Topic Details (Notes format)

How to Approach Algebraic Word Problems

Subject: Mathematics

Book: Maths Mastery

Algebraic word problems typically revolve around forming one or more equations based on a scenario. The steps: define variables, translate sentences into expressions, and solve systematically. For example: “A number is 5 less than twice another. If the sum is 23, find the numbers.” Let x be the first number, y the second. Then x = 2y – 5, x + y = 23. Solve to get y=14, x=23–14=9. Understanding how to parse language into algebraic form is pivotal in advanced mathematics, finance, or logical puzzles, turning everyday challenges into solvable equations.

Practice Questions

If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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What is the greatest common divisor (GCD) of 36 and 48?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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The probability of getting an even number when rolling a die is:

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The probability of rolling a sum of 7 with two dice is:

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