Mathematics, grade 8
32 topics for grade 8, 310 exercises. Each one starts with an explanation, then practice that adapts: get it right and the difficulty rises, get it wrong and the tutor takes the step apart.
Topics in this grade
Rational Expressions
A rational expression is built from numbers and letters.
12 exercises · about 30 min
Multiplying and Dividing Rational Fractions
Multiplying and dividing rational fractions works on the top and the bottom separately.
12 exercises · about 30 min
Linear Inequalities
A linear inequality says one side is larger or smaller than the other.
12 exercises
Quadratic Equations
A quadratic equation is one where the unknown appears squared and no higher.
12 exercises
The Function y = k/x
The function y = k/x pairs every nonzero x with k divided by x.
8 exercises · about 22 min
Vieta's Theorem
Vieta's theorem connects a quadratic equation's roots to its coefficients directly.
8 exercises · about 20 min
Biquadratic and Reducible Equations
A biquadratic equation has the form ax⁴ + bx² + c = 0.
9 exercises · about 22 min
Approximation and Measurement Error
Measurement error is the gap between an approximate value and the true value.
8 exercises · about 20 min
Frequency Tables and Polygons
A frequency table shows how often each value appears in a data set.
8 exercises · about 22 min
Functions
A function is a rule that turns each allowed x into exactly one y.
12 exercises
Square Roots
A square root of a number is what you multiply by itself to get it.
12 exercises
Quadrilaterals
Quadrilaterals are flat shapes with four straight sides and four corners.
12 exercises
Pythagorean Theorem
The Pythagorean theorem ties the three sides of a right triangle together.
12 exercises
Area and Volume
Area is the amount of flat space a shape covers.
12 exercises
Circle Geometry
Circle geometry looks at how a circle meets the straight shapes around it.
12 exercises
Similarity and Congruence
Two triangles are similar when their matching angles are equal.
8 exercises
Probability
Probability measures how likely an event is, from 0 to 1.
8 exercises
Statistics
Statistics is the study of collecting, organizing, and summarizing sets of numbers.
7 exercises
Rational Equations
A rational equation has a letter below the line on at least one side.
12 exercises · about 35 min
Powers with Integer Exponents
An exponent can be zero or below zero as well as above it.
12 exercises · about 30 min
Standard Form of a Number
Standard form writes a number as one digit, the rest, and a power of ten.
12 exercises · about 25 min
Thales Theorem and Midlines
Thales theorem says parallel lines cut matching pieces on every line they cross.
12 exercises · about 30 min
Sine, Cosine and Tangent of an Acute Angle
Sine, cosine and tangent compare two sides of a right triangle.
12 exercises · about 35 min
Properties of Numeric Inequalities
The properties of numeric inequalities say which operations keep a comparison true.
12 exercises · about 30 min
Intervals and Number Sets
A number stretch is every number between two bounds.
12 exercises · about 30 min
Roots of the nth Degree
A root of the nth degree asks what number, multiplied n times, gives a target.
6 exercises
Powers with Rational Exponents
A rational exponent writes a root and a power together in one compact form.
5 exercises
Equations and Inequalities with Absolute Value
Absolute value measures how far a number sits from zero, never negative.
6 exercises
Angles and Diagonals of a Convex Polygon
A convex polygon has every interior angle smaller than 180 degrees.
7 exercises · about 20 min
Centroid and Medians of a Triangle
A median connects a triangle's vertex to the midpoint of the opposite side.
6 exercises · about 20 min
Menelaus's and Ceva's Theorems
Menelaus's theorem tests whether three points, one on each side, are collinear.
6 exercises · about 25 min
Excircle of a Triangle
An excircle of a triangle touches one side and the other two sides' extensions.
6 exercises · about 20 min
Where this leads
These topics feed DTM (State Testing Center), NMT (National Multi-Subject Test), ZNO (External Independent Evaluation).
Start with a 15-minute diagnostic
It finds which of these topics are solid and which are shaky, then builds the plan from there.
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