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FAST Math Grade 8 study materials
FAST Math Grade 8 study resources

FAST Math Grade 8 practice questions

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Question 1Number Sense and Operations (real numbers, exponents, scientific notation)

What is the value of 5^0 + 3^2?

  1. 6
  2. 9
  3. 10 Correct answer.
  4. 14

Explanation

Any nonzero base raised to the zero power equals 1, so 5^0 = 1. Then 3^2 = 9, and 1 + 9 = 10.

Question 2Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equal to 7^5 · 7^3?

  1. 7^2
  2. 49^8
  3. 7^15
  4. 7^8 Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 7^5 · 7^3 = 7^(5+3) = 7^8. The base stays 7 and only the exponents are added.

Question 3Number Sense and Operations (real numbers, exponents, scientific notation)

Which number is written in correct scientific notation?

  1. 3.6 × 10^4 Correct answer.
  2. 12.5 × 10^3
  3. 36 × 10^2
  4. 0.42 × 10^5

Explanation

Scientific notation requires the first factor to be at least 1 and less than 10, multiplied by a power of 10. Only 3.6 × 10^4 has a coefficient in that range.

Question 4Number Sense and Operations (real numbers, exponents, scientific notation)

Which value is equivalent to 4^(-2)?

  1. 1/16 Correct answer.
  2. -16
  3. 1/8
  4. 16

Explanation

A negative exponent means the reciprocal of the positive power: 4^(-2) = 1/(4^2) = 1/16. The result is positive because the base is squared after taking the reciprocal.

Question 5Number Sense and Operations (real numbers, exponents, scientific notation)

Which number is irrational?

  1. √81
  2. √50 Correct answer.
  3. 0.75
  4. 22/7

Explanation

A number is irrational when it cannot be written as a ratio of integers. Since 50 is not a perfect square, √50 is irrational, while the other choices are exact rational values.

Question 6Number Sense and Operations (real numbers, exponents, scientific notation)

What is 6.4 × 10^3 written in standard form?

  1. 6400 Correct answer.
  2. 640
  3. 0.0064
  4. 64,000

Explanation

Multiplying by 10^3 moves the decimal point three places to the right. Moving 6.4 three places gives 6400.

Question 7Number Sense and Operations (real numbers, exponents, scientific notation)

What is the value of (2^3)^2?

  1. 2^9
  2. 2^6 Correct answer.
  3. 2^5
  4. 4^6

Explanation

A power raised to a power multiplies the exponents: (2^3)^2 = 2^(3·2) = 2^6. The base remains 2.

Question 8Number Sense and Operations (real numbers, exponents, scientific notation)

Which statement about the square root of 144 is true?

  1. It is a rational number equal to 12. Correct answer.
  2. It is 12 and also -12 as a principal value.
  3. It is 72 because you divide by 2.
  4. It is irrational because 144 is even.

Explanation

Since 12 · 12 = 144, the principal square root √144 equals 12, which is an integer and therefore rational. The symbol √ denotes the nonnegative root only.

Question 9Number Sense and Operations (real numbers, exponents, scientific notation)

Simplify (3 × 10^4)(2 × 10^6) and write the result in scientific notation.

  1. 6 × 10^24
  2. 6 × 10^12
  3. 6 × 10^10 Correct answer.
  4. 5 × 10^10

Explanation

Multiply the coefficients and add the exponents: 3·2 = 6 and 10^4·10^6 = 10^10, giving 6 × 10^10. The coefficient 6 is already between 1 and 10.

Question 10Number Sense and Operations (real numbers, exponents, scientific notation)

What is 8.1 × 10^(-3) written in standard form?

  1. -8100
  2. 0.0081 Correct answer.
  3. 8100
  4. 0.081

Explanation

A negative exponent moves the decimal point to the left. Moving 8.1 three places left gives 0.0081.

Question 11Number Sense and Operations (real numbers, exponents, scientific notation)

Simplify x^7 / x^3 for nonzero x.

  1. x^21
  2. x^4 Correct answer.
  3. x^10
  4. 1/x^4

Explanation

When dividing powers with the same base, subtract the exponents: x^7 / x^3 = x^(7-3) = x^4. The base stays x.

Question 12Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equivalent to 5 × 10^4 + 3 × 10^3?

