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Fred

Hi! I'm Fred the Owl, your math coach. This is an Iowa / ITBS-style Grade 8 Math practice built by FlyingMinds — exponents & scientific notation, linear equations & slope, systems, functions, the Pythagorean theorem, and 3-D volume, plus an Iowa Computation section. Pick an answer to see how to solve it.

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Math — Grade 8

FlyingMinds Iowa Test Prep — original, advanced practice built by FlyingMinds to help you become a critical thinker and pass the test

Grade 8ExponentsLinear & FunctionsSystemsPythagorean TheoremVolume & Geometry

📋 Test Overview

Test

Iowa / ITBS-style Math practice

Grade level

Grade 8

Length

practice + Iowa Computation + challenge + 4 explain prompts — more practice than Testing Mom's Grade 8 math sets

Skills

Exponents & roots · scientific notation · linear equations & slope · systems of equations · functions · Pythagorean theorem · volume of cylinders, cones & spheres · transformations & angles · rational vs irrational numbers · Iowa Computation (mark N if not given)

How it's upgraded

Each idea is taught first; every answer gets a worked explanation; arithmetic is verified

Standards

8.NS · 8.EE · 8.F · 8.G

⭐ 0 / 80 stars · ✍️ 0 / 4 explanations

📖 Learn 🎯 Practice 🏆 Challenge ✍️ Explain

Before you practice: Grade 8 math is the gateway to algebra: exponents, linear equations and slope, functions, the Pythagorean theorem, and 3-D volume.

📌 FlyingMinds rule: Show each step, label your answer, and check that it makes sense.

🔮 WARM-UP · NOT SCORED

🦉 Fred asks: How do you find the slope of a line between two points?

Starter: To find the slope, I would __________ because __________ .

🎯 Practice score: 0 / 68

🟢 Part A — Exponents & roots

An exponent shows repeated multiplication. A square root undoes squaring; a cube root undoes cubing.

8.EE · ExponentsEXPONENTS

1. 2⁵ equals —

10 16 32 25

8.EE · ExponentsEXPONENTS

2. The square root of 144 is —

12 72 14 121

8.EE · ExponentsEXPONENTS

3. 3² × 3³ equals — (add exponents)

3⁶ 3⁵ 9⁵ 3¹

8.EE · ExponentsEXPONENTS

4. 5⁰ equals —

0 5 50 1

8.EE · ExponentsEXPONENTS

5. The cube root of 27 is —

3 9 6 27

8.EE · ExponentsEXPONENTS

6. 2⁻² equals —

−4 4 1/4 1/2

8.EE · ExponentsEXPONENTS

7. (2³)² equals — (multiply exponents)

2⁵ 4⁶ 2⁹ 2⁶

8.EE · ExponentsEXPONENTS

8. √50 is between which two whole numbers?

6 and 7 7 and 8 8 and 9 5 and 6

🔵 Part B — Scientific notation

Scientific notation writes a number as a × 10ⁿ, where 1 ≤ a < 10. Positive n means large; negative n means small.

8.EE · Scientific notationNOTATION

9. Write 4,500 in scientific notation.

4.5 × 10³ 45 × 10² 4.5 × 10⁴ 0.45 × 10⁴

8.EE · Scientific notationNOTATION

10. Write 0.0006 in scientific notation.

6 × 10⁴ 0.6 × 10⁻³ 6 × 10⁻⁴ 6 × 10⁻³

8.EE · Scientific notationNOTATION

11. 3.2 × 10⁵ written in standard form is —

32,000 3,200,000 0.000032 320,000

8.EE · Scientific notationNOTATION

12. Which number is larger: 5 × 10³ or 8 × 10²?

8 × 10² 5 × 10³ they are equal cannot tell

8.EE · Scientific notationNOTATION

13. Write 72,000 in scientific notation.

7.2 × 10⁴ 72 × 10³ 7.2 × 10³ 0.72 × 10⁵

8.EE · Scientific notationNOTATION

14. 2 × 10⁻³ written in standard form is —

2,000 0.002 0.02 0.0002

🟡 Part C — Linear equations & slope

Slope = rise ÷ run = change in y ÷ change in x. In y = mx + b, m is the slope and b is the y-intercept.

