Algebra 1 Test PDF
Free preview of a printable Algebra 1 test with a complete step-by-step answer key. Common Core HSA aligned · balanced 5/3/2 difficulty.
1. Solve: 6x − 5 = 31
2. Simplify: 3(2x + 5) − 4x
3. Evaluate 2x² − 3 when x = 4
4. Solve: x + 5 < 12
5. Find the slope of y = −5x + 3
6. Solve the system: 2x + y = 7, x − y = 2
7. Factor: x² + 7x + 12
8. Solve: x² − 9 = 0
9. Solve by quadratic formula: x² − 5x + 2 = 0
10. A rectangle has area 60 and length 4 more than width. Find the dimensions.
1. x = 6
6x = 36 → x = 6
2. 2x + 15
6x + 15 − 4x = 2x + 15
3. 29
2(16) − 3 = 32 − 3 = 29
4. x < 7
x < 12 − 5 = 7
5. −5
y = mx + b → m = −5
6. x = 3, y = 1
Add: 3x = 9 → x = 3; y = x − 2 = 1
7. (x + 3)(x + 4)
Find pairs: 3 × 4 = 12, 3 + 4 = 7
8. x = ±3
(x − 3)(x + 3) = 0 → x = 3 or −3
9. x = (5 ± √17)/2
x = (5 ± √(25 − 8))/2 = (5 ± √17)/2
10. w = 6, l = 10
w(w + 4) = 60 → w² + 4w − 60 = 0 → (w − 6)(w + 10) = 0 → w = 6, l = 10
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Topics covered
Linear equations, inequalities, systems, factoring, quadratics, word problems.
Difficulty balance
5 easy / 3 medium / 2 hard — fair grading across abilities.
Answer key
Step-by-step solutions for every question.