Pre-Algebra
Variables · Equations · Ratios · Integers · Order of Operations
Q 01
Pre-Algebra
🧠 PEMDAS
Order of Operations
What is the value of 3 + 4 × 2 − 1?
📌 Quick Reminder
Multiply/Divide BEFORE Add/Subtract.
Try: 4 × 2 = 8 first → 3 + 8 − 1 = ?
Q 02
Pre-Algebra
🧠 ISOLATE x
Solving One-Step Equations
Solve for x:
x − 7 = 12
📌 Key Move
Do the OPPOSITE operation to both sides.
x − 7 = 12 → Add 7 to both sides → x = ?
Q 03
Pre-Algebra
🧠 RATIO = PART/WHOLE
Ratios & Proportions
A bag has 6 red marbles and 9 blue marbles. What is the ratio of red to blue marbles in simplest form?
📌 Simplify
6 : 9 → Divide both by GCF.
GCF(6, 9) = 3 → 6÷3 : 9÷3 = ?
Q 04
Pre-Algebra
🧠 NEGATIVE × NEGATIVE = POSITIVE
Integer Operations
A submarine is at −40 meters. It rises 15 meters, then descends 30 meters. What is its final depth?
📌 Number Line
Start: −40 → Rise = add (+) → Descend = subtract (−)
−40 + 15 − 30 = ?
Q 05
Pre-Algebra
🧠 DISTRIBUTE then COMBINE
Distributive Property
Simplify: 3(x + 5) − 2x
3(x + 5) − 2x = ?
📌 Steps
Step 1: Distribute → 3·x + 3·5 − 2x
Step 2: Combine like terms → x terms together, numbers together
Q 06
Pre-Algebra
🧠 PERCENT = PART ÷ WHOLE × 100
Percentages
A jacket costs $80. It is on sale at 25% off. How much do you pay?
📌 Shortcut
25% off → you pay 75% → 0.75 × $80 = ?
OR: Find 25% of 80 = 20 → 80 − 20 = ?
Q 07
Pre-Algebra
🧠 CONSTANT RATE = PROPORTIONAL
Proportional Relationships
Jake earns $9 per hour. Which equation shows how much he earns y dollars after x hours?
Q 08
Pre-Algebra
🧠 TWO-STEP: UNDO ADD/SUB FIRST
Two-Step Equations
Solve for n:
2n + 6 = 18
📌 Two Steps
Step 1: Subtract 6 → 2n = 12
Step 2: Divide by 2 → n = ?
Q 09
Pre-Algebra
🧠 INEQUALITY: FLIP when ÷ NEGATIVE
Inequalities
Which value of x is a solution to:
−3x < 12
📌 Flip Rule
Divide both sides by −3 → FLIP the inequality sign!
−3x < 12 → x > −4 → Which answer is greater than −4?
Q 10
Pre-Algebra
🧠 SLOPE = RISE ÷ RUN
Introduction to Functions & Slope
A line passes through (0, 2) and (4, 10). What is the slope of the line?
slope = (y₂ − y₁) ÷ (x₂ − x₁)
📌 Plug In
(10 − 2) ÷ (4 − 0) = 8 ÷ 4 = ?
Geometry
Angles · Area · Triangles · Circles · Pythagorean Theorem · Transformations
Q 11
Geometry
🧠 SUPPLEMENTARY = 180°
Angle Relationships
Two angles are supplementary. One angle measures 63°. What is the other angle?
📌 Memory Hook
Supplementary → S → Straight line = 180°
180° − 63° = ?
Q 12
Geometry
🧠 TRIANGLE: 180° TOTAL
Triangle Angle Sum
A triangle has angles of 47° and 85°. What is the third angle?
∠A + ∠B + ∠C = 180°
📌 Shortcut
Add the two known angles, subtract from 180.
47 + 85 = 132 → 180 − 132 = ?
Q 13
Geometry
🧠 AREA TRIANGLE = ½ × b × h
Area of Triangles
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
A = ½ × b × h
Q 14
Geometry
🧠 a² + b² = c²
Pythagorean Theorem
A right triangle has legs of 3 and 4. What is the hypotenuse?
a² + b² = c²
📌 Classic Triple: 3-4-5
3² + 4² = 9 + 16 = 25 → √25 = ?
Memorize: (3, 4, 5) and (5, 12, 13) are common right triangles!
Q 15
Geometry
🧠 CIRCLE A = π r²
Circles — Area
A circle has a diameter of 10 cm. What is its area? (Use π ≈ 3.14)
A = π r²
📌 Watch Out!
Diameter = 10 → radius = 10 ÷ 2 = 5
A = 3.14 × 5² = 3.14 × 25 = ?
Q 16
Geometry
🧠 PERIMETER = ADD ALL SIDES
Perimeter of Composite Shapes
A rectangle has a length of 12 m and a width of 5 m. What is the perimeter?
P = 2(l + w)
Q 17
Geometry
🧠 VOLUME BOX = l × w × h
Volume of Rectangular Prisms
A box is 4 cm long, 3 cm wide, and 5 cm tall. What is its volume?
V = l × w × h
Q 18
Geometry
🧠 SIMILAR: SAME SHAPE, DIFFERENT SIZE
Similar Triangles & Scale
Two similar triangles: the smaller has sides 3, 4, 5. The larger has its shortest side = 9. What is the scale factor?
📌 Scale Factor
Scale factor = Larger side ÷ Smaller corresponding side
9 ÷ 3 = ?
Q 19
Geometry
🧠 REFLECTION: FLIP over line
Transformations — Reflection
Point A is at (3, −2). It is reflected over the x-axis. What are the new coordinates?
📌 Rule
Reflect over x-axis → y changes sign, x stays
(x, y) → (x, −y) → (3, −2) → ?
Q 20
Geometry
🧠 CIRCUMFERENCE = π × d
Circles — Circumference
A circular wheel has a radius of 7 cm. How far does it travel in one full rotation? (Use π ≈ 3.14)
C = 2πr = πd
📌 One Rotation = Circumference
C = 2 × 3.14 × 7 = ?