Self-Study Workbook · 20 Questions

Pre-Algebra & Geometry
Terminology Quiz

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Pre-Algebra

Q01 — Q10
Q01 Pre-Algebra
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🔑 Topic: Order of Operations

Concept: PEMDAS tells you the sequence to evaluate any math expression.
Example: 2 + 3 × 4 → multiply first → 2 + 12 = 14 (NOT 20!)
🧠 Quick Memo: Please Excuse My Dear Aunt Sally = Parentheses · Exponents · Multiply/Divide · Add/Subtract

What is the value of 3 + 4 × 2 − 1 ?

Explanation
Step 1 — Multiply first: 4 × 2 = 8
Step 2 — Left to right: 3 + 8 − 1 = 10
⚠️ Trap: Many students add 3 + 4 first and get 14. Always follow PEMDAS!
Q02 Pre-Algebra
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🔑 Topic: Variables & Expressions

Concept: A variable is a letter that holds an unknown number. An expression has variables and/or numbers but NO equal sign.
Example: 5x + 3 → if x = 2, then 5(2) + 3 = 13
🧠 Quick Memo: Variable = mystery box — substitute to open it

If x = 4, what is the value of 3x − 5 ?

Explanation
Substitute x = 4: 3(4) − 5 = 12 − 5 = 7
⚠️ Trap: Some students compute 3 × 4 − 5 as 3 × (4−5) = −3. Always multiply before subtracting!
Q03 Pre-Algebra
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🔑 Topic: Integers — Negative Numbers

Concept: Subtracting a negative = adding a positive.
Example: 5 − (−3) = 5 + 3 = 8
🧠 Quick Memo: Two negatives → POSITIVE ( −(−x) = +x )

What is −8 − (−3) ?

Explanation
−8 − (−3) → flip the sign → −8 + 3 = −5
⚠️ Trap: Many students write −8 − 3 = −11, forgetting to flip the sign of −3.
Q04 Pre-Algebra
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🔑 Topic: Combining Like Terms

Concept: Like terms share the SAME variable AND exponent. Only like terms can be added/subtracted.
Example: 4x + 2y + 3x → combine 4x and 3x → 7x + 2y
🧠 Quick Memo: Same letter, same power = like (apples + apples, not apples + oranges)

Simplify: 5a + 3b − 2a + b

Explanation
Group like terms: (5a − 2a) + (3b + b) = 3a + 4b
⚠️ Trap: Students often mix a-terms and b-terms together. You cannot add 3a + 4b into one term!
Q05 Pre-Algebra
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🔑 Topic: Solving One-Step Equations

Concept: Do the OPPOSITE operation to isolate the variable.
Example: x + 5 = 12 → subtract 5 from both sides → x = 7
🧠 Quick Memo: Balance = do the same to BOTH sides

Solve: x − 7 = 9

Explanation
Add 7 to both sides: x − 7 + 7 = 9 + 7 → x = 16
⚠️ Trap: Students subtract 7 and get x = 2. You must ADD the opposite of −7.
Q06 Pre-Algebra
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🔑 Topic: Ratios & Proportions

Concept: A ratio compares two quantities. A proportion says two ratios are equal.
Cross-multiply to solve: a⁄b = c⁄d → a × d = b × c
🧠 Quick Memo: Cross × multiply to find the missing value

Solve for n: 3⁄4 = n⁄20

Explanation
Cross-multiply: 3 × 20 = 4 × n → 60 = 4n → n = 15
⚠️ Trap: n = 5 is a common error (dividing 20 by 4 without cross-multiplying).
Q07 Pre-Algebra
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🔑 Topic: Percent

Concept: Percent means "per hundred." To find a % of a number, multiply.
Example: 20% of 50 = 0.20 × 50 = 10
🧠 Quick Memo: % → ÷100 · "of" means × (multiply)

What is 35% of 80?

Explanation
0.35 × 80 = 28
⚠️ Trap: D (2800) comes from forgetting to divide by 100. Always convert % to a decimal first.
Q08 Pre-Algebra
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🔑 Topic: Exponents

Concept: An exponent tells you how many times to multiply the base by itself.
Example: 23 = 2 × 2 × 2 = 8
🧠 Quick Memo: Base × itself (exponent) times — NOT base × exponent!

What is 34 ?

Explanation
34 = 3 × 3 × 3 × 3 = 9 × 9 = 81
⚠️ Trap: A (12) = 3 × 4. Many students multiply base × exponent instead of repeated multiplication!
Q09 Pre-Algebra
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🔑 Topic: Distributive Property

Concept: a(b + c) = ab + ac — multiply the outside term by EACH inside term.
Example: 3(x + 4) = 3x + 12
🧠 Quick Memo: Distribute = share with everyone inside

Expand: 4(2x − 3)

Explanation
4 × 2x = 8x, then 4 × (−3) = −12 → 8x − 12
⚠️ Trap: A (8x − 3) = forgetting to multiply 4 by the −3. Distribute to BOTH terms!
Q10 Pre-Algebra
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🔑 Topic: Inequalities

Concept: Solve like an equation, BUT flip the inequality sign when you × or ÷ by a negative number.
Example: −2x < 6 → ÷(−2), flip sign → x > −3
🧠 Quick Memo: FLIP the sign when ÷ or × negative!

Solve: −3x ≤ 12

Explanation
Divide both sides by −3 AND flip: −3x ÷ (−3) ≤ 12 ÷ (−3) → x ≥ −4
⚠️ Trap: A = forgot to flip. B = forgot to flip AND got sign wrong. Always flip when dividing by negative!

