πŸ“ EXAM PREP Β· ALL UNITS

Pre-Algebra
Master Quiz

20 essential problems Β· Real exam difficulty
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20Questions
8Units
30Minutes
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πŸ“š Concepts & Formulas
πŸ”’
UNIT 1
Integers & Absolute Value
β–Ύ
β˜… MEMORIZE
  • Absolute value |x| = distance from 0; always β‰₯ 0
  • Adding integers: same sign β†’ add & keep sign; diff sign β†’ subtract & use larger sign
  • Negative Γ— Negative = Positive; Negative Γ— Positive = Negative
  • Dividing integers: same rule as multiplication for signs
|βˆ’7| = 7    |+7| = 7
(βˆ’3) Γ— (βˆ’4) = +12
(βˆ’5) + (+3) = βˆ’2
(βˆ’12) Γ· (βˆ’4) = +3
EXAMPLE
What is |βˆ’9| + (βˆ’4)?
= 9 + (βˆ’4) = 5
βž—
UNIT 2
Fractions, Decimals & Percents
β–Ύ
β˜… MEMORIZE
  • To multiply fractions: multiply numerators, multiply denominators
  • To divide fractions: multiply by the reciprocal (Keep–Change–Flip)
  • Percent = Part Γ· Whole Γ— 100
  • To convert fraction to decimal: divide numerator by denominator
(a/b) Γ— (c/d) = ac/bd
(a/b) Γ· (c/d) = (a/b) Γ— (d/c)
Part = Whole Γ— (Percent/100)
EXAMPLE
What is (3/4) Γ· (1/2)?
= (3/4) Γ— (2/1) = 6/4 = 3/2 = 1.5
⚑
UNIT 3
Order of Operations (PEMDAS)
β–Ύ
β˜… MEMORIZE
  • Parentheses first
  • Exponents second
  • Multiplication & Division (left to right)
  • Addition & Subtraction (left to right)
P β†’ E β†’ M/D β†’ A/S
Example: 3 + 2 Γ— 4Β² βˆ’ (5βˆ’1)
= 3 + 2 Γ— 16 βˆ’ 4
= 3 + 32 βˆ’ 4 = 31
EXAMPLE
Evaluate: 10 βˆ’ 2Β³ + (6 Γ· 3)
= 10 βˆ’ 8 + 2 = 4
πŸ”£
UNIT 4
Variables & Expressions
β–Ύ
β˜… MEMORIZE
  • Variable: a letter representing an unknown value
  • Coefficient: number in front of a variable (e.g. 3 in 3x)
  • Like terms: same variable & same exponent β€” can be combined
  • Distributive Property: a(b + c) = ab + ac
5x + 3x = 8x (like terms)
2x + 3y β‰  5xy (unlike terms)
3(x + 4) = 3x + 12
EXAMPLE
Simplify: 4x + 2y βˆ’ x + 5y
= 3x + 7y
βš–οΈ
UNIT 5
Solving One-Step & Two-Step Equations
β–Ύ
β˜… MEMORIZE
  • Use inverse operations to isolate the variable
  • Whatever you do to one side, do to the other
  • Two-step: undo addition/subtraction first, then multiplication/division
  • Always check your answer by substituting back
One-step: x + 5 = 12 β†’ x = 7
Two-step: 2x βˆ’ 3 = 11
β†’ 2x = 14 β†’ x = 7
EXAMPLE
Solve: 3x + 6 = 21
3x = 15 β†’ x = 5
πŸ“Š
UNIT 6
Ratios, Proportions & Rates
β–Ύ
β˜… MEMORIZE
  • Ratio: comparison of two quantities (a : b or a/b)
  • Proportion: two equal ratios (a/b = c/d)
  • Cross-multiply to solve proportions: ad = bc
  • Unit rate: rate with denominator of 1 (e.g. 60 mph)
a/b = c/d β†’ ad = bc
3/4 = x/12 β†’ 4x = 36 β†’ x = 9
Rate = Distance Γ· Time
EXAMPLE
If 5 pens cost $3, how much do 15 pens cost?
5/3 = 15/x β†’ x = $9
πŸ“
UNIT 7
Geometry Basics (Area & Perimeter)
β–Ύ
β˜… MEMORIZE
  • Rectangle: Area = l Γ— w; Perimeter = 2(l + w)
  • Triangle: Area = (1/2) Γ— b Γ— h
  • Circle: Area = Ο€rΒ²; Circumference = 2Ο€r
  • Pythagorean Theorem: aΒ² + bΒ² = cΒ² (right triangles only)
Rectangle: A = lw, P = 2l + 2w
Triangle: A = (1/2)bh
Circle: A = Ο€rΒ², C = 2Ο€r
Right β–³: aΒ² + bΒ² = cΒ²
EXAMPLE
Area of a triangle with base 8 and height 5?
A = (1/2)(8)(5) = 20 sq units
πŸ“ˆ
UNIT 8
Graphing & Coordinate Plane
β–Ύ
β˜… MEMORIZE
  • Ordered pair: (x, y) β€” x is horizontal, y is vertical
  • Slope: rise Γ· run = (yβ‚‚βˆ’y₁) Γ· (xβ‚‚βˆ’x₁)
  • Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
  • Origin = (0, 0); Quadrants I–IV labeled counter-clockwise
Slope m = (yβ‚‚ βˆ’ y₁) / (xβ‚‚ βˆ’ x₁)
y = mx + b
Quadrant I: (+, +)   II: (βˆ’, +)
Quadrant III: (βˆ’, βˆ’)   IV: (+, βˆ’)
EXAMPLE
Slope between (1, 2) and (3, 8)?
m = (8βˆ’2)/(3βˆ’1) = 6/2 = 3
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