Variation with 30 Questions on Variation – JAMB, WAEC & NECO CBT Variation with Practice Test (Timed 10 Minutes) | Edwin Ogie Library

Mathematics • Algebra • Exam Prep

Variation in Mathematics

Variation explains how one quantity changes in relation to another. It is an important topic in mathematics because it helps students solve real-life and exam questions involving proportional relationships, rates, and percentage changes.

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1. Direct Variation

Direct variation means that as one quantity increases, the other increases in the same ratio.

y ∝ x   or   y = kx

Example: If y = 20 when x = 4, find y when x = 10.

Solution: k = 20 ÷ 4 = 5, so y = 5 × 10 = 50.

2. Inverse Variation

Inverse variation means that as one quantity increases, the other decreases.

y ∝ 1/x   or   y = k/x

Example: If y = 3 when x = 8, find y when x = 16.

Solution: k = 3 × 8 = 24, so y = 24 ÷ 16 = 1.5.

3. Joint Variation

Joint variation occurs when a quantity varies directly as two or more variables at the same time.

z = kxy

Example: If z = 30 when x = 2 and y = 5, find z when x = 3 and y = 4.

Solution: k = 30 ÷ (2 × 5) = 3, so z = 3 × 3 × 4 = 36.

4. Partial Variation

Partial variation includes both a variable part and a constant part.

y = kx + c

Example: If y = 2x + 5, find y when x = 7.

Solution: y = 2(7) + 5 = 19.

Percentage Increase and Decrease

Percentage change is often tested in exams. Use the original value as your base.

Percentage Increase = [(New − Old) ÷ Old] × 100%

Percentage Decrease = [(Old − New) ÷ Old] × 100%

Quick tip: If a value changes from 80 to 100, the increase is 20, and the percentage increase is 25%.

Short Practice Questions

• If y varies directly as x and y = 12 when x = 3, find y when x = 8.
• If y varies inversely as x and y = 6 when x = 4, find y when x = 12.
• If a quantity increases from 50 to 65, what is the percentage increase?

Try solving them before checking the answers. Practice improves speed and accuracy in exams.

Frequently Asked Questions

What is variation in mathematics?

Variation is the way one quantity changes as another quantity changes.

What is the formula for direct variation?

The formula is y = kx, where k is the constant of proportionality.

What is the formula for inverse variation?

The formula is y = k/x, where k is a constant.

Why is variation important?

It helps students solve practical and examination questions involving proportional relationships.

Conclusion

Variation is a very important topic in mathematics. Once you understand direct, inverse, joint, and partial variation, many exam questions become easier to solve. Keep practicing the examples, and use percentage change formulas carefully.

For more lessons and practice materials, visit Edwin Ogie Library.

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Advanced CBT Practice System

A modern CBT-style test for JAMB, WAEC, and NECO practice. It includes candidate details, question shuffle, auto-save, one-question pages, navigation grid, review flagging, grading, corrections, and a printable result report.

Test Length30 questions

Time Limit10 minutes

FeaturesTimer, review, grading

ModeJAMB / WAEC / NECO

Question 1 of 30
Candidate: Not started

10:00

Instructions: Enter your name, choose the exam type, then click Start Quiz. The timer begins immediately. Use the Next and Previous buttons to move through the pages. You may flag questions for review before submission.

Candidate Name

Exam Type JAMB WAEC NECO Mixed CBT

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Exam: CBT Practice Page 1

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Result

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