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πŸ““ My Math Workbook
Pre-Algebra Γ— Geometry Β· Self-Study Edition
⭐ KEY PROBLEMS βœ… MULTIPLE CHOICE πŸ”₯ TRICKY ONES
Progress 0 / 20 answered
πŸ“˜ Pre-Algebra
Integers Β· Fractions Β· Equations Β· Ratios Β· Exponents
⚑ MEMORY POINT
Negative Γ— Negative = Positive  Β·   Negative Γ— Positive = Negative
"Same signs β†’ βž•   Different signs β†’ βž–"
TOPIC 1 Β· Integer Operations
1 Multiplying Integers
πŸ“– EXAMPLE
\((-3) \times (-4) = ?\)
β†’ Both negative β†’ answer is positive
β†’ \(3 \times 4 = 12\)  βˆ΄ answer = 12
Evaluate:  \((-7) \times (-3)\)
✏️ Your scratch work here…
⚑ MEMORY POINT
Order of Operations: PEMDAS
Parentheses β†’ Exponents β†’ Multiply/Divide β†’ Add/Subtract
TOPIC 2 Β· Order of Operations
2 PEMDAS β€” Don't Rush!
πŸ“– EXAMPLE
\(2 + 3 \times 4 = ?\)
❌ Wrong way: \(5 \times 4 = 20\)
βœ… Right way: \(2 + 12 = 14\)  (multiply first!)
Evaluate:  \(5 + 2 \times (8 - 3)^2 \div 10\)
✏️ Show each step…
⚑ MEMORY POINT
Adding fractions: SAME denominator first!
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}\)  β† find LCD!
TOPIC 3 Β· Fraction Addition
3 Adding Fractions with Different Denominators
πŸ“– EXAMPLE
\(\dfrac{1}{3} + \dfrac{1}{4}\) β†’ LCD = 12
\(= \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}\)
\(\dfrac{2}{5} + \dfrac{3}{4} = ?\)
✏️ Find LCD here…
⚑ MEMORY POINT
Solving one-step equations: INVERSE operation!
If \(x + 5 = 9\) β†’ subtract 5 from both sides
"Whatever you do to one side, do to the other!"
TOPIC 4 Β· One-Step Equations
4 Solving for x β€” Balance the Scale
πŸ“– EXAMPLE
\(x - 7 = 12\)
β†’ Add 7 to both sides: \(x = 19\)
Solve:  \(3x = 45\)
⚑ MEMORY POINT
Two-step equation: ADD/SUBTRACT first, then MULTIPLY/DIVIDE
\(2x + 3 = 11\) β†’ subtract 3 β†’ \(2x = 8\) β†’ divide 2 β†’ \(x = 4\)
TOPIC 5 Β· Two-Step Equations πŸ”₯ TRICKY
5 Negative Coefficient Trap!
πŸ“– EXAMPLE
\(-2x + 6 = 14\)
β†’ Subtract 6: \(-2x = 8\)
β†’ Divide by βˆ’2: \(x = -4\) ← sign flips!
Solve:  \(-3x + 9 = 21\)
⚑ MEMORY POINT
Percent = "Per hundred"
\(\text{Percent} = \dfrac{\text{part}}{\text{whole}} \times 100\)
TOPIC 6 Β· Percents
6 Finding Percent of a Number
πŸ“– EXAMPLE
What is 30% of 80?
β†’ \(0.30 \times 80 = 24\)
What is 15% of 60?
⚑ MEMORY POINT
Ratio = comparison of two quantities
\(a : b = \dfrac{a}{b}\)  Β·   Cross-multiply to solve proportions!
TOPIC 7 Β· Ratios & Proportions
7 Cross-Multiplication πŸ”₯ TRICKY
πŸ“– EXAMPLE
\(\dfrac{3}{4} = \dfrac{x}{12}\)
β†’ Cross-multiply: \(3 \times 12 = 4 \times x\)
β†’ \(36 = 4x\) β†’ \(x = 9\)
\(\dfrac{5}{8} = \dfrac{x}{24}\)  β†’ find \(x\)
⚑ MEMORY POINT
Exponent rule: \(a^m \times a^n = a^{m+n}\)
Same base β†’ ADD exponents! (Don't multiply the base!)
TOPIC 8 Β· Exponents
8 Product Rule β€” ADD the Exponents!
πŸ“– EXAMPLE
\(2^3 \times 2^4 = 2^{3+4} = 2^7 = 128\)
❌ Common mistake: \(4^7\) ← WRONG (don't change the base!)
Simplify:  \(x^3 \cdot x^5\)
⚑ MEMORY POINT
Absolute value = distance from zero
\(|{-5}| = 5\)  Β·  \(|5| = 5\)  Β·  Always non-negative!
TOPIC 9 Β· Absolute Value πŸ”₯ TRICKY
9 Absolute Value Expression
πŸ“– EXAMPLE
\(|{-3}| + |4| = 3 + 4 = 7\)
\(-|{-3}| = -3\) ← the negative is OUTSIDE the bars!
Evaluate:  \(-|{-8}| + |3|\)
⚑ MEMORY POINT
Distributive Property: \(a(b + c) = ab + ac\)
Multiply the outside number to EVERY term inside!