8.EE/8.F · LinearLINEAR

15. The slope of the line through (0, 0) and (2, 6) is —

1/3 2 3 6

8.EE/8.F · LinearLINEAR

16. In y = 4x − 5, the slope is —

−5 5 1 4

8.EE/8.F · LinearLINEAR

17. In y = 4x − 5, the y-intercept is —

4 −5 5 0

8.EE/8.F · LinearLINEAR

18. Solve: 3x + 7 = 22.

x = 5 x = 7 x = 9 x = 15

8.EE/8.F · LinearLINEAR

19. A line with slope 0 is —

vertical steep diagonal horizontal

8.EE/8.F · LinearLINEAR

20. The slope of the line through (1, 2) and (3, 8) is —

2 1/3 3 6

8.EE/8.F · LinearLINEAR

21. Solve: 2(x − 3) = 10.

x = 8 x = 5 x = 2 x = 13

8.EE/8.F · LinearLINEAR

22. A proportional line (direct variation) always passes through —

the point (1, 1) the y-axis at 5 no points the origin (0, 0)

🟣 Part D — Systems of equations

A system is two equations. The solution is the (x, y) point where the lines cross — the values that make BOTH true.

8.EE · SystemsSYSTEMS

23. The solution to a system of two lines is —

the y-intercept only the steeper slope the point where the lines intersect any point on one line

8.EE · SystemsSYSTEMS

24. If two lines are parallel, the system has —

one solution no solution infinitely many solutions a negative solution

8.EE · SystemsSYSTEMS

25. Solve the system: y = x and y = 4. The solution is —

(4, 4) (0, 4) (4, 0) (1, 4)

8.EE · SystemsSYSTEMS

26. Two identical lines (same equation) have —

no solution exactly one solution two solutions infinitely many solutions

8.EE · SystemsSYSTEMS

27. In the system x + y = 10 and x = 6, then y = —

6 10 4 16

8.EE · SystemsSYSTEMS

28. The point that solves a system must lie —

on neither line on BOTH lines only on the x-axis at the origin always

⚪ Part E — Functions

A function gives exactly ONE output for each input. y = mx + b is a linear function; a constant rate of change makes it linear.

8.F · FunctionsFUNCTIONS

29. A relation is a FUNCTION if each input has —

many outputs no output exactly one output two outputs

8.F · FunctionsFUNCTIONS

30. Which represents a function? (each x once)

(1,2), (1,3), (2,4) (1,2), (2,4), (3,6) (5,1), (5,2) (0,0), (0,9)

8.F · FunctionsFUNCTIONS

31. In the function y = 2x + 1, when x = 3, y = —

7 6 5 9

8.F · FunctionsFUNCTIONS

32. A function with a constant rate of change is —

always curved never graphable a single point linear (a straight line)

8.F · FunctionsFUNCTIONS

33. The rate of change of a linear function is its —

y-intercept input slope origin

8.F · FunctionsFUNCTIONS

34. If y = 5x, then y changes by ___ each time x increases by 1.

1 0 25 5

🟢 Part F — The Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

8.G · PythagoreanGEOMETRY

35. In a right triangle with legs 3 and 4, the hypotenuse is —

5 7 12 25

8.G · PythagoreanGEOMETRY

36. In a right triangle with legs 6 and 8, the hypotenuse is —

14 10 48 100

8.G · PythagoreanGEOMETRY

37. In the equation a² + b² = c², the side c is the —

shortest leg hypotenuse right angle base only

8.G · PythagoreanGEOMETRY

38. A triangle has legs 5 and 12. The hypotenuse is —

17 60 169 13

8.G · PythagoreanGEOMETRY

39. The Pythagorean Theorem works only for —

right triangles all triangles circles squares

8.G · PythagoreanGEOMETRY

40. If a = 8, c = 10, then b = —

2 18 6 12

🔵 Part G — Volume: cylinders, cones & spheres

Cylinder V = πr²h. Cone V = ⅓πr²h. Sphere V = 4/3 πr³. Use π ≈ 3.14.

