Math 8 (Grade 8) Midterm — Full-Course Review

Math Grade 8 30 multiple choice + 2 written

Free printable Math 8 midterm (Grade 8): 30 multiple-choice questions plus 2 written responses covering Exponents & Scientific Notation, Real Numbers & the Pythagorean Theorem, Linear Equations, Functions, Systems of Equations, Transformations, Volume & Scatter Plots. 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: Exponents & Scientific Notation · Real Numbers & the Pythagorean Theorem · Linear Equations · Functions · Systems of Equations · Transformations, Volume & Scatter Plots

Part 1: Multiple Choice

What is (8 × 10^9) ÷ (2 × 10^3)?
1. A. 4 × 10^12
2. B. 4 × 10^6
3. C. 6 × 10^6
4. D. 4 × 10^3
What is the value of 4^(-2)?
1. A. -8
2. B. -16
3. C. 1/16
4. D. 1/8
What is (3 × 10^4)(2 × 10^3)?
1. A. 6 × 10^7
2. B. 6 × 10^12
3. C. 5 × 10^7
4. D. 6 × 10^1
Which expression is equal to 3^4 × 3^2?
1. A. 9^6
2. B. 3^8
3. C. 3^2
4. D. 3^6
How is 0.00045 written in scientific notation?
1. A. 4.5 × 10^4
2. B. 4.5 × 10^-3
3. C. 4.5 × 10^-4
4. D. 4.5 × 10^-5
The decimal 0.333... has a 3 that repeats forever. Which fraction is equal to it?
1. A. 1/30
2. B. 33/100
3. C. 1/3
4. D. 3/10
A right triangle has a hypotenuse of 13 inches and one leg of 5 inches. How long is the other leg?
1. A. 18 inches
2. B. 8 inches
3. C. √194 inches
4. D. 12 inches
What is the distance between the points (1, 2) and (4, 6) on a coordinate plane?
1. A. 7
2. B. 5
3. C. 25
4. D. √13
Which set of side lengths forms a right triangle?
1. A. 7, 8, 10
2. B. 5, 11, 12
3. C. 9, 12, 15
4. D. 4, 5, 6
A 10-foot ladder leans against a wall. Its base is 6 feet from the wall. How high up the wall does the ladder reach?
1. A. 8 feet
2. B. √136 feet
3. C. 16 feet
4. D. 4 feet
Solve: 0.5x - 1.2 = 0.3x + 0.4
1. A. x = 0.8
2. B. x = 2
3. C. x = 4
4. D. x = 8
How many solutions does 4(x + 2) = 4x + 8 have?
1. A. No solution
2. B. Infinitely many solutions
3. C. Exactly one solution, x = 0
4. D. Exactly one solution, x = 2
Which equation describes a line with slope -3 and y-intercept 5?
1. A. y = 3x + 5
2. B. y = -3x - 5
3. C. y = 5x - 3
4. D. y = -3x + 5
Which equation describes the line with slope 4/3 that passes through (0, -2)?
1. A. y = -2x + 4/3
2. B. y = (4/3)x - 2
3. C. y = (4/3)x + 2
4. D. y = (3/4)x - 2
Solve: 3(x - 2) = 2(x + 4)
1. A. x = 10
2. B. x = 14
3. C. x = 2
4. D. x = -14
Which function is nonlinear?
1. A. y = -x
2. B. y = x^2 + 1
3. C. y = 4x - 2
4. D. y = x/2 + 3
A linear function has these values: when x = 1, 2, 3, 4, y = 7, 9, 11, 13. Which rule fits?
1. A. y = 2x + 7
2. B. y = x + 6
3. C. y = 7x
4. D. y = 2x + 5
A graph shows a car's speed over time: the speed rises, stays level, then falls to zero. Which story fits the graph?
1. A. A car cruises at a steady speed, speeds up, then parks
2. B. A car slows down, stops, then speeds up
3. C. A car stays parked the entire time
4. D. A car speeds up from a stop, cruises at a steady speed, then slows to a stop
Function A is y = 2x + 7. Function B has these values: when x = 1, 2, 3, y = 4, 9, 14. Which statement is true?
1. A. Function B has the greater rate of change, 4
2. B. Function A has the greater rate of change, 7
3. C. Function A has the greater rate of change, 2
4. D. Function B has the greater rate of change, 5
If f(x) = 3x - 4, what is f(5)?
1. A. -11
2. B. 19
3. C. 3
4. D. 11
Which system has the solution (1, -2)?
1. A. y = x + 3 and y = -2x
2. B. y = 2x - 4 and y = x + 1
3. C. y = -x - 1 and y = 3x
4. D. y = x - 3 and y = -2x
How many solutions does the system y = 3x + 2 and y = 3x - 5 have?
1. A. Infinitely many solutions
2. B. No solution
3. C. Exactly two solutions
4. D. Exactly one solution
What is the solution to the system 3x + 2y = 16 and x - 2y = 0?
1. A. (4, 2)
2. B. (2, 4)
3. C. (4, -2)
4. D. (2, 5)
A school sold 20 tickets to a play for $127. Adult tickets cost $8 and student tickets cost $5. How many adult tickets were sold?
1. A. 9
2. B. 15
3. C. 11
4. D. 12
The sum of two numbers is 30 and their difference is 8. What is the larger number?
1. A. 22
2. B. 19
3. C. 11
4. D. 15
What is the volume of a sphere with radius 3 m?
1. A. 108π cubic meters
2. B. 12π cubic meters
3. C. 36π cubic meters
4. D. 27π cubic meters
What is the volume of a cone with radius 3 inches and height 4 inches?
1. A. 36π cubic inches
2. B. 12π cubic inches
3. C. 48π cubic inches
4. D. 4π cubic inches
Which transformation does NOT always produce a figure congruent to the original?
1. A. Translation
2. B. Rotation
3. C. Reflection
4. D. Dilation
A line of fit for test scores is y = 2.5x + 60, where x is hours studied. What score does it predict for 8 hours?
1. A. 85
2. B. 20
3. C. 80
4. D. 68
The point (3, -2) is translated 4 units left and 5 units up. What is the new point?
1. A. (-1, 3)
2. B. (-1, -7)
3. C. (7, -7)
4. D. (7, 3)