  1. 53 × 10^2
  2. 8 × 10^7
  3. 5.3 × 10^4 Correct answer.
  4. 8 × 10^4

Explanation

Rewrite the second term with the same power of ten: 3 × 10^3 = 0.3 × 10^4. Then 5 × 10^4 + 0.3 × 10^4 = 5.3 × 10^4.

Question 13Number Sense and Operations (real numbers, exponents, scientific notation)

Estimate √30 to the nearest integer and state which two integers it lies between.

  1. Between 4 and 5, closer to 4
  2. Between 4 and 5, closer to 5
  3. Between 6 and 7, closer to 6
  4. Between 5 and 6, closer to 5 Correct answer.

Explanation

Since 5^2 = 25 and 6^2 = 36, √30 lies between 5 and 6. Because 30 is closer to 25 than to 36, √30 is about 5.48, closer to 5.

Question 14Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equivalent to (2x^3)^4?

  1. 2x^12
  2. 8x^12
  3. 16x^12 Correct answer.
  4. 16x^7

Explanation

Apply the exponent to every factor: 2^4 = 16 and (x^3)^4 = x^12. The result is 16x^12.

Question 15Number Sense and Operations (real numbers, exponents, scientific notation)

A grain of sand has a mass of about 2.5 × 10^(-5) grams. What is the total mass of 8 × 10^6 grains?

  1. 2 × 10^2 grams
  2. 2.5 × 10^11 grams
  3. 2 × 10^1 grams Correct answer.
  4. 2 × 10^12 grams

Explanation

Multiply coefficients and add exponents: (2.5)(8) = 20 and 10^(-5)·10^6 = 10^1, giving 20 × 10^1. Converting to scientific notation yields 2 × 10^2... wait, 20 × 10^1 = 200 = 2 × 10^2. The correct value is 2 × 10^2 grams.

Question 16Number Sense and Operations (real numbers, exponents, scientific notation)

Which list orders these numbers from least to greatest: 3/4, √2, 0.7, 7/9?

  1. 7/9, 0.7, 3/4, √2
  2. 3/4, 0.7, 7/9, √2
  3. 0.7, 7/9, 3/4, √2 Correct answer.
  4. 0.7, 3/4, 7/9, √2

Explanation

Convert to decimals: 0.7 = 0.700, 7/9 ≈ 0.778, 3/4 = 0.75, and √2 ≈ 1.414. Ordering gives 0.7 < 3/4 < 7/9 < √2, so the correct list must place 3/4 before 7/9.

Question 17Number Sense and Operations (real numbers, exponents, scientific notation)

Simplify (4 × 10^5) / (8 × 10^(-2)) and express the result in scientific notation.

  1. 0.5 × 10^7
  2. 5 × 10^7
  3. 5 × 10^6 Correct answer.
  4. 2 × 10^3

Explanation

Divide coefficients and subtract exponents: 4/8 = 0.5 and 10^(5-(-2)) = 10^7, giving 0.5 × 10^7. Converting to scientific notation gives 5 × 10^6.

Question 18Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression equals 1/27 using a negative exponent?

  1. 3^(-27)
  2. 27^(-1/3)
  3. (-3)^3
  4. 3^(-3) Correct answer.

Explanation

Since 27 = 3^3, its reciprocal is 1/3^3 = 3^(-3). A negative exponent denotes the reciprocal of the positive power.

Question 19Number Sense and Operations (real numbers, exponents, scientific notation)

The number 0.000407 is written in scientific notation as which expression?

  1. 4.07 × 10^(-4) Correct answer.
  2. 4.07 × 10^(-3)
  3. 40.7 × 10^(-5)
  4. 4.07 × 10^4

Explanation

Move the decimal point four places right to get 4.07, so the exponent is -4. Thus 0.000407 = 4.07 × 10^(-4).

Question 20Number Sense and Operations (real numbers, exponents, scientific notation)

Which statement correctly compares 2√5 and 3√2?

  1. 2√5 > 3√2 because 20 > 18 Correct answer.
  2. 2√5 and 3√2 are irrational and cannot be compared
  3. 2√5 < 3√2 because 20 < 18
  4. 2√5 = 3√2 because both simplify to √10

Explanation

Square both: (2√5)^2 = 4·5 = 20 and (3√2)^2 = 9·2 = 18. Since both are positive and 20 > 18, it follows that 2√5 > 3√2.

