Self-Study Workbook · Math Fundamentals
20 essential questions · answer in your own words · check instantly
A letter that represents an unknown number is called a ___.
Example
In 3x + 5 = 11, the letter x is the ___.
→ It could be 1, 2, or any number until you solve it.
The number multiplied by a variable is called the ___.
Example
4y² − 3y + 9
• coefficient of y² = 4
• coefficient of y = −3
• 9 is a constant (no variable attached)
A number with no variable — its value never changes — is called a ___.
Practice
In 6a − 8 = 10, which numbers are constants? → −8 and 10
Terms that have exactly the same variable and exponent are called ___.
Tricky Case — don't mix up!
2x² + 5x² → can combine → 7x² ✅
2x² + 5x → CANNOT combine ❌ (exponents differ)
The rule a(b + c) = ab + ac is called the ___ property.
Example
3(x + 4) = 3·x + 3·4 = 3x + 12
Common mistake: 3(x + 4) ≠ 3x + 4 ← forgot to distribute to 4!
A mathematical statement that shows two expressions are equal (uses an "=" sign) is called an ___.
Equation vs. Expression
2x + 3 → Expression (no "=" sign)
2x + 3 = 7 → Equation (has "=" sign) ✅
In 53, the small raised number 3 is called the ___. It tells you how many times to multiply the base by itself.
Watch out!
23 = 8 ← not 6! (2×3 = 6 is WRONG)
23 means 2 × 2 × 2 = 8
The distance from a number to zero on the number line — always non-negative — is called its ___.
Common Trap
|−5| = ? → Answer: 5 (not −5)
−|5| = ? → Answer: −5 (negative sign is OUTSIDE the bars)
A mathematical statement that compares two values using <, >, ≤, ≥, or ≠ is called an ___.
Reading Practice
x > 3 → "x is greater than 3"
x ≤ 5 → "x is less than or equal to 5"
⚠️ When you multiply/divide by a negative, FLIP the sign!
The rule that says you must solve parentheses → exponents → multiply/divide → add/subtract in that order is called ___.
Classic Trap
2 + 3 × 4 = ?
Wrong: 2+3=5, then 5×4=20 ❌
Right: 3×4=12, then 2+12=14 ✅
The total distance around the outside of a shape is called its ___.
Example — Rectangle 6 × 4
Perimeter = 6 + 4 + 6 + 4 = 20
Or: P = 2(l + w) = 2(6+4) = 20
⚠️ Don't confuse with Area (which uses × not +)
The amount of space inside a 2D figure, measured in square units, is called its ___.
Key Formulas
Rectangle: A = l × w
Triangle: A = 12 × b × h
Circle: A = πr²
Lines in the same plane that never intersect and are always the same distance apart are called ___ lines.
vs. Perpendicular
Parallel: same direction, never meet ∥
Perpendicular: meet at exactly 90° ⊥
Two figures that have exactly the same shape AND size are called ___.
Congruent vs. Similar
🔷🔷 Two identical triangles → Congruent
🔷🔹 One big, one small triangle → Similar (same angles, different size)
In a right triangle, the side opposite the right angle — always the longest side — is called the ___.
Pythagorean Theorem
Legs: 3, 4 → 3² + 4² = c²
9 + 16 = 25 → c = 5
The side with length 5 is the hypotenuse.
Two angles that add up to 180° are called ___ angles.
Quick Drill
If one angle is 110°, its supplement = 180° − 110° = 70°
If one angle is 35°, its complement = 90° − 35° = 55°
The distance from the center of a circle to any point on its edge is called the ___.
Radius vs. Diameter vs. Circumference
radius r → diameter d = 2r → circumference C = 2πr
If radius = 5: diameter = 10, circumference ≈ 31.4
The amount of 3D space a solid occupies, measured in cubic units, is called its ___.
Key Formulas
Rectangular prism: V = l × w × h
Cube (side s): V = s³
Cylinder: V = πr²h
The corner point where two sides of a polygon meet — or the tip of an angle — is called a ___.
Count the Vertices
Triangle → 3 vertices
Rectangle → 4 vertices
Pentagon → 5 vertices
A shape always has the same number of sides as vertices!
The perimeter (distance around) of a circle is called its ___. Use the formula C = 2πr.
Example
Circle with radius = 7:
C = 2 × π × 7 ≈ 2 × 3.14 × 7 ≈ 43.96
⚠️ Use diameter if given: C = πd