Math Operations and Conversions

Study Notes

Numbers and Operations

Fractions:
- Simplification: cancel out common factors
- Addition and subtraction: find common denominator
- Multiplication: multiply numerators and denominators separately
- Division: invert and multiply
Decimals and Percentages:
- Conversion: move decimal point to convert between decimals and percentages
- Percentage increase/decrease: calculate percentage change
Ratios and Proportions:
- Simple ratios: reduce to simplest form
- Equivalent ratios: multiply/divide by same number
- Proportional calculations: set up proportion and solve

Algebra

Linear Equations:
- Simplify and solve: add/subtract same value to both sides, multiply/divide both sides by same value
- Graphical representation: x-axis and y-axis
Quadratic Equations:
- Factorization: solve by factorizing
- Quadratic formula: use when factorization is not possible
Formulae and Transposition:
- Rearrangement: transpose formula to isolate specific variable
- Substitution: substitute given values into formula

Geometry and Trigonometry

Points, Lines, and Angles:
- Properties of points, lines, and angles
- Types of angles: acute, obtuse, right, straight, reflex
Triangles:
- Properties: congruent, similar, right-angled
- Pythagorean theorem: a^2 + b^2 = c^2
- Trigonometric ratios: sine, cosine, tangent
Circles:
- Properties: center, radius, circumference, diameter
- Circumference and area calculations

Graphs and Charts

Types of Graphs:
- Linear: straight line
- Non-linear: curved line
- Quadratic: parabola
Graphical Representation:
- Plotting points: x-axis and y-axis
- Interpreting graphs: identify trends, maxima, and minima

Statistics and Probability

Descriptive Statistics:
- Mean, median, mode
- Range and interquartile range
Probability:
- Basic concepts: event, experiment, probability scale
- Calculating probability: theoretical and experimental probability

Numbers and Operations

A fraction can be simplified by canceling out common factors between the numerator and denominator.
To add or subtract fractions, find a common denominator and then add or subtract the numerators.
To multiply fractions, multiply the numerators and denominators separately.
To divide fractions, invert the second fraction and then multiply.
Decimals and percentages can be converted by moving the decimal point.
To calculate a percentage increase or decrease, find the percentage change.

Algebra

Linear equations can be simplified and solved by adding or subtracting the same value to both sides, and then multiplying or dividing both sides by the same value.
Linear equations can be represented graphically on the x-axis and y-axis.
Quadratic equations can be solved by factorization or by using the quadratic formula when factorization is not possible.
Formulae can be rearranged to isolate a specific variable by transposing the formula.
Substitution involves substituting given values into a formula.

Geometry and Trigonometry

Points, lines, and angles have specific properties, and there are different types of angles, including acute, obtuse, right, straight, and reflex angles.
Triangles can be congruent, similar, or right-angled, and the Pythagorean theorem states that a^2 + b^2 = c^2.
Trigonometric ratios include sine, cosine, and tangent.
Circles have properties such as a center, radius, circumference, and diameter, and circumference and area can be calculated.

Graphs and Charts

Linear graphs have a straight line, non-linear graphs have a curved line, and quadratic graphs have a parabola shape.
Graphs can be plotted by using points on the x-axis and y-axis, and graphs can be interpreted to identify trends, maxima, and minima.

Statistics and Probability

Descriptive statistics include calculating the mean, median, mode, range, and interquartile range.
Probability involves understanding events, experiments, and the probability scale, and probability can be calculated theoretically or experimentally.

Description

Test your understanding of various mathematical operations including fractions, decimals, percentages, ratios, and proportions. Learn how to simplify, add, subtract, multiply, and divide fractions, as well as convert between decimals and percentages.