LEARN MATH

✅ Grade 9 Math Terms (1–25) with Definitions

1. Algebraic Expression
A combination of variables, numbers, and operations (e.g., 3x + 2).

2. Equation
A mathematical sentence that shows two expressions are equal (e.g., 2x + 5 = 11).

3. Inequality
A mathematical statement comparing two expressions using symbols like , ≤, or ≥.

4. Linear Equation in Two Variables
An equation in the form Ax + By = C where A, B, and C are constants.

5. Slope (m)
A measure of the steepness of a line:
▶ Slope = (change in y) / (change in x)

6. Y-Intercept (b)
The point where a line crosses the y-axis (x = 0).

7. Quadratic Equation
An equation in the form ax² + bx + c = 0, where a ≠ 0.

8. Factoring
The process of breaking down a quadratic or polynomial into a product of simpler expressions.

9. Completing the Square
A method of solving quadratic equations by making a perfect square trinomial.

10. Quadratic Formula
A formula used to solve quadratic equations:
▶ x = (-b ± √(b² - 4ac)) / 2a

11. Discriminant
The part under the square root in the quadratic formula: b² - 4ac — tells the number/type of solutions.

12. Function
A relation where each input (x) has one unique output (y).

13. Domain
The set of all possible input values (x-values) of a function.

14. Range
The set of all possible output values (y-values) of a function.

15. Direct Variation
A linear relationship in the form y = kx, where k is the constant of variation.

16. Inverse Variation
A relationship in which y = k/x, where k ≠ 0.

17. Arithmetic Sequence
A sequence where each term is found by adding a constant difference (d).

18. Geometric Sequence
A sequence where each term is found by multiplying by a constant ratio (r).

19. Pythagorean Theorem
In a right triangle:
▶ a² + b² = c², where c is the hypotenuse.

20. Trigonometry
The study of relationships between angles and sides of triangles.

21. Sine (sin)
In a right triangle: sin(θ) = opposite / hypotenuse

22. Cosine (cos)
In a right triangle: cos(θ) = adjacent / hypotenuse

23. Tangent (tan)
In a right triangle: tan(θ) = opposite / adjacent

24. Probability
The measure of how likely an event is to occur, from 0 (impossible) to 1 (certain).

25. Mean, Median, Mode
- Mean: The average of numbers
- Median: The middle value when data is ordered
- Mode: The most frequent number in a set.

SOH CAH TOA

Mathematicians may all seem to ‘look alike-not because of their appearance, but because of the qualities they share. They are curious, disciplined, and persistent. They train their minds to search for patterns, solve problems, and never give up until they find answers.

We should look up to them because they remind us that success does not come instantly, but through hard work, patience, and creativity. Mathematicians have given us the tools to understand the world from simple counting to the technology we enjoy today.

As students, when you show curiosity, perseverance, and a love for learning, you already carry the same spirit that makes mathematicians truly remarkable. Let us be inspired by their dedication and strive to develop the same mindset of problem solvers who make a difference in the world.

"DEFINITION OF TERMS" (F &H)

✓Factor: A number that divides into another number exactly. The factors of 10 are 1, 2, 5, and 10 (1 x 10, 2 x 5, 5 x 2, 10 x 1).

✓Factoring: The process of breaking numbers down into all of their factors.

✓Factorial Notation: Often used in combinatorics, factorial notations require that you multiply a number by every number smaller than it. The symbol used in factorial notation is ! When you see x!, the factorial of x is needed.

✓Factor Tree: A graphical representation showing the factors of a specific number.

✓Fibonacci Sequence: Named after Italian number theorist Leonardo Pisano Fibonacci, it's a sequence beginning with a 0 and 1 whereby each number is the sum of the two numbers preceding it. For example, "0, 1, 1, 2, 3, 5, 8, 13, 21, 34..." is a Fibonacci sequence.

✓Figure: Two-dimensional shapes.

✓Finite: Not infinite; has an end.

✓Flip: A reflection or mirror image of a two-dimensional shape.

✓Formula: A rule that numerically describes the relationship between two or more variables.

✓Fraction: A quantity that is not whole that contains a numerator and denominator. The fraction representing half of 1 is written as 1/2.

✓Frequency: The number of times an event can happen in a given period of time; often used in probability calculations.

✓Furlong: A unit of measurement representing the side length of one square acre. One furlong is approximately 1/8 of a mile, 201.17 meters, or 220 yards.

✓Geometry: The study of lines, angles, shapes, and their properties. Geometry studies physical shapes and object dimensions.

✓Graphing Calculator: A calculator with an advanced screen capable of showing and drawing graphs and other functions.

✓Graph Theory: A branch of mathematics focused on the properties of graphs.

✓Greatest Common Factor: The largest number common to each set of factors that divides both numbers exactly. The greatest common factor of 10 and 20 is 10.

✓Hexagon: A six-sided and six-angled polygon.

✓Histogram: A graph that uses bars that equal ranges of values.

✓Hyperbola: A type of conic section or symmetrical open curve. The hyperbola is the set of all points in a plane, the difference of whose distance from two fixed points in the plane is a positive constant.

✓Hypotenuse: The longest side of a right-angled triangle, always opposite to the right angle itself.