Part 2: Written Response

Car Rental A charges $40 plus $0.25 per mile. Car Rental B charges $25 plus $0.40 per mile. Write and solve an equation to find the number of miles at which the costs are equal, and find that cost. Show your work.
Triangle ABC has vertices A(1, 1), B(4, 1), and C(1, 3). Reflect it over the y-axis, then translate the image 2 units down. Give the final coordinates and explain whether the area changes. Show your work.

Answer Key — Math 8 (Grade 8) Midterm — Full-Course Review

B — 4 × 10^6 Divide 8 ÷ 2 = 4 and subtract exponents 9 - 3 = 6.
C — 1/16 A negative exponent means reciprocal: 1/4² = 1/16.
A — 6 × 10^7 Multiply 3 × 2 = 6 and add exponents 4 + 3 = 7.
D — 3^6 Same base: add exponents, 4 + 2 = 6.
C — 4.5 × 10^-4 Move the decimal 4 places right to get 4.5, so the exponent is -4.
C — 1/3 1 ÷ 3 = 0.333... with the 3 repeating.
D — 12 inches 13² - 5² = 169 - 25 = 144, and √144 = 12.
B — 5 Legs are 3 and 4: √(3² + 4²) = √25 = 5.
C — 9, 12, 15 9² + 12² = 81 + 144 = 225 = 15².
A — 8 feet √(10² - 6²) = √64 = 8 feet.
D — x = 8 0.2x = 1.6, so x = 8.
B — Infinitely many solutions Both sides simplify to 4x + 8, so every x works.
D — y = -3x + 5 Slope-intercept form is y = mx + b with m = -3, b = 5.
B — y = (4/3)x - 2 The point (0, -2) is the y-intercept, so b = -2 and m = 4/3.
B — x = 14 3x - 6 = 2x + 8, so x = 14.
B — y = x^2 + 1 Squaring x makes the graph a curve, not a line.
D — y = 2x + 5 Slope is 2; at x = 1, 2(1) + 5 = 7.
D — A car speeds up from a stop, cruises at a steady speed, then slows to a stop Rising, level, then falling speed means speed up, cruise, then stop.
D — Function B has the greater rate of change, 5 B rises 5 per unit of x; A rises only 2.
D — 11 3(5) - 4 = 15 - 4 = 11.
D — y = x - 3 and y = -2x 1 - 3 = -2 and -2(1) = -2, so both equations are true.
B — No solution Same slope, different y-intercepts: the lines are parallel.
A — (4, 2) Add the equations: 4x = 16, so x = 4 and y = 2.
A — 9 8a + 5(20 - a) = 127 gives 3a = 27, so a = 9.
B — 19 x + y = 30 and x - y = 8 give 2x = 38, so x = 19.
C — 36π cubic meters V = (4/3)πr³ = (4/3)π(27) = 36π.
B — 12π cubic inches V = (1/3)πr²h = (1/3)π(9)(4) = 12π.
D — Dilation A dilation changes size unless the scale factor is 1.
C — 80 2.5(8) + 60 = 20 + 60 = 80.
A — (-1, 3) x: 3 - 4 = -1; y: -2 + 5 = 3.

Written Response — Look-Fors

Equation 40 + 0.25m = 25 + 0.40m; 15 = 0.15m; m = 100; substitute to check. Final answer: 100 miles, where both cost $65.
Reflection over y-axis: (x, y) to (-x, y); then subtract 2 from y; rigid motions keep size; area (1/2)(3)(2) = 3. Final answer: A'(-1, -1), B'(-4, -1), C'(-1, 1); area stays 3 square units.

Math 8 (Grade 8) Midterm — Full-Course Review

Part 1: Multiple Choice

Part 2: Written Response

Written Response — Look-Fors

More Math 8 midterms