Question 21Number Sense and Operations (real numbers, exponents, scientific notation)

Simplify (2^5 · 2^(-2)) / 2^4.

  1. 2^11
  2. 2^7
  3. 2^(-1) Correct answer.
  4. 2^3

Explanation

In the numerator, add exponents: 2^5 · 2^(-2) = 2^3. Then divide by 2^4 by subtracting: 2^(3-4) = 2^(-1), which equals 1/2.

Question 22Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equivalent to 3√12 - √27?

  1. 9√3
  2. 6√3
  3. 3√3 Correct answer.
  4. √3

Explanation

Simplify each radical: 3√12 = 3·2√3 = 6√3 and √27 = 3√3. Then 6√3 - 3√3 = 3√3.

Question 23Number Sense and Operations (real numbers, exponents, scientific notation)

Which value of n makes the equation (5^n · 5^4) / 5^9 = 5^2 true?

  1. n = 7 Correct answer.
  2. n = 3
  3. n = 11
  4. n = 15

Explanation

Combine exponents on the left: n + 4 - 9 = n - 5. Setting n - 5 = 2 gives n = 7, and substituting confirms 5^7 · 5^4 / 5^9 = 5^2.

Question 24Number Sense and Operations (real numbers, exponents, scientific notation)

Simplify √72 / √2 and state whether the result is rational.

  1. 36, which is rational
  2. 6, which is irrational
  3. 6, which is rational Correct answer.
  4. √36, which is irrational

Explanation

Use the quotient property: √72/√2 = √(72/2) = √36 = 6. Since 6 is an integer, the result is rational.

Question 25Number Sense and Operations (real numbers, exponents, scientific notation)

A number is written as 6.02 × 10^23. If this is multiplied by 10^(-5), what is the new value in scientific notation?

  1. 6.02 × 10^28
  2. 6.02 × 10^18 Correct answer.
  3. 6.02 × 10^23 × 10^5
  4. 0.602 × 10^18

Explanation

Multiplying by 10^(-5) adds -5 to the exponent: 23 + (-5) = 18. The coefficient stays 6.02, giving 6.02 × 10^18.

Question 26Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equivalent to ∛(x^9 · y^6) for positive x and y?

  1. x^3 y^2 Correct answer.
  2. x^12 y^9
  3. x^6 y^3
  4. x^3 y^3

Explanation

A cube root divides each exponent by 3, since ∛(x^9) = x^(9/3) = x^3 and ∛(y^6) = y^(6/3) = y^2. Multiplying gives x^3 y^2.

Question 27Number Sense and Operations (real numbers, exponents, scientific notation)

A calculator displays 4.7E-6. Which number is this?

  1. 0.00000047
  2. 470,000
  3. 0.0000047 Correct answer.
  4. 4,700,000

Explanation

The E-6 notation means 4.7 × 10^(-6), and a negative exponent on 10 moves the decimal point 6 places to the left. Starting from 4.7 and shifting six places left gives 0.0000047.

Question 28Number Sense and Operations (real numbers, exponents, scientific notation)

Which expression is equivalent to √50 + √18 - √8?

  1. 4√2
  2. √60
  3. 2√10
  4. 6√2 Correct answer.

Explanation

Simplify each radical first: √50 = 5√2, √18 = 3√2, and √8 = 2√2. Combining like radicals gives 5√2 + 3√2 - 2√2 = 6√2.

Question 29Number Sense and Operations (real numbers, exponents, scientific notation)

Which statement about the value of (0.0004)^(-1/2) is true?

  1. It is rational and equals 50. Correct answer.
  2. It is rational and equals 0.02.
  3. It is irrational and lies between 0.01 and 0.03.
  4. It is irrational and lies between 40 and 60.

Explanation

Rewrite 0.0004 as 4 × 10^(-4). Then (4 × 10^(-4))^(-1/2) = 4^(-1/2) · 10^2 = (1/2)(100) = 50, which is rational.

Question 30Number Sense and Operations (real numbers, exponents, scientific notation)

The mass of a molecule is about 3.2 × 10^(-22) grams. A sample contains 5.0 × 10^17 molecules. Which is the mass of the sample in scientific notation?

