Algebra I (Grades 8–9) Midterm — Full-Course Review

Math Grades 8–9 30 multiple choice + 2 written

Free printable Algebra I midterm (Grades 8–9): 30 multiple-choice questions plus 2 written responses covering Expressions & Equations, Inequalities, Linear Functions, Systems of Equations, Exponents & Exponential Functions, Polynomials, Factoring & Quadratics. Answer key included — customize it in the Midterm Maker.

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Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Expressions & Equations · Inequalities · Linear Functions · Systems of Equations · Exponents & Exponential Functions · Polynomials, Factoring & Quadratics

Part 1: Multiple Choice

Solve: (2/3)x - 4 = 10
1. A. x = 21
2. B. x = 6
3. C. x = 4
4. D. x = 9 1/3
Solve: 0.4(x - 10) = 0.2x + 3
1. A. x = 17.5
2. B. x = 5
3. C. x = 70
4. D. x = 35
Solve A = (1/2)bh for h.
1. A. h = 2Ab
2. B. h = b/(2A)
3. C. h = A/(2b)
4. D. h = 2A/b
Evaluate 2a^2 - 3b when a = -3 and b = 4.
1. A. 30
2. B. -30
3. C. 6
4. D. -6
Simplify: 4(2x - 3) - (x - 5)
1. A. 9x - 7
2. B. 7x - 7
3. C. 7x - 17
4. D. 7x + 2
Solve: -3 < 2x + 1 ≤ 9
1. A. -2 ≤ x < 4
2. B. -2 < x ≤ 4
3. C. -4 < x ≤ 2
4. D. -1 < x ≤ 5
Solve: 2(x - 1) ≤ 3x + 4
1. A. x ≤ 2
2. B. x ≥ 6
3. C. x ≥ -6
4. D. x ≤ -6
Solve: |x - 2| ≥ 3
1. A. x ≤ -1 or x ≥ 5
2. B. -1 ≤ x ≤ 5
3. C. x ≥ 5
4. D. x ≤ -5 or x ≥ 1
A phone plan costs $35 per month plus $0.05 per text. Kai can spend at most $50 per month. What is the greatest number of texts he can send?
1. A. 300
2. B. 30
3. C. 1,700
4. D. 700
Solve: -4x + 7 > 23
1. A. x < 4
2. B. x < -4
3. C. x > -7.5
4. D. x > -4
Which line is parallel to y = -4x + 1 and passes through (0, 6)?
1. A. y = (1/4)x + 6
2. B. y = 4x + 6
3. C. y = -4x + 1
4. D. y = -4x + 6
A repair costs C = 15h + 40 dollars, where h is hours worked. What does 15 represent?
1. A. The total cost is $15
2. B. The cost increases $15 for each hour of work
3. C. The base fee is $15
4. D. The job takes 15 hours
If f(x) = -2x + 9, for what value of x does f(x) = 1?
1. A. 4
2. B. -4
3. C. 5
4. D. 7
What is the slope of the line through (-2, 5) and (4, -7)?
1. A. -1/2
2. B. -6
3. C. 2
4. D. -2
Which equation describes the line through (1, 4) with slope 3?
1. A. y = 3x + 1
2. B. y = 3x - 1
3. C. y = 4x + 3
4. D. y = 3x + 4
Solve the system: 2x + y = 7 and 3x - y = 8
1. A. (2, 3)
2. B. (1, 3)
3. C. (3, -1)
4. D. (3, 1)
Solve the system: 4x + 3y = 10 and 2x - 3y = -4
1. A. (1, -2)
2. B. (-1, 2)
3. C. (2, 1)
4. D. (1, 2)
Which point is a solution of the system y ≥ x and y < -x + 4?
1. A. (1, 2)
2. B. (3, 2)
3. C. (2, 2)
4. D. (0, 5)
Solve the system: y = x + 2 and 3x + y = 18
1. A. (4, 2)
2. B. (5, 3)
3. C. (6, 4)
4. D. (4, 6)
Plan A costs $20 per month plus $0.10 per minute. Plan B costs $35 per month plus $0.05 per minute. For how many minutes do the plans cost the same?
1. A. 150
2. B. 30
3. C. 550
4. D. 300
A value is modeled by y = 1000(0.8)^t. What is y when t = 2?
1. A. 800
2. B. 1,280
3. C. 640
4. D. 600
The function y = 200(1.05)^t models a population after t years. What does 1.05 tell you?
1. A. The population grows 105% each year
2. B. The population grows 5% each year
3. C. The population decreases 5% each year
4. D. The population grows 0.05% each year
What is the value of 27^(2/3)?
1. A. 18
2. B. 8
3. C. 9
4. D. 3
A culture starts with 50 bacteria and doubles every hour. How many bacteria are there after 5 hours?
1. A. 500
2. B. 3,200
3. C. 1,600
4. D. 250
Which table shows an exponential function? Each table lists y for x = 0, 1, 2, 3.
1. A. y = 3, 6, 9, 12
2. B. y = 3, 5, 9, 15
3. C. y = 1, 4, 9, 16
4. D. y = 3, 6, 12, 24
Multiply: (x + 4)(x - 3)
1. A. x^2 - x - 12
2. B. x^2 - 12
3. C. x^2 + x - 12
4. D. x^2 + 7x - 12
What is the vertex of the graph of y = (x - 2)^2 + 5?
1. A. (5, 2)
2. B. (2, -5)
3. C. (2, 5)
4. D. (-2, 5)
How many real solutions does 2x^2 - 4x + 5 = 0 have?
1. A. No real solutions
2. B. Two real solutions
3. C. Three real solutions
4. D. One real solution
Factor: x^2 + 7x + 12
1. A. (x + 2)(x + 6)
2. B. (x - 3)(x - 4)
3. C. (x + 1)(x + 12)
4. D. (x + 3)(x + 4)
Factor: 2x^2 + 7x + 3
1. A. (x + 1)(x + 3)
2. B. (2x + 1)(x - 3)
3. C. (2x + 1)(x + 3)
4. D. (2x + 3)(x + 1)

