Core terminology that trips up most students — master these first.
PRE-ALG · 01
In the expression 7x, what is the number multiplied by a variable called?
COEF = CO + EFFICIENT → "the number working with the variable"
Think: in 7x, the 7 is right in front of the variable. The special name starts with "co-".
A coefficient is the numerical factor multiplied by a variable in a term. In 7x, 7 is the coefficient; in -3y², −3 is the coefficient. If no number appears (e.g., x), the coefficient is understood to be 1.
PRE-ALG · 02
A letter like x, y, or n that represents an unknown or changing value is called a ___.
VARY → VARIABLE — it can vary (change)!
Root word: vary = to change. What math word comes from "vary"?
A variable is a symbol (usually a letter) used to represent an unknown or changing value. Contrast with a constant, which never changes. In 2x + 5, x is the variable and 5 is the constant.
PRE-ALG · 03
Which term correctly describes the 5 in the expression 3x + 5? — a number that does NOT change
CONSTant = stays CONSTant (fixed, never moves)
A number alone (no variable attached) that stays the same. Related English word: "consistently."
A constant is a fixed number that does not change. In 3x + 5, the 5 is a constant because its value is always 5, regardless of x. Compare: 3x changes when x changes, so 3x is NOT a constant.
PRE-ALG · 04
4x − 2 is a math ___, NOT an equation. Why? Because it has no = sign.
EXPRESSION = EX-PRESS out values, but no = sign!
An equation has an = sign. This one doesn't. What do we call a math phrase without an equals sign?
An expression is a mathematical phrase containing numbers, variables, and/or operations — but no equals sign. Examples: 4x − 2, 3 + 7, x². An equation has an = sign: 4x − 2 = 10. Students frequently confuse these two!
PRE-ALG · 05
2x + 3 = 11 — the presence of the = sign makes this a math ___.
EQUAL sign → EQUATION. Both start with "equ-"!
The key: it has an equals sign (=). The word shares its root with "equal."
An equation is a mathematical statement that two expressions are equal, shown with an = sign. 2x + 3 = 11 is an equation — solving it gives x = 4. Remember: expressions don't have =, equations do.
PRE-ALG · 06
In 5x² − 3x + 7, each part separated by + or − signs is called a ___. How many are there in this expression?
TERM = each piece. 3 terms here: 5x², −3x, 7
Count the parts: 5x² / −3x / 7. Each separated chunk is called a ___.
A term is a single number, variable, or product of numbers and variables separated by + or − signs. In 5x² − 3x + 7: the three terms are 5x², −3x, and 7. A single-term expression is called a monomial; two terms = binomial; three = trinomial.
PRE-ALG · 07
Why can you combine 3x and 5x but NOT 3x and 5x²? Because only ___ ___ can be combined.
LIKE TERMS = same variable + same exponent. "LIKE" friends go together!
3x and 5x share the exact same variable part (x). They are "___" to each other.
Like terms have the same variable(s) raised to the same power(s). 3x + 5x = 8x ✓. But 3x + 5x² cannot be simplified — different exponents! Common mistake: combining 2x and 2y (different variables — NOT like terms).
PRE-ALG · 08
In x3, the small raised 3 tells you how many times to multiply x by itself. This raised number is the ___.
The little number written above and to the right of the base. Often called "power" too.
An exponent indicates repeated multiplication of the base. x3 = x × x × x. The base is x; the exponent is 3. Common confusion: 23 = 8, NOT 6 (don't multiply 2×3 — multiply 2×2×2).
PRE-ALG · 09
What rule (or its name) tells us to evaluate 2 + 3 × 4 as 14 and NOT 20? Hint: remembered with PEMDAS
PEMDAS is the mnemonic. The full name of the rule is "order of ___."
The order of operations (PEMDAS) specifies the sequence: Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right). In 2 + 3 × 4: multiply first → 3 × 4 = 12, then 2 + 12 = 14. Most common test mistake: doing left-to-right without following PEMDAS.
PRE-ALG · 10
A statement like x > 5 or x ≤ 3 uses symbols (>, <, ≥, ≤) instead of =. It is called an ___.
IN-EQUAL-ITY = NOT equal. "in-" prefix means NOT.
The root word is "equal." Add a prefix meaning "not equal." The result describes a range, not one exact answer.
An inequality is a mathematical statement comparing two expressions using <, >, ≤, or ≥. Unlike an equation (one answer), an inequality usually has infinitely many solutions shown on a number line. Tricky: when you multiply or divide both sides by a negative number, flip the inequality symbol!
Geometry · 10 Questions
Shape, Space & Measurement
Essential geometry vocabulary — from angles to theorems.
GEO · 01
Two angles that add up to 90° are called ___ angles.
