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exam prep

exam prep articles on the Math Mental blog, with worked examples solved step by step.

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  1. How to calculate percentages in your head: 10%, 1% and growth factors

    To find x% of a value, multiply the value by x/100. In your head, start from 10% (divide by 10) and 1% (divide by 100) and combine them: 15% = 10% + 5%. For increases and discounts, multiply by the factor: +20% is ×1.2 and −20% is ×0.8.

    • Tutorial
    • 2 min read

  2. The rule of three: direct, inverse and compound proportion with examples

    Tell whether quantities are directly or inversely proportional, set up a simple or compound rule of three without memorizing arrows, and check it with worked examples.

    • Tutorial
    • 3 min read

  3. Simple vs. compound interest: the difference, formulas and examples

    See the difference between simple and compound interest, the formulas I = P·r·t and A = P(1 + r)^t, equivalent rates and worked examples step by step.

    • Tutorial
    • 2 min read

  4. How to solve quadratic equations: the quadratic formula and sum and product

    Solve quadratic equations with the quadratic formula, the discriminant, sum and product of roots, and factoring for incomplete equations, step by step.

    • Tutorial
    • 2 min read

  5. Logarithms: definition, properties and worked examples

    Understand what a logarithm is, when it exists, the product, quotient and power rules, change of base and how to solve exponential equations, with worked examples.

    • Tutorial
    • 2 min read

  6. Mean, median and mode: how to calculate them and when to use each

    Calculate the arithmetic mean, weighted mean, median and mode with worked examples, and learn which measure of central tendency to use with outliers or categorical data.

    • Tutorial
    • 3 min read

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