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GA Milestones Math Grade 8 study materials
GA Milestones Math Grade 8 study resources

GA Milestones Math Grade 8 practice questions

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Question 1Mathematics content standards (Grade 8) - domain weights not enumerated in source

A square has an area of 144 square centimeters. What is the side length of the square?

  1. 12 cm Correct answer.
  2. 72 cm
  3. 24 cm
  4. 36 cm

Explanation

The area of a square is the side length squared, so the side length is the square root of the area. The square root of 144 is 12 because 12 × 12 = 144. Therefore the side length is 12 cm.

Question 2Mathematics content standards (Grade 8) - domain weights not enumerated in source

Which number is irrational?

  1. the fraction 22/7
  2. the square root of 2 Correct answer.
  3. 0.75
  4. the square root of 49

Explanation

An irrational number cannot be written as a ratio of two integers, and its decimal form neither terminates nor repeats. The square root of 2 is approximately 1.41421356..., which never terminates or repeats, so it is irrational. The other choices are all rational.

Question 3Mathematics content standards (Grade 8) - domain weights not enumerated in source

A right triangle has legs of length 6 units and 8 units. What is the length of the hypotenuse?

  1. the square root of 28 units
  2. 48 units
  3. 10 units Correct answer.
  4. 14 units

Explanation

The Pythagorean theorem states that in a right triangle the sum of the squares of the legs equals the square of the hypotenuse. Here 6² + 8² = 36 + 64 = 100, and the square root of 100 is 10. So the hypotenuse is 10 units.

Question 4Mathematics content standards (Grade 8) - domain weights not enumerated in source

What is the value of 5³?

  1. 25
  2. 125 Correct answer.
  3. 243
  4. 15

Explanation

A positive integer exponent tells how many times to use the base as a factor. Here 5³ means 5 × 5 × 5, which equals 125. Multiplying the base by the exponent, 5 × 3 = 15, is a common error but is not what exponents mean.

Question 5Mathematics content standards (Grade 8) - domain weights not enumerated in source

A line passes through the points (0, 3) and (4, 11). What is the slope of this line?

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

Explanation

Slope equals the change in y divided by the change in x between two points. The change in y is 11 − 3 = 8, and the change in x is 4 − 0 = 4. Dividing gives 8 ÷ 4 = 2, so the slope is 2.

Question 6Mathematics content standards (Grade 8) - domain weights not enumerated in source

Which equation represents a line with a y-intercept of −2 and a slope of 3?

  1. y = −2x + 3
  2. y = 3x + 2
  3. y = 2x − 3
  4. y = 3x − 2 Correct answer.

Explanation

In slope-intercept form y = mx + b, m is the slope and b is the y-intercept. A slope of 3 and a y-intercept of −2 give y = 3x + (−2), which is written y = 3x − 2. The constant term is the value of y when x is 0.

Question 7Mathematics content standards (Grade 8) - domain weights not enumerated in source

A scatter plot shows a strong negative linear association between hours of exercise per week and resting heart rate. Which description best fits the data?

  1. Exercise and resting heart rate have no relationship.
  2. As exercise increases, resting heart rate tends to decrease. Correct answer.
  3. Resting heart rate stays constant regardless of exercise.
  4. As exercise increases, resting heart rate tends to increase.

Explanation

A negative association means that as one variable increases, the other tends to decrease. Since exercise hours increase along the horizontal axis, a negative association means resting heart rate tends to fall as exercise rises. A strong association means the points cluster closely around a downward-sloping line.

Question 8Mathematics content standards (Grade 8) - domain weights not enumerated in source

Which of these is a rational number?

  1. 0.333... repeating forever Correct answer.
  2. the square root of 5
  3. the square root of 10
  4. π

Explanation

A rational number can be written as a fraction of two integers. A decimal that repeats forever, such as 0.333..., equals 1/3 and is therefore rational. Numbers such as π and non-perfect square roots have non-repeating, non-terminating decimals and are irrational.

Question 9Mathematics content standards (Grade 8) - domain weights not enumerated in source

The equation y = 4x describes a proportional relationship. What is the constant of proportionality?

  1. x
  2. 4 Correct answer.
  3. y
  4. 1/4

Explanation

A proportional relationship has the form y = kx, where k is the constant of proportionality. Comparing y = 4x with y = kx shows that k = 4. That means y is always 4 times x, and the graph passes through the origin.

