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Direct and Inverse Proportion
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
When two quantities are in direct proportion their ratio y/x stays fixed. The graph is a straight line through the origin with gradient k.
Multiply any matching pair of x and y and you always get the same k. The graph is a reciprocal curve that hugs but never touches the axes.
y proportional to x-squared gives a parabola; y proportional to 1/x-squared is the inverse-square law of light and gravity (double the distance, quarter the effect).
There is only one unknown, k. Substitute the given values once, solve for k, and the relationship is complete for all values.
Hard words & meanings
| proportion | a fixed relationship where the ratio or product of two quantities stays constant as they change |
| constant of proportionality | the fixed value k in y = kx or y = k/x that ties the two variables together |
| direct proportion | as one quantity increases the other increases at the same ratio; y = kx |
| inverse proportion | as one quantity increases the other decreases so the product stays fixed; y = k/x |
| inverse square law | y proportional to 1/x-squared; doubling x reduces y to a quarter |
| origin | the point (0, 0) where the axes cross; a direct-proportion line always passes through it |
| asymptote | a line a curve gets infinitely close to but never touches |
| gradient | the steepness of a line; for y = kx the gradient equals k |
Model exam answers, grammar & audio
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