TOPIC 10 Β· Distributive Property πŸ”₯ TRICKY
10 Distributing Negatives
πŸ“– EXAMPLE
\(-2(x - 5)\)
β†’ \(-2 \cdot x + (-2) \cdot (-5)\)
β†’ \(-2x + 10\)  β† negative Γ— negative = positive!
Expand:  \(-4(3x - 2)\)
πŸ“ Geometry
Angles Β· Triangles Β· Area Β· Pythagorean Β· Circles Β· Perimeter
⚑ MEMORY POINT
Supplementary angles = add up to 180Β°
Complementary angles = add up to 90Β°
"S for Straight (180) Β· C for Corner (90)"
TOPIC 11 Β· Angle Relationships
11 Supplementary vs Complementary
πŸ“– EXAMPLE
Two angles are supplementary. One is 110Β°.
β†’ \(180Β° - 110Β° = 70Β°\)  β† the other angle
Two angles are complementary. One angle is 34Β°. What is the other?
⚑ MEMORY POINT
Triangle Angle Sum: Always 180Β°
\(\angle A + \angle B + \angle C = 180Β°\)
TOPIC 12 Β· Triangle Angles πŸ”₯ TRICKY
12 Finding the Missing Angle
πŸ“– EXAMPLE
Triangle with angles 50Β°, 70Β°, and ?
β†’ \(50 + 70 + x = 180\) β†’ \(x = 60Β°\)
A triangle has angles of \(55Β°\) and \(82Β°\). What is the third angle?
⚑ MEMORY POINT
Area of Triangle = \(\dfrac{1}{2} \times base \times height\)
"Half of rectangle" β€” the height must be perpendicular!
TOPIC 13 Β· Area of Triangle
13 Area β€” Don't Forget the Half!
\[A = \frac{1}{2} \times b \times h\]
Find the area of a triangle with base = 10 cm and height = 7 cm.
⚑ MEMORY POINT
Pythagorean Theorem: \(a^2 + b^2 = c^2\)
c = hypotenuse (longest side, opposite the right angle)
TOPIC 14 Β· Pythagorean Theorem πŸ”₯ TRICKY
14 Finding the Hypotenuse
\[a^2 + b^2 = c^2\]
πŸ“– EXAMPLE
Legs: 3 and 4 β†’ \(3^2 + 4^2 = 9 + 16 = 25\) β†’ \(c = \sqrt{25} = 5\)
A right triangle has legs of 5 and 12. Find the hypotenuse.
⚑ MEMORY POINT
Perimeter = add ALL sides
Rectangle: \(P = 2l + 2w\)  Β·  "Two lengths + Two widths"
TOPIC 15 Β· Perimeter
15 Rectangle Perimeter
\[P = 2l + 2w\]
A rectangle has length 9 m and width 4 m. Find the perimeter.
⚑ MEMORY POINT
Circle:   \(A = \pi r^2\)  Β·  \(C = 2\pi r\)
Area uses rΒ² Β· Circumference uses r only!
TOPIC 16 Β· Circle Area πŸ”₯ TRICKY
16 Area of a Circle β€” Diameter Trap!
πŸ“– EXAMPLE
Diameter = 10 β†’ radius = 5
\(A = \pi r^2 = \pi \times 25 = 25\pi \approx 78.5\)
A circle has a diameter of 12 cm. Find its area. (Use \(\pi \approx 3.14\))
✏️ r = d ÷ 2 = ?
⚑ MEMORY POINT
Vertical angles are EQUAL
They form an "X" β€” opposite angles match!
TOPIC 17 Β· Vertical Angles
17 Vertical Angles β€” Same or Different?
πŸ“– EXAMPLE
Two lines cross β†’ 4 angles form.
Angle 1 = 65Β° β†’ Vertical angle (angle 3) = 65Β°
Adjacent angle (angle 2) = 180Β° βˆ’ 65Β° = 115Β°
Two lines intersect. One angle is 72Β°. What is its vertical angle?
⚑ MEMORY POINT
Volume of Rectangular Prism: \(V = l \times w \times h\)
"Length Γ— Width Γ— Height β€” fill the box!"
TOPIC 18 Β· Volume
18 Volume of Rectangular Prism
\[V = l \times w \times h\]
Find the volume of a box with length 6 cm, width 4 cm, height 5 cm.
⚑ MEMORY POINT
Parallel lines cut by transversal:
Alternate interior angles = EQUAL
Co-interior (same-side) angles = 180Β°
TOPIC 19 Β· Parallel Lines & Transversals πŸ”₯ TRICKY
19 Alternate Interior Angles
πŸ“– EXAMPLE
Two parallel lines are cut by a transversal.
One alternate interior angle = 115Β°
β†’ Its alternate interior angle = 115Β° (equal!)
Parallel lines are cut by a transversal. One co-interior (same-side interior) angle is 65Β°. What is the other co-interior angle?
⚑ MEMORY POINT
Sum of interior angles of a polygon:
\((n - 2) \times 180Β°\)   where n = number of sides
Triangle(3) = 180Β° Β· Quadrilateral(4) = 360Β° Β· Pentagon(5) = 540Β°
TOPIC 20 Β· Polygon Angles πŸ”₯ TRICKY
20 Interior Angle Sum of a Hexagon
\[\text{Sum} = (n - 2) \times 180Β°\]
πŸ“– EXAMPLE
Pentagon (n = 5): \((5-2) \times 180Β° = 3 \times 180Β° = 540Β°\)
What is the sum of interior angles of a hexagon (6 sides)?
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