18 free guides
Learn it,
do not just get it.
Every guide shows the method, works real numbers through it, names the mistake that costs the marks, and ends with practice problems and their answers. No sign-up, and the steps are never behind a paywall.
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Subjects
Math
2 guides. Percentages, averages, and ratios.
Algebra
3 guides. Linear equations, including variables on both sides.
Geometry
2 guides. Right triangles and the Pythagorean theorem.
Calculus
3 guides. Derivatives as instantaneous rate of change.
Statistics
2 guides. Mean, median, and which one a question wants.
Physics
2 guides. Newton's second law and net force.
Chemistry
2 guides. Balancing equations in a fixed order that always works.
Biology
2 guides. Mitosis and meiosis, and where variation comes from.
Every guide
How to Solve Proportions, Step by Step
A proportion is two equal ratios. Cross multiply, solve, and check the units line up. Three worked examples, the common mistakes, and practice with answers.
How to Find a Percentage
Percent of a number, what percent one number is of another, and percentage change. Three formulas, three worked examples, and the mistakes that flip the answer.
How to Solve Equations With Variables on Both Sides
Gather the variables on one side, the constants on the other, divide, and check. Three worked examples including a negative answer, plus the mistakes that cost marks.
How to Factor Quadratic Equations
Factoring when a is 1, factoring when it is not, and the difference of squares. Three worked examples, the traps, and practice problems with answers.
The Quadratic Formula, Explained
The formula, what the discriminant tells you before you start, and three worked examples: two real roots, an irrational pair, and no real solutions.
The Pythagorean Theorem, Explained
a squared plus b squared equals c squared, what each letter has to be, and how to find a leg rather than the hypotenuse. Three worked examples and practice.
How to Find the Area of a Triangle
Half base times height, the right-triangle shortcut, and the sine formula for when you have two sides and the angle between them. Worked examples and practice.
What Is a Derivative?
A derivative is the instantaneous rate of change: the slope of the curve at one point. What that means, where the power rule comes from, and three worked examples.
What Is an Integral?
An integral accumulates: it adds up infinitely many small pieces to give area under a curve or total change. Indefinite versus definite, with worked examples.
Derivative vs Integral
One measures rate, the other accumulates it. Why they are inverses, what each one gives you, and how to tell which a question wants.
Standard Deviation, Explained
What standard deviation measures, the five steps to calculate it, and why sample and population versions divide by different numbers. Worked examples and practice.
Mean vs Median
The mean uses every value; the median ignores how extreme the extremes are. Which one a skewed data set needs, with worked examples and practice.
How to Calculate Force
Newton's second law, what counts as the net force, and how to get acceleration when a question only gives you a velocity change. Three worked examples and practice.
Speed vs Velocity
Speed is a scalar built on distance; velocity is a vector built on displacement. Why a completed lap has zero velocity, with worked examples and practice.
How to Balance Chemical Equations
Balance in a fixed order instead of guessing: metals, then other elements, then hydrogen, then oxygen. Three worked examples including combustion, plus practice.
How to Calculate Molar Mass
Add the atomic masses, multiplied by how many of each atom the formula contains. Worked examples for a simple compound, one with brackets, and a hydrate.
Mitosis vs Meiosis
Two divisions or one, four daughter cells or two, identical or varied. The differences that carry marks, with worked examples and practice questions.
How to Read a Punnett Square
Set up the square, fill it in, and read both ratios off it. Monohybrid crosses, a test cross, and a sex-linked example, with practice questions.
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