C comes before S → Complementary (90°) before Supplementary (180°)
90° = a right angle. Two angles "completing" a right angle. The word starts with "comp-".
Complementary angles sum to 90°. Example: 30° and 60° are complementary. Don't confuse with supplementary (180°). Memory trick: Complementary → Corner (90°), Supplementary → Straight line (180°).
GEO · 02
Two angles that add up to 180° and form a straight line are called ___ angles.
SUPPLEMENTARY = 180° = Straight line. S comes after C alphabetically!
A straight line = 180°. These two angles "supplement" each other to form that straight line. Starts with "supp-".
Supplementary angles sum to 180°. Example: 110° + 70° = 180°. They form a straight angle (straight line). Very common mistake: mixing up supplementary (180°) and complementary (90°).
GEO · 03
The total distance around the outside boundary of a shape is its ___.
PERI = around (like peri-scope). PERIMETER = measure around!
"Peri-" is Greek for "around." Add "-meter" (measure). What is the word?
Perimeter = sum of all sides (distance around). Rectangle: P = 2l + 2w. Square: P = 4s. Don't confuse with area (the space inside). Perimeter is measured in units (cm, m); area in square units (cm², m²).
GEO · 04
The amount of space inside a 2-D shape, measured in square units, is called the ___. Not the same as the distance around!
AREA = inside space. Unit is always SQUARED (cm², m²).
For a rectangle, the formula is length × width. The answer is in square units. Very short word — 4 letters.
Area measures the 2-D space inside a shape. Rectangle: A = l × w. Triangle: A = ½ × b × h. Circle: A = πr². Always use square units. Most common error: using perimeter formula when area is asked, or forgetting to square the radius for circles.
GEO · 05
Lines that run in the same direction and never meet, always the same distance apart, are called ___ lines.
PARALLEL has two ll's side by side → ‖ they never cross!
The word itself contains a visual clue: look at the double-l in the spelling. Symbol: ‖
Parallel lines never intersect and remain equidistant. Symbol: AB ‖ CD. Contrast with perpendicular lines (meet at 90°) and intersecting lines (meet at any angle). Rail tracks are a real-world example of parallel lines.
GEO · 06
Two lines that intersect at a 90° right angle are called ___ lines. Symbol: ⊥
PERPENDICULAR → ⊥ shape. The symbol looks like a T — two lines crossing at 90°!
The symbol is ⊥. They meet at exactly 90°. The word starts with "perp-".
Perpendicular lines meet at exactly 90° (a right angle), indicated by a small square at the intersection. Example: the corner of a room, the letter T. Don't confuse with parallel (never meet). A line perpendicular to the x-axis is vertical.
GEO · 07
In a right triangle, the side opposite the right angle — always the longest side — is the ___.
HYPOtenuse = HYPO (under) + tenuse. It's the side UNDER the right angle.
Used in the Pythagorean theorem: a² + b² = c². The "c" is always this side.
The hypotenuse is always opposite the 90° angle and is the longest side in a right triangle. Pythagorean theorem: a² + b² = c², where c = hypotenuse. Common mistake: calling a leg the hypotenuse. The hypotenuse is ONLY in right triangles — not other triangle types.
GEO · 08
When two shapes have exactly the same size AND shape, we say they are ___. Symbol: ≅
CONGRUENT ≅ same size + same shape. "con-" = together, "gruent" = agreeing.
The symbol ≅ means this. You can flip, rotate, or slide one to perfectly match the other. Not just similar — identical in size.
Congruent figures are identical in shape and size (≅). They can be reflections, rotations, or translations of each other. Contrast with similar (~): same shape, different size. Common error: using "congruent" when you mean "similar."
GEO · 09
The distance from the center of a circle to any point on the circle is called the ___.
RADIUS = ray from center. Diameter = 2 × radius. r → d = 2r.
The diameter is twice this measurement. This word also describes a "ray" going outward from the center.
The radius (r) goes from the center to the edge of a circle. Diameter = 2r. Area = πr². Circumference = 2πr. Extremely common mistake: using diameter instead of radius in the area formula. Always halve the diameter to get r first!
GEO · 10
The amount of 3-D space a solid figure occupies, measured in cubic units (cm³, m³), is called the ___.
VOLUME = 3-D space. Unit is always CUBED (³). Area=2D→², Volume=3D→³.
For a rectangular prism: length × width × height. Answer uses units like cm³. Similar word: "voluminous" = very large in space.
Volume measures 3-D space. Rectangular prism: V = l × w × h. Cylinder: V = πr²h. Cube: V = s³. Always use cubic units. Common error: confusing area (cm²) and volume (cm³), or using 2-D area formula for 3-D shapes.