  1. 1.6 × 10^(-4) grams Correct answer.
  2. 1.6 × 10^40 grams
  3. 1.6 × 10^(-5) grams
  4. 1.6 × 10^(-39) grams

Explanation

Multiply the coefficients and add the exponents: (3.2)(5.0) × 10^(-22+17) = 16 × 10^(-5). Since 16 is not between 1 and 10, rewrite it as 1.6 × 10^1, giving 1.6 × 10^(-4).

Question 31Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Which value of x makes the equation 5x - 7 = 3x + 9 true?

  1. 4
  2. 8 Correct answer.
  3. 16
  4. -8

Explanation

Subtract 3x from both sides to get 2x - 7 = 9, then add 7 to obtain 2x = 16, so x = 8. Substituting 8 into both sides gives 33 = 33, confirming the solution.

Question 32Expressions, Equations and Inequalities (linear relationships, systems, radicals)

A line passes through the points (0, -3) and (4, 5). What is the slope of this line?

  1. -2
  2. 4
  3. 1/2
  4. 2 Correct answer.

Explanation

Slope equals the change in y divided by the change in x: (5 - (-3)) / (4 - 0) = 8/4 = 2. The line rises 2 units for every 1 unit it moves right.

Question 33Expressions, Equations and Inequalities (linear relationships, systems, radicals)

What is the value of the square root of 144?

  1. 14
  2. 12 Correct answer.
  3. 24
  4. 72

Explanation

A square root of 144 is a number whose square is 144. Since 12 x 12 = 144, the principal square root is 12.

Question 34Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Which ordered pair is a solution to the system 2x + y = 7 and x - y = 2?

  1. (2, 3)
  2. (3, 1) Correct answer.
  3. (1, 3)
  4. (4, -1)

Explanation

Adding the two equations eliminates y: 3x = 9, so x = 3. Substituting into x - y = 2 gives 3 - y = 2, so y = 1, and (3, 1) satisfies both equations.

Question 35Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Which inequality represents all numbers that are at most 5 units from 0 on a number line?

  1. |x| < 5
  2. |x| ≤ 5 Correct answer.
  3. |x| ≥ 5
  4. |x| > 5

Explanation

Absolute value measures distance from 0, so |x| ≤ 5 describes every number whose distance is 5 or less. This includes both 5 and -5 because the phrase says at most, allowing equality.

Question 36Expressions, Equations and Inequalities (linear relationships, systems, radicals)

The equation y = -4x + 6 is graphed. What is the y-intercept of the graph?

  1. -4
  2. 6 Correct answer.
  3. -6
  4. 4

Explanation

In slope-intercept form y = mx + b, the constant b is the y-intercept. Here b = 6, so the line crosses the y-axis at (0, 6).

Question 37Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Simplify the expression (sqrt 50) + (sqrt 18).

  1. 68
  2. 8 sqrt 2 Correct answer.
  3. 4 sqrt 17
  4. 2 sqrt 68

Explanation

Rewrite each radical using perfect-square factors: sqrt 50 = 5 sqrt 2 and sqrt 18 = 3 sqrt 2. Adding like radicals gives 5 sqrt 2 + 3 sqrt 2 = 8 sqrt 2.

Question 38Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Solve the inequality 3x - 4 > 11.

  1. x > 5 Correct answer.
  2. x > 15
  3. x > 7
  4. x < 5

Explanation

Add 4 to both sides to get 3x > 15, then divide by the positive 3, giving x > 5. Dividing by a positive number does not reverse the inequality symbol.

Question 39Expressions, Equations and Inequalities (linear relationships, systems, radicals)

A line has slope 3 and passes through the point (2, 5). Which equation describes this line?

  1. y = 3x - 1 Correct answer.
  2. y = 3x + 5
  3. y = 3x + 11
  4. y = 2x + 3

Explanation

Using point-slope form, y - 5 = 3(x - 2), which expands to y - 5 = 3x - 6, so y = 3x - 1. Checking the point: 3(2) - 1 = 5, which matches.

Question 40Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Two lines are graphed: y = 2x + 1 and y = 2x - 4. How many solutions does this system of equations have?

  1. Exactly one solution
  2. Exactly two solutions
  3. Infinitely many solutions
  4. No solution Correct answer.

Explanation

Both lines have slope 2 but different y-intercepts, so they are parallel and never intersect. A system of parallel lines has no solution.

Question 41Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Simplify the expression (3 sqrt 5)(2 sqrt 10).

