TOP EDU PREP · Algebra 1 Exam

Core Practice
20 Problems

All major units covered · Exam-style multiple choice · Step-by-step solutions

Concept Review
Unit 1 · Real Numbers

Operations & Absolute Value

Absolute value |a| = distance from zero, always ≥ 0. When subtracting a negative, flip to addition.

|a| ≥ 0 always
a − (−b) = a + b
neg × neg = positive
|−8| + |3| − |−2| = 8 + 3 − 2 = 9
Unit 2 · Algebraic Expressions

Simplifying & Evaluating

Combine like terms (same variable, same power). To evaluate, substitute values then follow order of operations.

3x + 2x = 5x (like terms)
3x + 2y ≠ simplify further (unlike)
Evaluate 2a² − 3b, a=3, b=4 → 2(9) − 12 = 6
Unit 3 · Linear Equations

Solving One & Two Step

Isolate the variable. Use inverse operations. Distribute first if parentheses are present. Always verify by substitution.

2(x + 3) = 18
x + 3 = 9 → x = 6
Check: 2(6+3) = 18 ✓
Unit 4 · Inequalities

Solving & Graphing

Same as equations BUT: multiplying/dividing both sides by a negative FLIPS the inequality sign.

−3x ≥ 12 → x ≤ −4 (flip!)
2x − 3 < 7 → x < 5 (no flip)
Unit 5 · Functions

Function Notation

f(x) means "plug x in". Each input has exactly one output (vertical line test for graphs).

f(x) = 2x − 5
f(4) = 2(4) − 5 = 8 − 5 = 3
Unit 6 · Linear Graphs

Slope & Intercepts

Slope m = rise/run = (y₂−y₁)/(x₂−x₁). y-intercept: set x=0. x-intercept: set y=0.

slope = (y₂−y₁) / (x₂−x₁)
y = mx + b (slope-intercept form)
Through (2,3)(6,11): slope = (11−3)/(6−2) = 2
Unit 7 · Systems of Equations

Substitution & Elimination

Add/subtract equations to eliminate one variable (elimination). Or solve one for a variable and substitute (substitution).

x+y=10, x−y=4
Add: 2x=14 → x=7, y=3
Unit 8 · Exponents

Exponent Rules

Key rules you must memorize for every Algebra exam.

x^a · x^b = x^(a+b)
(x^a)^b = x^(ab)
(ab)^n = a^n · b^n
x^0 = 1 (x≠0)
(2x²)³ = 2³ · x⁶ = 8x⁶
Unit 9 · Polynomials

FOIL & Expanding

FOIL: First · Outer · Inner · Last. Combine like terms after expanding.

(x+a)(x+b) = x² + (a+b)x + ab
(x+3)(x−5): a=3, b=−5
= x² + (−2)x + (−15) = x²−2x−15
Unit 10 · Factoring & Quadratics

Factoring & Zero Product

Find two numbers that multiply to c and add to b in x² + bx + c. Zero Product Property: if ab=0 then a=0 or b=0.

x²−7x+12: need × = 12, + = −7
→ (x−3)(x−4) (check: −3×−4=12 ✓)
Set each = 0: x=3 or x=4
Question 0 of 20 Score: 0/0