Question 10Mathematics content standards (Grade 8) - domain weights not enumerated in source

A cube has a volume of 27 cubic inches. What is the length of one edge of the cube?

  1. 13.5 in
  2. 9 in
  3. the square root of 27 in
  4. 3 in Correct answer.

Explanation

The volume of a cube is the edge length cubed, so the edge length is the cube root of the volume. The cube root of 27 is 3 because 3 × 3 × 3 = 27. Thus each edge measures 3 inches.

Question 11Mathematics content standards (Grade 8) - domain weights not enumerated in source

What is the value of 2⁻³?

  1. 1/6
  2. −8
  3. 1/8 Correct answer.
  4. −6

Explanation

A negative exponent means the reciprocal of the base raised to the positive exponent. So 2⁻³ = 1/2³ = 1/8. The negative sign in the exponent does not make the result negative.

Question 12Mathematics content standards (Grade 8) - domain weights not enumerated in source

Simplify: (3 × 10⁴) × (2 × 10³). Write the answer in scientific notation.

  1. 6 × 10⁷ Correct answer.
  2. 6 × 10⁵
  3. 5 × 10⁷
  4. 6 × 10¹²

Explanation

Multiply the coefficients and add the exponents when multiplying powers with the same base. Here 3 × 2 = 6 and 10⁴ × 10³ = 10⁷, giving 6 × 10⁷. This is already in scientific notation because 6 is between 1 and 10.

Question 13Mathematics content standards (Grade 8) - domain weights not enumerated in source

Solve for x: 3x − 7 = 2x + 5.

  1. −12
  2. 2
  3. 6
  4. 12 Correct answer.

Explanation

Subtract 2x from both sides to get x − 7 = 5, then add 7 to both sides to get x = 12. Substituting 12 back into the original equation gives 29 on both sides, confirming the solution.

Question 14Mathematics content standards (Grade 8) - domain weights not enumerated in source

Two lines are graphed on the same coordinate plane. Line p has slope 2/3 and line q has slope −3/2. What is true about lines p and q?

  1. They are parallel.
  2. They are the same line.
  3. They intersect at exactly the origin.
  4. They are perpendicular. Correct answer.

Explanation

Two lines are perpendicular when their slopes are negative reciprocals, meaning their product is −1. Multiplying (2/3)(−3/2) gives −1, so lines p and q are perpendicular. Parallel lines would need identical slopes.

Question 15Mathematics content standards (Grade 8) - domain weights not enumerated in source

A system of two linear equations has no solution. What must be true of the graphs of the equations?

  1. The lines are the same line.
  2. The lines intersect at exactly one point.
  3. The lines both pass through the origin.
  4. The lines are parallel and distinct. Correct answer.

Explanation

A solution of a system corresponds to a point where the graphs intersect. If there is no solution, the lines never meet, which happens only when they are parallel and not the same line. Parallel lines share the same slope but have different y-intercepts.

Question 16Mathematics content standards (Grade 8) - domain weights not enumerated in source

The function f is defined by f(x) = −2x + 9. What is f(−3)?

  1. 6
  2. 3
  3. −15
  4. 15 Correct answer.

Explanation

To evaluate f(−3), substitute −3 for x: f(−3) = −2(−3) + 9. The product −2 times −3 is 6, and 6 + 9 = 15. So f(−3) = 15.

Question 17Mathematics content standards (Grade 8) - domain weights not enumerated in source

A sequence is defined by the rule aₙ = 3n + 1 for n = 1, 2, 3, .... What is the 10th term of the sequence?

  1. 34
  2. 13
  3. 30
  4. 31 Correct answer.

Explanation

Substitute n = 10 into the rule: a₁₀ = 3(10) + 1. That gives 30 + 1 = 31. The rule is an explicit formula, so the 10th term can be found directly without listing earlier terms.

Question 18Mathematics content standards (Grade 8) - domain weights not enumerated in source

A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?

  1. 8 cm
  2. 12 cm Correct answer.
  3. the square root of 194 cm
  4. 18 cm

Explanation

The Pythagorean theorem gives a² + b² = c², where c is the hypotenuse. Here 5² + b² = 13², so 25 + b² = 169 and b² = 144. The positive square root of 144 is 12, so the other leg is 12 cm.

