asked Questions

What are the important topics in Direct and Inverse Variations for ICSE Class 8 Mathematics?
Key topics in Direct and Inverse Variations include Variation and Its Types, Direct Variation: Tables, Missing Values, and Examples, Inverse Variation: Tables and Missing Values, Arrow Method. Study these first, then practise questions on each for Class 8 exams.
How many flashcards are available for Direct and Inverse Variations?
There are 26 flashcards for Direct and Inverse Variations covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Direct and Inverse Variations for Class 8 exams?
Learn the core ideas first, then work through the 61 practice questions on Direct and Inverse Variations. Revise definitions regularly and use flashcards for quick recall before the exam.

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