PEMDAS = Parentheses → Exponents → Multiply/Divide → Add/Subtract
🧠 Say: "Please Excuse My Dear Aunt Sally"
Evaluate: 3 + 2 × 4
✦ First, multiply: 2 × 4 = 8
✦ Then add: 3 + 8 = 11 ✅
Step 1: Inside ( ): 2² = 4, so 4 − 1 = 3
Step 2: Multiply: 3 × 3 = 9
Step 3: Add: 5 + 9 = 14
✅ Answer is A) 14
ISOLATE the variable — do the OPPOSITE operation on both sides.
🧠 "What's done to x, undo it!"
Solve: x + 7 = 12
✦ Subtract 7 from both sides: x = 12 − 7 = 5 ✅
Step 1: Add 4 to both sides → 3x = 18
Step 2: Divide both sides by 3 → x = 6
✅ Answer is C) x = 6
UNDO in reverse order: first ±, then ×÷
🧠 "Reverse the recipe!"
Solve: 2x + 3 = 11
✦ Subtract 3: 2x = 8 → Divide by 2: x = 4 ✅
Step 1: Subtract 10 → −2x = −6
Step 2: Divide by −2 → x = 3
⚠️ Dividing two negatives = positive!
✅ Answer is B) x = 3
SLOPE = Rise over Run = m = (y₂−y₁)/(x₂−x₁)
🧠 "Rise UP, Run RIGHT"
Points: (1, 2) and (3, 6)
✦ m = (6−2)/(3−1) = 4/2 = 2 ✅
m = (9 − 3) / (2 − (−1)) = 6 / 3 = 2
⚠️ Watch out: 2 − (−1) = 3, not 1!
✅ Answer is C) m = 2
y = mx + b → m = slope, b = y-intercept
🧠 "m is the Mountain (slope), b is the Beginning (y-axis)"
Line: y = 3x − 2 → slope = 3, y-intercept = −2 ✅
Divide by 2: y = 3x − 5
Now in y = mx + b form → b = −5
⚠️ Many students forget to divide −10 by 2!
✅ Answer is B) b = −5
DISTRIBUTE: a(b + c) = ab + ac
🧠 "Share the love with EVERY term inside!"
Simplify: 3(x + 4)
✦ 3·x + 3·4 = 3x + 12 ✅
Step 1: Distribute −2: −2·3x = −6x, −2·(−5) = +10
Step 2: −6x + 10 + 4x = −2x + 10
⚠️ Negative × Negative = Positive!
✅ Answer is D) −2x + 10
SUBSTITUTION: Solve one equation → plug into the other
🧠 "Replace, then solve!"
y = x + 1 and x + y = 5
✦ Sub y: x + (x+1) = 5 → 2x = 4 → x = 2, y = 3 ✅
Substitute y = 2x−1 into x + y = 8:
x + (2x − 1) = 8 → 3x − 1 = 8 → 3x = 9 → x = 3
Then y = 2(3) − 1 = 5
✅ Answer is B) x = 3
GCF FIRST: Always look for Greatest Common Factor before anything else!
🧠 "Can I take something OUT of all terms?"
Factor: 6x² + 9x
✦ GCF = 3x → 3x(2x + 3) ✅
GCF of 4x² and 16x = 4x
4x² ÷ 4x = x and 16x ÷ 4x = 4
Result: 4x(x − 4)
⚠️ A, B, D are not fully factored (GCF isn't fully pulled out)
✅ Answer is C) 4x(x − 4)
FLIP the inequality sign when multiplying or dividing by a NEGATIVE!
🧠 "Multiply/divide negative → sign flips like a pancake 🥞"
Solve: −3x < 9
✦ Divide by −3 → FLIP sign: x > −3 ✅
Step 1: Subtract 2 → −4x ≤ 8
Step 2: Divide by −4 → FLIP ≤ to ≥ → x ≥ −2
⚠️ Most common mistake: forgetting to flip the sign!
✅ Answer is B) x ≥ −2
SAME BASE: Multiply → add exponents: xᵃ · xᵇ = xᵃ⁺ᵇ
POWER: (xᵃ)ᵇ = xᵃˣᵇ
🧠 "Multiply = Add exponents. Power = Multiply exponents."