Question 19Mathematics content standards (Grade 8) - domain weights not enumerated in source

A dilation with center at the origin maps point (4, −6) to point (2, −3). What is the scale factor of the dilation?

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

Explanation

In a dilation centered at the origin, each coordinate of the image equals the scale factor times the original coordinate. Dividing 2 by 4 gives 1/2, and dividing −3 by −6 also gives 1/2. Both coordinates agree, so the scale factor is 1/2, which shrinks the figure.

Question 20Mathematics content standards (Grade 8) - domain weights not enumerated in source

A trend line for a data set is y = 1.5x + 20, where x is the number of weeks since a plant was potted and y is its height in centimeters. What does the slope of 1.5 represent?

  1. The predicted growth of 1.5 cm per week Correct answer.
  2. The number of weeks until the plant reaches 20 cm
  3. The total height after 1.5 weeks
  4. The plant's height when potted

Explanation

In a linear model the slope is the rate of change of the predicted output per one-unit increase in the input. Since x is measured in weeks and y in centimeters, a slope of 1.5 means the predicted height increases 1.5 cm each week. The y-intercept of 20 represents the starting height.

Question 21Mathematics content standards (Grade 8) - domain weights not enumerated in source

The graph of y = x² is translated 3 units to the right. Which equation represents the new graph?

  1. y = x² + 3
  2. y = (x + 3)²
  3. y = (x − 3)² Correct answer.
  4. y = x² − 3

Explanation

A horizontal shift of a function f(x) by h units to the right is written f(x − h). Replacing x with (x − 3) shifts every point 3 units right, so the image of y = x² is y = (x − 3)². Adding or subtracting outside the square shifts the graph vertically instead.

Question 22Mathematics content standards (Grade 8) - domain weights not enumerated in source

A scatter plot of study time versus test score shows points tightly clustered around a line with a positive slope. Which statement best describes the correlation?

  1. Strong negative correlation
  2. Strong positive correlation Correct answer.
  3. No correlation
  4. Weak negative correlation

Explanation

Correlation strength describes how closely points follow a line, and its direction follows the slope. Points tightly clustered around an upward-sloping line indicate a strong positive correlation. A negative correlation would require the line to slope downward.

Question 23Mathematics content standards (Grade 8) - domain weights not enumerated in source

The equation 5x + 2y = 20 is graphed. What are the x-intercept and y-intercept of the line?

  1. x-intercept 5, y-intercept 2
  2. x-intercept 4, y-intercept 10 Correct answer.
  3. x-intercept 2, y-intercept 5
  4. x-intercept 10, y-intercept 4

Explanation

To find the x-intercept, set y = 0, giving 5x = 20 and x = 4. To find the y-intercept, set x = 0, giving 2y = 20 and y = 10. So the line crosses the x-axis at 4 and the y-axis at 10.

Question 24Mathematics content standards (Grade 8) - domain weights not enumerated in source

A line passes through (2, 5) and (6, 13). Which equation represents the line?

  1. y = 2x + 1 Correct answer.
  2. y = 2x + 5
  3. y = 4x − 3
  4. y = 1/2x + 4

Explanation

The slope is (13 − 5)/(6 − 2) = 8/4 = 2. Using point-slope form with (2, 5): y − 5 = 2(x − 2), which simplifies to y = 2x + 1. Substituting either point confirms the equation.

Question 25Mathematics content standards (Grade 8) - domain weights not enumerated in source

Solve the system: 2x + 3y = 12 and x − y = 1. What is the value of x + y?

  1. 5 Correct answer.
  2. 7
  3. 3
  4. 1

Explanation

From x − y = 1 we get x = y + 1. Substituting into 2x + 3y = 12 gives 2(y + 1) + 3y = 12, so 5y + 2 = 12 and y = 2. Then x = 3, and x + y = 3 + 2 = 5.

Question 26Mathematics content standards (Grade 8) - domain weights not enumerated in source

What is the value of (2³)² ÷ 2⁴?

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

Explanation

Apply the power-of-a-power rule: (2³)² = 2⁶. Then divide by subtracting exponents: 2⁶ ÷ 2⁴ = 2² = 4.

Question 27Mathematics content standards (Grade 8) - domain weights not enumerated in source

A square has an area of 50 square centimeters. Between which two consecutive integers does its side length lie?

