Core Concepts & Key Formulas
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LCM & GCF
Number Theory · Unit 1
⭐ MUST MEMORIZE
GCF × LCM = a × b
GCF: highest factor both share
LCM: smallest multiple both share
Find GCF by listing common factors or using prime factorization.
Find LCM = (a × b) ÷ GCF
Quick Example
LCM of 12 and 18?
✓ 12=2²×3, 18=2×3² → LCM=2²×3²=36
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Fractions & Percentages
Arithmetic · Unit 2
⭐ MUST MEMORIZE
a/b + c/d = (ad + bc) / bd
% change = (change ÷ original) × 100
Discount = original × (rate/100)
Always find the LCD before adding or subtracting fractions.
25% off means you pay 75% of original price.
Quick Example
3/4 + 2/5 = ?
✓ LCD=20: 15/20 + 8/20 = 23/20
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Ratios & Proportions
Arithmetic · Unit 3
⭐ MUST MEMORIZE
Ratio a:b → parts are a and b
Total parts = a + b
Each part = Total ÷ (a+b)
If boys:girls = 3:4 and there are 21 boys, then 1 part = 7, total = 7×7 = 49.
Quick Example
Ratio 3:4, boys=21. Total students?
✓ 1 part=7, girls=28, total=49
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Geometry Essentials
Geometry · Unit 4
⭐ MUST MEMORIZE
Triangle Area = ½ × base × height
Rectangle Area = length × width
Rectangle Perimeter = 2(l + w)
Circle Area = π × r²
Circle Circumference = 2πr
Triangle angles SUM = 180°
Diameter = 2 × radius. Always halve diameter first!
Quick Example
Triangle: base=8, height=5. Area?
✓ ½×8×5 = 20 cm²
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Algebra & Equations
Algebra · Unit 5
⭐ MUST MEMORIZE
Solve: isolate the variable
ax + b = c → x = (c − b) ÷ a
Word problems: define variable first!
Whatever you do to one side, do to the other.
For "twice as many" problems: let smaller = x, larger = 2x.
Quick Example
3x + 7 = 22. Find x.
✓ 3x=15 → x=5
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Statistics & Probability
Data & Probability · Unit 6
⭐ MUST MEMORIZE
Mean = sum ÷ count
Median = middle value (sorted list)
Mode = most frequent value
P(event) = favorable ÷ total
P(A AND B) = P(A) × P(B) [independent]
Always SORT the list before finding the median!
For compound independent events, multiply probabilities.
Quick Example
Scores: 82, 76, 90, 76, 96. Median?
✓ Sorted: 76,76,82,90,96 → median=82
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Counting & Sequences
Combinatorics · Unit 7
⭐ MUST MEMORIZE
Arrangements (no repeat): n × (n−1) × ...
Find pattern rule → apply to next term
Common patterns: ×2+1, +odd numbers, ×ratio
For 2-digit numbers from n digits (no repeat): n×(n−1) possibilities.
Always check a pattern rule against ALL given terms before using it.
Quick Example
Sequence: 2, 5, 11, 23, 47, ___
✓ Rule: ×2+1 → 47×2+1=95
Answer Key & Full Solutions