Mathematics, grade 10
36 topics for grade 10, 281 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
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
Stereometry (3D Geometry)
Stereometry studies points, lines and flat planes that extend without end through three-dimensional space.
10 exercises
Irrational Equations
An irrational equation hides the unknown number inside a root.
6 exercises
Irrational Inequalities
An irrational inequality compares an expression that hides the unknown inside a root to another expression.
6 exercises
Even, Odd, Bounded and Periodic Functions
A function is even when swapping x for -x never changes its value.
7 exercises
Basic Polyhedra: Prisms and Pyramids
A polyhedron is a solid shape whose whole surface is made of flat polygon pieces.
6 exercises
Trigonometry
Trigonometry connects the angle of a rotation to the position of a point moving around a circle.
20 exercises
Trigonometric Equations
A trigonometric equation asks which angles make a sine, cosine or tangent equal to a given number.
17 exercises
Logarithms
A logarithm answers one question: what power turns a fixed base into a given number?
6 exercises
Exponential Function
An exponential function raises a fixed positive number to a variable power, written y = a^x.
6 exercises
Logarithmic Function
A logarithmic function reads y as the logarithm of x, written y equals log base a of x.
6 exercises
Sets and Set Operations
Sets are collections of distinct objects, called elements, grouped together as one whole.
7 exercises
Set Cardinality and Venn Diagrams
The cardinality of a set is its number of elements, written n(A).
8 exercises · about 22 min
Propositional Logic
A proposition is a statement that is either true or false, never both.
8 exercises · about 22 min
Predicates and Quantifiers
A predicate is a statement whose truth depends on a variable, like P(x).
9 exercises · about 24 min
Simple and Compound Interest
Simple interest adds a fixed amount to the original sum every single year.
8 exercises · about 22 min
Rational Equations and Their Systems
A rational equation sets two rational expressions equal to each other.
9 exercises · about 24 min
Exponential Equations
An exponential equation has the unknown in an exponent, like a^x = b.
8 exercises · about 24 min
Graphs of Sine and Cosine Functions
The graph of y=sinx repeats every 2π, tracing a smooth wave between -1 and 1.
9 exercises · about 24 min
Logarithmic Equations and Inequalities
A logarithmic equation has the unknown inside a logarithm, like log_a(x)=b.
9 exercises · about 24 min
Trigonometric Form of Complex Numbers
The trigonometric form writes a complex number as r(cosφ+i·sinφ), using its distance and angle.
9 exercises · about 26 min
Polynomial Division and the Remainder Theorem
Dividing one polynomial by another works much like dividing whole numbers, giving a quotient and a remainder.
6 exercises
The Method of Intervals
The method of intervals solves an inequality by finding where an expression equals zero.
7 exercises
Mathematical Induction
Mathematical induction proves a statement is true for every whole number by climbing an infinite staircase.
6 exercises
Power Functions
A power function writes y as x raised to a fixed exponent, such as y = x³.
7 exercises
Equations and Inequalities with Parameters
A parameter is a letter that stands for a fixed but unstated number inside an equation.
6 exercises
Graphs of Equations and Inequalities in Two Variables
An equation in x and y usually draws a curve made of every point that makes it true.
6 exercises
Parallelism of Lines and Planes in Space
Two lines in space can be parallel, crossing, or skew, going different directions without ever meeting.
7 exercises
Perpendicularity of Lines and Planes in Space
A line is perpendicular to another line when the angle between their directions is a right angle.
12 exercises
Distances in Space
The distance from a point to a plane is the length of the one perpendicular segment between them.
6 exercises
Vectors in Space
A vector in space carries three coordinates, one along each of three directions at right angles.
10 exercises
Symmetry in Space
Point symmetry maps each point to a matching point, with a fixed center exactly halfway between them.
6 exercises
Cross-Sections of Polyhedra
A cross-section is the flat polygon where a cutting plane slices through a polyhedron.
6 exercises
Cosine Theorem for a Trihedral Angle
A trihedral angle has three flat faces meeting at one vertex, like a box's corner.
5 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.
Start free
