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Self-Study Math · Terminology

Pre-Algebra &
Geometry Terms

20 essential problems. Type your answer, press Check — fireworks for correct, 5-second hints for wrong.

PROGRESS 0 of 20 answered
Part 01
Pre-Algebra Terminology
Q 01
Variable
A letter used to represent an unknown number. In the expression 3x + 5, what is the variable?
KEY: letter = unknown
Example
In 2y − 7 = 11, the variable is y because it's the letter standing in for a number we don't know yet.
Show hint
Look at the expression 3x + 5 — which symbol is a letter, not a number?
Q 02
Coefficient
The number multiplied by a variable. In 7m, what is the coefficient?
KEY: number IN FRONT of letter
Example
5x² → coefficient is 5  |  −3y → coefficient is −3  |  k → coefficient is 1 (invisible 1!)
Show hint
7m means 7 × m. Which part is the number being multiplied?
Q 03
Constant
A fixed value that does NOT change. In 4x + 9, which part is the constant?
KEY: constant = never changes
Example
2a + 6 → constant is 6  |  x − 3 → constant is −3  |  5y → no constant (or 0)
Show hint
In 4x + 9, the 4x can change depending on x. What stays fixed no matter what?
Q 04
Like Terms
Terms with the same variable AND same exponent. From the list 3x, 5y, 7x, 2x², which two are like terms?
KEY: same letter + same power
Example
3x and 7x → like terms ✓ (both have x¹)
3x and 2x² → NOT like terms ✗ (different exponents)
Show hint
Look for two terms with exactly the same letter and exponent. 3x means x to the power 1.
Q 05
Order of Operations
The rule for which operation to do first. What does the "E" stand for in PEMDAS / BODMAS?
KEY: PEMDAS = Please Excuse My Dear Aunt Sally
Solve: 3 + 2 × 4 = ?
Wrong way: (3+2) × 4 = 20 ✗  |  Right way: 3 + (2×4) = 11 ✓
Show hint
P=Parentheses, E=?, M=Multiplication, D=Division, A=Addition, S=Subtraction
Q 06
Integer
Integers include positive whole numbers, zero, and negative whole numbers. Is −5 an integer? (yes / no)
KEY: …−3, −2, −1, 0, 1, 2, 3… NO fractions!
Common Trap!
−5 → integer ✓ | 0 → integer ✓ | ½ → NOT integer ✗ | 3.2 → NOT integer ✗
Q 07
Absolute Value
The distance from zero on a number line — always ≥ 0. What is |−8|?
KEY: |number| = distance = always positive
|−8| = ?     |+8| = ?     Both distances from 0 are the same.
Q 08
Inequality
A statement that two values are NOT equal, using symbols like <, >, ≤, ≥. What does the symbol ≥ mean in words?
KEY: < less than | > greater than | ≤ at most | ≥ at least
Example
x ≥ 5 means x can be 5, 6, 7, 8, … (5 is included!)
x > 5 means x can be 6, 7, 8, … (5 is NOT included)
Q 09
Prime Number
A number with exactly 2 factors: 1 and itself. Is 1 a prime number? (yes / no)
KEY: exactly 2 factors — 1 has only 1 factor, so NOT prime!
Common Trap! (Most Missed)
1 → only 1 factor (itself) → NOT prime ✗
2 → factors: 1 and 2 → prime ✓ (only even prime!)
9 → factors: 1, 3, 9 → NOT prime ✗ (3 factor exists)
Q 10
Distributive Property
Multiply the outside number by each term inside the parentheses. Simplify: 3(x + 4)
KEY: a(b + c) = ab + ac → distribute to ALL
3(x + 4) = 3 · x + 3 · 4 = ?
Show hint
3 × x = 3x, and 3 × 4 = 12. Connect them with +.
Geometry
Part 02
Geometry Terminology
Q 11
Complementary Angles
Two angles that add up to 90°. If one angle is 35°, what is its complement?
KEY: Complementary = Corner (90°) | Supplementary = Straight (180°)
Complement: 90° − 35° = ?°
Q 12
Supplementary Angles
Two angles that add up to 180°. If one angle is 110°, what is its supplement?
KEY: Supplementary = Straight line = 180°
Common Trap!
Complementary ≠ Supplementary. C comes before S → 90° comes before 180°.
Q 13
Perimeter
The total distance around a shape. What is the perimeter of a rectangle with length 8 and width 3?
KEY: Perimeter = Path around = add ALL sides
P = 2(l + w) = 2(8 + 3) = ?
Q 14
Area
The space inside a 2D shape. What is the area of a triangle with base 10 and height 6?
KEY: Area = inside space | Triangle = ½ × b × h
A = 12 × b × h = 12 × 10 × 6 = ?
Q 15
Parallel Lines
Lines that never meet and stay the same distance apart. Which symbol represents parallel? AB ∥ CD or AB ⊥ CD?
KEY: ∥ = parallel (two rails) | ⊥ = perpendicular (cross)
Visual Memory
∥ looks like two parallel lines → parallel
⊥ looks like a T-shape crossing → perpendicular (90°)
Q 16
Pythagorean Theorem
In a right triangle: a² + b² = c² where c is the hypotenuse. If a = 3 and b = 4, find c.
KEY: c = hypotenuse = longest side = opposite right angle
32 + 42 = c2
9 + 16 = c2
c = √25 = ?
Q 17
Circumference
The perimeter of a circle. Formula: C = 2πr. If radius = 7, what is C? (Use π ≈ 3.14, round to nearest whole number)
KEY: Circumference = Circle's perimeter | C = πd = 2πr
C = 2 × 3.14 × 7 = ?
Q 18
Vertical Angles
When two lines intersect, the angles across from each other are always equal. If one vertical angle is 65°, what is the other vertical angle?
KEY: Vertical angles = always EQUAL (X shape)
Common Trap!
"Vertical" doesn't mean up-down here! It means the angles that share the same vertex (corner point) across from each other.
Q 19
Volume of a Rectangular Prism
The 3D space inside a box. Formula: V = l × w × h. Find volume with l=5, w=4, h=3.
KEY: Volume = 3D = l × w × h | Area = 2D = l × w
V = 5 × 4 × 3 = ?
Q 20
Sum of Interior Angles
The total of all inside angles in a polygon. Formula: (n − 2) × 180°. What is the sum of interior angles in a pentagon (5 sides)?
KEY: triangle=180° | quad=360° | pentagon=540° | hexagon=720°
(n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = ?°
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