  1. 30 sqrt 5
  2. 6 sqrt 15
  3. 30 sqrt 2 Correct answer.
  4. 6 sqrt 50

Explanation

Multiply coefficients and radicands: 3 x 2 = 6 and sqrt 5 x sqrt 10 = sqrt 50. Since sqrt 50 = 5 sqrt 2, the product is 6 x 5 sqrt 2 = 30 sqrt 2.

Question 42Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Solve the inequality -2x + 6 ≤ 14.

  1. x ≤ 4
  2. x ≥ 4
  3. x ≥ -4 Correct answer.
  4. x ≤ -4

Explanation

Subtract 6 from both sides to get -2x ≤ 8, then divide by -2 and reverse the inequality: x ≥ -4. Reversing is required whenever dividing by a negative number.

Question 43Expressions, Equations and Inequalities (linear relationships, systems, radicals)

A line passes through (-2, 7) and (4, -5). Which equation represents the line in point-slope form?

  1. y - 7 = -1/2(x + 2)
  2. y - 7 = 2(x + 2)
  3. y - 7 = -2(x + 2) Correct answer.
  4. y + 7 = -2(x - 2)

Explanation

The slope is (-5 - 7)/(4 - (-2)) = -12/6 = -2. Using the point (-2, 7) in y - y1 = m(x - x1) gives y - 7 = -2(x + 2).

Question 44Expressions, Equations and Inequalities (linear relationships, systems, radicals)

The system 4x + 3y = 10 and 4x + 3y = 10 is graphed. Which statement about the system is true?

  1. It has exactly two solutions because the lines intersect twice.
  2. It has no solution because the coefficients are equal.
  3. It has exactly one solution because there are two equations.
  4. It has infinitely many solutions because the two equations describe the same line. Correct answer.

Explanation

Identical equations describe the same line, so every point on that line satisfies both. A consistent dependent system therefore has infinitely many solutions.

Question 45Expressions, Equations and Inequalities (linear relationships, systems, radicals)

What is the value of the cube root of 64?

  1. 16
  2. 2
  3. 8
  4. 4 Correct answer.

Explanation

A cube root of 64 is a number whose cube is 64. Since 4 x 4 x 4 = 64, the cube root is 4.

Question 46Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Simplify the expression sqrt 72 divided by sqrt 2.

  1. 2 sqrt 6
  2. 6 Correct answer.
  3. 36
  4. sqrt 70

Explanation

The quotient of square roots equals the square root of the quotient: sqrt 72 / sqrt 2 = sqrt(72/2) = sqrt 36 = 6.

Question 47Expressions, Equations and Inequalities (linear relationships, systems, radicals)

A line is perpendicular to y = (1/3)x + 2 and passes through the origin. What is the equation of this line?

  1. y = 3x
  2. y = -(1/3)x
  3. y = -3x Correct answer.
  4. y = (1/3)x

Explanation

Perpendicular lines have slopes that are negative reciprocals, so the slope is -3. Passing through the origin gives y = -3x.

Question 48Expressions, Equations and Inequalities (linear relationships, systems, radicals)

The graph of y = |x - 3| + 2 is drawn. What are the coordinates of the vertex of this graph?

  1. (2, 3)
  2. (-3, 2)
  3. (3, -2)
  4. (3, 2) Correct answer.

Explanation

The absolute value function y = |x - h| + k has its vertex at (h, k). Here h = 3 and k = 2, so the vertex is (3, 2).

Question 49Expressions, Equations and Inequalities (linear relationships, systems, radicals)

Solve the equation sqrt(x + 7) = 4.

  1. x = 16
  2. x = -3
  3. x = 9 Correct answer.
  4. x = 23

Explanation

Square both sides to get x + 7 = 16, then subtract 7 to obtain x = 9. Checking: sqrt(9 + 7) = sqrt 16 = 4, so the solution is valid.

Question 50Expressions, Equations and Inequalities (linear relationships, systems, radicals)

The graph of y = -2x + 5 is translated 3 units down. What is the equation of the new line?

  1. y = -2x - 3
  2. y = -2x + 2 Correct answer.
  3. y = -5x + 5
  4. y = -2x + 8

Explanation

A vertical translation changes only the y-intercept. Moving 3 units down subtracts 3 from the constant: 5 - 3 = 2, giving y = -2x + 2.