Geometry

Q11 — Q20
Q11 Geometry
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🔑 Topic: Area of a Triangle

Formula: Area = 1⁄2 × base × height
Example: base = 6, height = 4 → A = 1⁄2 × 6 × 4 = 12
🧠 Quick Memo: Triangle = HALF of a rectangle → ½ × b × h

A triangle has base = 10 cm and height = 7 cm. What is its area?

Explanation
A = ½ × 10 × 7 = ½ × 70 = 35 cm²
⚠️ Trap: A (70) = forgot the ½. Most common mistake — triangle formula always has that ½!
Q12 Geometry
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🔑 Topic: Pythagorean Theorem

Formula: a² + b² = c² (c = hypotenuse, the longest side)
Example: a = 3, b = 4 → 9 + 16 = 25 → c = √25 = 5
🧠 Quick Memo: Leg² + Leg² = Hypotenuse² (only for RIGHT triangles!)

A right triangle has legs of 6 and 8. What is the hypotenuse?

Explanation
6² + 8² = 36 + 64 = 100 → c = √100 = 10
⚠️ Trap: A (14) = adding 6 + 8. You must SQUARE the legs first, then take the square root!
Q13 Geometry
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🔑 Topic: Circumference of a Circle

Formulas: C = 2πr (using radius) OR C = πd (using diameter)
Example: r = 5 → C = 2π(5) = 10π ≈ 31.4
🧠 Quick Memo: C = πd (pie · diameter) or 2πr · diameter = 2 × radius

What is the circumference of a circle with radius = 7? (Use π ≈ 3.14)

Explanation
C = 2 × 3.14 × 7 = 6.28 × 7 = 43.96
⚠️ Trap: C (153.86) = πr² — that's the AREA formula, not circumference!
Q14 Geometry
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🔑 Topic: Supplementary & Complementary Angles

Complementary: two angles that add up to 90°
Supplementary: two angles that add up to 180°
Example: If angle A = 65°, its supplement = 180° − 65° = 115°
🧠 Quick Memo: Complementary = Corner (90°) · Supplementary = Straight line (180°)

An angle measures 47°. What is its supplementary angle?

Explanation
Supplementary = 180° − 47° = 133°
⚠️ Trap: A (43°) = 90° − 47° = that's the COMPLEMENTARY angle. C (127°) is 180° − 53°, a calculation error.
Q15 Geometry
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🔑 Topic: Perimeter of a Rectangle

Formula: P = 2(l + w) or P = 2l + 2w
Example: l = 8, w = 3 → P = 2(8 + 3) = 2(11) = 22
🧠 Quick Memo: Perimeter = walk around ALL sides · Rectangle has 2 lengths + 2 widths

A rectangle is 9 m long and 5 m wide. What is its perimeter?

Explanation
P = 2(9 + 5) = 2(14) = 28 m
⚠️ Trap: A (45) = 9 × 5 — that's the AREA! Perimeter ≠ multiplication of sides.
Q16 Geometry
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🔑 Topic: Types of Triangles by Angles

Acute: ALL angles < 90°  |  Right: ONE angle = 90°  |  Obtuse: ONE angle > 90°
Example: A triangle with angles 30°, 60°, 90° → one angle = 90° → Right triangle
🧠 Quick Memo: Obtuse = OVER 90° (one big blunt angle) · Acute = all SMALL angles

A triangle has angles of 120°, 35°, and 25°. What type is it?

Explanation
One angle (120°) is greater than 90° → Obtuse triangle
⚠️ Check: 120 + 35 + 25 = 180 ✓. Equilateral = all angles 60°, totally different!
Q17 Geometry
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🔑 Topic: Sum of Interior Angles

Formula: Sum = (n − 2) × 180°, where n = number of sides
Example: Pentagon (5 sides): (5−2) × 180 = 3 × 180 = 540°
🧠 Quick Memo: (sides − 2) × 180 · Triangle = (3−2)×180 = 180° always!

What is the sum of interior angles of a hexagon (6 sides)?

Explanation
(6 − 2) × 180 = 4 × 180 = 720°
⚠️ Trap: C (360°) = exterior angles of ANY polygon sum to 360°. That's a different concept!
Q18 Geometry
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🔑 Topic: Volume of a Rectangular Prism

Formula: V = l × w × h
Example: l = 4, w = 3, h = 2 → V = 4 × 3 × 2 = 24 cm³
🧠 Quick Memo: Volume = fill the box · l × w × h · unit is always CUBED (³)

A box is 5 cm long, 4 cm wide, 3 cm tall. What is its volume?

Explanation
V = 5 × 4 × 3 = 60 cm³
⚠️ Trap: C (20) = 5 × 4, forgetting to multiply by height. Volume needs ALL THREE dimensions!
Q19 Geometry
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🔑 Topic: Vertical Angles

Concept: Vertical angles are formed when two lines cross. They are ALWAYS equal.
Example: Two lines cross; one angle = 55° → its vertical angle = 55°
🧠 Quick Memo: Vertical = opposite = EQUAL (the X shape — opposite corners match)

Two lines intersect. One angle is 72°. What is the measure of its vertical angle?

Explanation
Vertical angles are equal → 72°
⚠️ Trap: C (108°) = 180° − 72° — that's the SUPPLEMENTARY angle (adjacent, not vertical)!
Q20 Geometry
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🔑 Topic: Area of a Circle

Formula: A = πr²
Example: r = 3 → A = π × 3² = 9π ≈ 28.26
🧠 Quick Memo: A = πr² · "pie are squared" — r is SQUARED, not doubled!

What is the area of a circle with radius = 5? (Use π ≈ 3.14)

Explanation
A = π × 5² = 3.14 × 25 = 78.5
⚠️ Trap: B (31.4) = 2πr — that's the CIRCUMFERENCE! Area uses r², not just r.

Quiz Complete! 🎉

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