8.G · VolumeGEOMETRY

41. A cylinder has radius 3 and height 10. Using π ≈ 3.14, its volume is —

282.6 94.2 31.4 188.4

8.G · VolumeGEOMETRY

42. A cone has radius 3 and height 10. Using π ≈ 3.14, its volume is —

282.6 28.26 94.2 31.4

8.G · VolumeGEOMETRY

43. A sphere has radius 3. Using π ≈ 3.14, its volume is —

84.78 28.26 339.12 113.04

8.G · VolumeGEOMETRY

44. A cone's volume compared to a cylinder with the same base and height is —

the same one third double four times

8.G · VolumeGEOMETRY

45. A cylinder has radius 2 and height 5. Using π ≈ 3.14, its volume is —

31.4 20 125.6 62.8

8.G · VolumeGEOMETRY

46. Which formula gives the volume of a sphere?

πr²h 4/3 πr³ ⅓πr²h 2πr

🟣 Part H — Transformations & angles

Translations slide, reflections flip, rotations turn, and dilations resize. Angle rules help find missing measures.

8.G · TransformationsGEOMETRY

47. A transformation that SLIDES a figure without turning it is a —

rotation reflection translation dilation

8.G · TransformationsGEOMETRY

48. A transformation that FLIPS a figure over a line is a —

reflection translation rotation dilation

8.G · TransformationsGEOMETRY

49. A transformation that RESIZES a figure (larger or smaller) is a —

translation reflection dilation rotation

8.G · TransformationsGEOMETRY

50. Translations, reflections, and rotations produce a figure that is —

always larger congruent to the original always smaller a different shape

8.G · TransformationsGEOMETRY

51. Two angles that add to 90° are —

complementary supplementary vertical straight

8.G · TransformationsGEOMETRY

52. Two angles that add to 180° are —

complementary right acute supplementary

⚪ Part I — Rational & irrational numbers

A rational number can be written as a fraction; an irrational number (like π or √2) cannot and never repeats or ends.

8.NS · Real numbersNUMBER

53. Which number is IRRATIONAL?

1/2 √2 0.75 −4

8.NS · Real numbersNUMBER

54. Which number is RATIONAL?

0.25 √3 π √5

8.NS · Real numbersNUMBER

55. The number π is —

a whole number rational an integer irrational

8.NS · Real numbersNUMBER

56. A repeating decimal like 0.333… is —

irrational not a number rational (equals 1/3) a whole number

8.NS · Real numbersNUMBER

57. Which is the best estimate of √20?

about 10 about 2 about 4.5 about 20

8.NS · Real numbersNUMBER

58. Every integer is also a —

irrational number square root negative rational number

🧮 Part — Iowa format: Computation

Iowa style: Work out the exact answer. If your answer is not one of the first three choices, mark N — not given.

8.EE · ComputationCOMPUTATION

59. 5,628 + 3,794 = ?

9,322 9,422 9,522 N — not given

8.EE · ComputationCOMPUTATION

60. 10,003 − 4,567 = ?

5,436 5,536 5,446 N — not given

8.EE · ComputationCOMPUTATION

61. 64 × 25 = ?

1,500 1,600 1,700 N — not given

8.EE · ComputationCOMPUTATION

62. 2,016 ÷ 8 = ?

242 252 262 N — not given

8.EE · ComputationCOMPUTATION

63. 4³ = ?

12 64 81 N — not given

8.EE · ComputationCOMPUTATION

64. √169 = ?

11 12 14 N — not given

8.EE · ComputationCOMPUTATION

65. (−8) × (−7) = ?

−56 48 63 N — not given

8.EE · ComputationCOMPUTATION

66. 3.5 × 10² = ?

35 350 3,500 N — not given

8.EE · ComputationCOMPUTATION

67. 15% of 240 = ?

24 36 48 N — not given

8.EE · ComputationCOMPUTATION

68. (−15) + 9 = ?

−6 6 −24 N — not given

🏆 Challenge score: 0 / 19

🏆 Challenge round. Multi-step reasoning for sharp Grade 8 thinkers.