Part 2: Written Response

A taxi charges $3.50 plus $2.25 per mile. (a) Write a linear function C(m). (b) Find the cost of a 12-mile ride. (c) How many miles was a ride that cost $41.75? Identify the slope and y-intercept in context. Show your work.
A ball is thrown upward from an 80-foot platform. Its height is h = -16t^2 + 64t + 80, where t is seconds. (a) When does the ball hit the ground? (b) What is its maximum height, and when does it occur? Show your work.

Answer Key — Algebra I (Grades 8–9) Midterm — Full-Course Review

A — x = 21 Add 4: (2/3)x = 14. Multiply by 3/2: x = 21.
D — x = 35 0.4x - 4 = 0.2x + 3 gives 0.2x = 7, so x = 35.
D — h = 2A/b Multiply both sides by 2, then divide by b.
C — 6 2(-3)² - 3(4) = 2(9) - 12 = 6.
B — 7x - 7 8x - 12 - x + 5 = 7x - 7.
B — -2 < x ≤ 4 Subtract 1 from all parts, then divide all parts by 2.
C — x ≥ -6 2x - 2 ≤ 3x + 4 gives -6 ≤ x.
A — x ≤ -1 or x ≥ 5 x - 2 ≤ -3 or x - 2 ≥ 3, so x ≤ -1 or x ≥ 5.
A — 300 35 + 0.05t ≤ 50 gives 0.05t ≤ 15, so t ≤ 300.
B — x < -4 -4x > 16; dividing by -4 reverses the sign: x < -4.
D — y = -4x + 6 Parallel lines share the slope -4; the y-intercept is 6.
B — The cost increases $15 for each hour of work The slope, 15, is the cost added per hour.
A — 4 -2x + 9 = 1 gives -2x = -8, so x = 4.
D — -2 (-7 - 5) ÷ (4 - (-2)) = -12 ÷ 6 = -2.
A — y = 3x + 1 4 = 3(1) + b, so b = 1.
D — (3, 1) Add the equations: 5x = 15, so x = 3 and y = 1.
D — (1, 2) Add: 6x = 6, so x = 1; then 4 + 3y = 10 gives y = 2.
A — (1, 2) 2 ≥ 1 is true and 2 < 3 is true.
D — (4, 6) 3x + x + 2 = 18 gives x = 4, then y = 6.
D — 300 20 + 0.10m = 35 + 0.05m gives 0.05m = 15, so m = 300.
C — 640 1000(0.8)² = 1000(0.64) = 640.
B — The population grows 5% each year 1.05 = 1 + 0.05, so the growth rate is 5% per year.
C — 9 Cube root of 27 is 3, and 3² = 9.
C — 1,600 50 × 2⁵ = 50 × 32 = 1,600.
D — y = 3, 6, 12, 24 Each y is multiplied by 2, a constant ratio.
C — x^2 + x - 12 x² - 3x + 4x - 12 = x² + x - 12.
C — (2, 5) Vertex form y = (x - h)² + k has vertex (h, k).
A — No real solutions The discriminant (-4)² - 4(2)(5) = -24 is negative.
D — (x + 3)(x + 4) 3 and 4 multiply to 12 and add to 7.
C — (2x + 1)(x + 3) Check: 2x² + 6x + x + 3 = 2x² + 7x + 3.

Written Response — Look-Fors

C(m) = 2.25m + 3.50; slope 2.25 dollars per mile, y-intercept $3.50 starting fee; C(12) = 27 + 3.50; 2.25m + 3.50 = 41.75 gives 2.25m = 38.25. Final answers: $30.50 and 17 miles.
Set h = 0 and factor: -16(t^2 - 4t - 5) = -16(t - 5)(t + 1) = 0; reject t = -1; vertex t = -b/(2a) = -64/(-32) = 2; h(2) = -64 + 128 + 80. Final answers: hits the ground at 5 seconds; maximum height 144 feet at 2 seconds.

Algebra I (Grades 8–9) Midterm — Full-Course Review

Part 1: Multiple Choice

Part 2: Written Response

Written Response — Look-Fors

More Algebra I midterms