Simplify: x³ · x²
✦ Add exponents: x⁵ ✅
Step 1: (2x³)² = 2² · (x³)² = 4x⁶
Step 2: Multiply by x: 4x⁶ · x = 4x⁷
⚠️ Common error: forgetting 2² = 4 (only gets x⁷ but writes 2x⁷)
✅ Answer is C) 4x⁷
Answer all questions to see your result!
COMPLEMENTARY = add up to 90° 🧠 "C comes before S, 90 before 180"
SUPPLEMENTARY = add up to 180°
Angle A = 35°. Supplement = 180 − 35 = 145° ✅
Supplementary → sum = 180°
(3x + 20) + (x + 40) = 180
4x + 60 = 180 → 4x = 120 → x = 30
✅ Answer is C) x = 30
TRIANGLE SUM = 180° always!
🧠 "Three angles, one rule: always 180!"
Angles 60°, 70°, x°: x = 180 − 60 − 70 = 50° ✅
4x + (2x + 12) + (3x − 3) = 180
9x + 9 = 180 → 9x = 171 → x = 19
✅ Answer is B) x = 19
a² + b² = c² — c is always the HYPOTENUSE (longest side)
🧠 "Legs squared, add 'em up = hypotenuse squared"
Legs: 3, 4 → c² = 9 + 16 = 25 → c = 5 ✅
5² + 12² = c²
25 + 144 = 169
c = √169 = 13
✅ This is the famous 5-12-13 Pythagorean triple!
✅ Answer is C) 13
TRIANGLE AREA = ½ × base × height
🧠 "Half a rectangle = a triangle!"
Triangle: base = 8, height = 5
✦ A = ½ × 8 × 5 = 20 units² ✅
A = ½ × 14 × 9 = ½ × 126 = 63 cm²
⚠️ Answer A (126) is the most common error — students skip the ½!
✅ Answer is B) 63 cm²
C = 2πr or πd (perimeter of circle)
A = πr² (area)
🧠 "Twice around is C, r² inside is A"
Circle with r = 5 → Area = π(5²) = 25π ≈ 78.5 ✅
diameter = 10, so C = πd = 3.14 × 10 = 31.4 cm
⚠️ Choice A (62.8) = using d as if it were radius (2 × 3.14 × 10)!
✅ Answer is B) 31.4 cm
ALTERNATE INTERIOR angles = equal (Z-shape 🤙)
CO-INTERIOR angles = 180° (same side, supplementary)
🧠 "Z = equal, C = 180°"
If parallel lines cut by transversal, angle = 70° → alternate interior angle = 70° ✅
Co-interior → sum = 180:
(4x + 10) + (2x + 20) = 180
6x + 30 = 180 → 6x = 150 → x = 25
✅ Answer is D) x = 25
VOLUME = Base Area × Height = B × h
🧠 "Stack the base all the way up!"
Rectangular prism: 4×3 base, height = 5
✦ V = 12 × 5 = 60 units³ ✅
Base area = 6 × 4 = 24 cm²
V = 24 × 5 = 120 cm³
⚠️ Choice D (60) = only multiplied 2 dimensions, forgot the third!
✅ Answer is C) 120 cm³
PERIMETER = Add ALL sides (walk around the outside!)
🧠 "Perimeter = Path around the edge 🚶"
Rectangle: length = 8, width = 3
✦ P = 2(8+3) = 22 units ✅
Let w = width, l = 3w
2(3w + w) = 48 → 2(4w) = 48 → 8w = 48 → w = 6
✅ Answer is B) w = 6 cm
EXTERIOR ANGLE = sum of the TWO non-adjacent interior angles
🧠 "The outside angle = the two far inside angles added!"
Interior angles 50° and 70° → Exterior angle = 50 + 70 = 120° ✅
Exterior Angle = sum of two remote interior angles
65 + x = 110 → x = 45°
⚠️ Don't confuse with the adjacent interior angle (70°, which is supplementary to 110°)
✅ Answer is B) 45°
SSS = 3 sides equal → Congruent ✅
SAS = 2 sides + included angle → Congruent ✅
AAA = only angles → NOT congruent (just similar!) ❌
🧠 "AAA = Same Shape but NOT Same Size!"
△ABC has sides 5, 7, 9. △DEF has sides 5, 7, 9 → Congruent by SSS ✅
AB = DE (side), ∠B = ∠E (angle), BC = EF (side)
The angle ∠B is BETWEEN sides AB and BC → this is SAS!
⚠️ AAA proves SIMILARITY only, not congruence
✅ Answer is B) SAS
Answer all questions to see your result!