Grade 8 MathCHALLENGE

69. A right triangle has legs 9 and 12. Its hypotenuse is —

21 15 225 18

Grade 8 MathCHALLENGE

70. Solve: 4x − 3 = 2x + 9.

x = 6 x = 3 x = 12 x = 2

Grade 8 MathCHALLENGE

71. The slope of the line through (2, 3) and (6, 11) is —

2 1/2 4 8

Grade 8 MathCHALLENGE

72. Light travels about 3 × 10⁸ m/s. In standard form that is —

30,000,000 3,000,000 0.00000003 300,000,000 m/s

Grade 8 MathCHALLENGE

73. A cylinder has radius 5 and height 4. Using π ≈ 3.14, its volume is —

62.8 314 157 628

Grade 8 MathCHALLENGE

74. In y = mx + b, a line passes through (0, 2) with slope 3. Its equation is —

y = 2x + 3 y = 3x − 2 y = 3x + 2 y = x + 5

Grade 8 MathCHALLENGE

75. 2³ × 2⁴ equals —

2¹² 4⁷ 2⁷ 2¹

Grade 8 MathCHALLENGE

76. Which number is irrational?

√7 0.5 3/4 −9

Grade 8 MathCHALLENGE

77. A cone and a cylinder share the same base and height; the cylinder holds 90 cm³. The cone holds —

90 cm³ 30 cm³ 270 cm³ 45 cm³

Grade 8 MathCHALLENGE

78. Solve the system: y = 2x and x + y = 9.

x = 6, y = 3 x = 9, y = 0 x = 4.5, y = 4.5 x = 3, y = 6

Grade 8 MathCHALLENGE

79. If 2ⁿ = 32, then n = —

5 4 6 16

Grade 8 MathCHALLENGE

80. A figure is reflected, then translated. The new figure is —

larger smaller congruent to the original a different shape

8.SPCHALLENGE

81. A class makes a scatter plot of hours studied (x) versus test score (y). As the points move right, they also tend to move up. What is the pattern of association?

Positive association Negative association No association Nonlinear association

8.SPCHALLENGE

82. Most points on this scatter plot lie close to a rising line, but one point sits far above and away from the rest. The single point that does not fit the pattern is best called the —

slope outlier intercept cluster

8.SPCHALLENGE

83. A line of best fit for plant data is y = 2x + 5, where x is weeks and y is height in centimeters. What does the slope of 2 mean, and how tall is the plant predicted to be at 6 weeks?

The plant grows about 2 cm per week; at 6 weeks it is about 17 cm. The plant grows about 5 cm per week; at 6 weeks it is about 12 cm. The plant grows about 2 cm per week; at 6 weeks it is about 12 cm. The plant starts at 2 cm; at 6 weeks it is about 6 cm.

8.SPCHALLENGE

84. A two-way table records whether students own a bike and whether they walk to school.

	Walks	Does not walk
Owns bike	10	30
No bike	24	16

Among the 40 bike owners, what fraction walk to school?

About 60% 25% 75% 40%

8.SPCHALLENGE

85. This stem-and-leaf plot shows quiz scores (stem = tens, leaf = ones).

6 | 2 5
7 | 0 3 3 8
8 | 1 4
9 | 5

How many students scored in the 70s?

2 students 3 students 4 students 9 students

Grade 8 MathCHALLENGE

86. A bus travels 144 miles in 3 hours at a steady speed. At that same rate, how far will it travel in 5 hours, and how long would 240 miles take?

240 miles in 5 hours; 240 miles takes 5 hours. 200 miles in 5 hours; 240 miles takes 6 hours. 288 miles in 5 hours; 240 miles takes 4 hours. 240 miles in 5 hours; 240 miles takes 6 hours.

8.SPCHALLENGE

87. A statistical question is one you expect to answer by collecting data that varies. Which of these is a statistical question?

How many days are in the month of June? How many hours of sleep do students in my grade get each night? What is the boiling point of water at sea level? How many sides does a hexagon have?

✍️ Write it. Explain your thinking. Fred checks length, key words, and mechanics.

✍️ EXPLAIN #1 · SCORED

🦉 Fred asks: Explain how to find the slope of the line through (1, 2) and (4, 11). Show your steps.

Sentence starter: To find the slope, I would __________ because __________ .

✍️ EXPLAIN #2 · SCORED

🦉 Fred asks: Explain how the Pythagorean theorem finds a missing side of a right triangle, with an example.

Sentence starter: The Pythagorean theorem says __________, so for legs 3 and 4 __________ .

✍️ EXPLAIN #3 · SCORED

🦉 Fred asks: Explain the difference between a rational and an irrational number, with an example of each.

Sentence starter: A rational number is __________, but an irrational number is __________, for example __________ .

✍️ EXPLAIN #4 · CHALLENGE · SCORED

🦉 Fred asks: Why does a cone hold exactly one third as much as a cylinder with the same base and height? Explain.

Sentence starter: A cone holds one third of the cylinder because __________, so if the cylinder holds 90 it __________ .

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