Mathematics, grade 9
31 topics for grade 9, 285 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
Linear Inequalities
A linear inequality says one side is larger or smaller than the other.
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
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
Quadratic Function
A quadratic function squares the input and its graph is a curve called a parabola.
12 exercises
Arithmetic and Geometric Progressions
An arithmetic progression adds the same number at every step.
12 exercises
Trigonometric Addition and Double-Angle Formulas
An addition formula finds sine or cosine of a sum or difference of two angles.
8 exercises · about 25 min
Trigonometric Reduction and Sum-to-Product Formulas
A reduction formula rewrites sine or cosine of a large angle using a small one.
8 exercises · about 25 min
Quadratic Inequalities
A quadratic inequality asks where a squared expression sits above or below zero.
12 exercises
Vectors
Vectors are quantities with both a size and a direction.
12 exercises
Coordinate Geometry
Coordinate geometry describes shapes by numbers instead of pictures.
12 exercises
Stereometry (3D Geometry)
Stereometry studies points, lines and flat planes that extend without end through three-dimensional space.
10 exercises
Geometric Transformations
Geometric transformations move or resize a figure by a fixed rule.
12 exercises
Systems of Inequalities
A system of inequalities asks for the numbers that satisfy every line at once.
12 exercises · about 30 min
Proving Inequalities
Proving an inequality means showing it holds for every allowed number, not for a few.
12 exercises · about 30 min
Properties of Functions
The properties of a function say which inputs it accepts and where its value is zero.
12 exercises · about 30 min
Transformations of Graphs
A graph transformation moves or stretches a whole curve by changing its rule.
12 exercises · about 30 min
Systems of Second-Degree Equations
A system of second-degree equations pairs two lines.
12 exercises · about 30 min
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
Random Variables and Expected Value
A random variable is simply a number attached to each possible outcome of a random experiment.
5 exercises
Cylinders and Cones: Surface Area
A cylinder is formed by two identical circles connected by a curved side, like a can.
6 exercises · about 25 min
Sphere and Ball
A ball is every point within a fixed distance of one center, like a bowling ball.
6 exercises · about 20 min
Volumes of Prisms, Pyramids, Cylinders, Cones, and Spheres
Prisms and pyramids are polyhedra with flat faces.
8 exercises · about 25 min
Law of Cosines and Law of Sines
The Law of Cosines relates a triangle's three sides to one of its angles.
6 exercises · about 25 min
Triangle Area: Two Sides and an Angle, and Heron's Formula
Two sides and their included angle give a triangle's area directly.
6 exercises · about 20 min
Inscribed and Circumscribed Circles of a Regular Polygon
A regular polygon's circumscribed circle passes through every vertex.
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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