  1. 7 and 8 Correct answer.
  2. 6 and 7
  3. 5 and 6
  4. 8 and 9

Explanation

The side length is √50. Since 7² = 49 and 8² = 64, and 49 < 50 < 64, the value √50 lies between 7 and 8.

Question 28Mathematics content standards (Grade 8) - domain weights not enumerated in source

A cylinder has a radius of 3 inches and a height of 10 inches. Using π ≈ 3.14, what is the volume of the cylinder?

  1. 94.2 cubic inches
  2. 188.4 cubic inches
  3. 282.6 cubic inches Correct answer.
  4. 31.4 cubic inches

Explanation

The volume of a cylinder is V = πr²h. Substituting gives 3.14 × 9 × 10 = 282.6 cubic inches.

Question 29Mathematics content standards (Grade 8) - domain weights not enumerated in source

A cone and a cylinder have the same base radius and the same height. The volume of the cylinder is 81 cubic units. What is the volume of the cone?

  1. 243 cubic units
  2. 27 cubic units Correct answer.
  3. 81 cubic units
  4. 40.5 cubic units

Explanation

The volume of a cone is one third of the volume of a cylinder with the same base and height. So the cone's volume is 81 ÷ 3 = 27 cubic units.

Question 30Mathematics content standards (Grade 8) - domain weights not enumerated in source

Which set of side lengths can form a right triangle?

  1. 4, 5, 6
  2. 3, 4, 6
  3. 5, 11, 12
  4. 6, 8, 10 Correct answer.

Explanation

A triangle is right if a² + b² = c² for the two shorter sides and the longest side. Here 6² + 8² = 36 + 64 = 100 = 10².

Question 31Mathematics content standards (Grade 8) - domain weights not enumerated in source

A line is drawn on a coordinate plane with a slope of 0. Which statement describes the line?

  1. It rises from left to right.
  2. It is vertical.
  3. It is horizontal. Correct answer.
  4. It falls from left to right.

Explanation

Slope measures vertical change divided by horizontal change. A slope of 0 means there is no vertical change as x increases, so the line is horizontal.

Question 32Mathematics content standards (Grade 8) - domain weights not enumerated in source

A transformation maps every point (x, y) to (x + 5, y − 2). Which description matches this transformation?

  1. A reflection across the line y = x
  2. A translation 5 units right and 2 units down Correct answer.
  3. A translation 5 units left and 2 units up
  4. A rotation of 90 degrees about the origin

Explanation

Adding 5 to the x-coordinate shifts points 5 units to the right, and subtracting 2 from the y-coordinate shifts them 2 units down. This is a translation.

Question 33Mathematics content standards (Grade 8) - domain weights not enumerated in source

Solve for x: 5(x − 2) = 3x + 4.

  1. 1
  2. 7 Correct answer.
  3. 3
  4. −7

Explanation

Distribute to get 5x − 10 = 3x + 4. Subtract 3x from both sides to get 2x − 10 = 4, then add 10 to get 2x = 14, so x = 7.

Question 34Mathematics content standards (Grade 8) - domain weights not enumerated in source

What is the solution of the system 3x + y = 11 and y = x + 3?

  1. (5, 2)
  2. (4, 7)
  3. (1, 4)
  4. (2, 5) Correct answer.

Explanation

Substitute y = x + 3 into the first equation to get 3x + x + 3 = 11, so 4x = 8 and x = 2. Then y = 2 + 3 = 5.

Question 35Mathematics content standards (Grade 8) - domain weights not enumerated in source

A function is defined by f(x) = 3x − 5. For what value of x is f(x) = 16?

  1. 11
  2. 7 Correct answer.
  3. 3
  4. 21

Explanation

Set 3x − 5 = 16, then add 5 to get 3x = 21, so x = 7. Checking: f(7) = 21 − 5 = 16.

Question 36Mathematics content standards (Grade 8) - domain weights not enumerated in source

The graph of a linear function passes through the points (0, 4) and (3, 10). Which function describes the same relationship?

  1. y = 6x + 4
  2. y = 3x + 4
  3. y = 2x + 4 Correct answer.
  4. y = 2x + 10

Explanation

The y-intercept is 4 because the line passes through (0, 4). The slope is (10 − 4)/(3 − 0) = 2, so the equation is y = 2x + 4.

Question 37Mathematics content standards (Grade 8) - domain weights not enumerated in source

A line has the equation 4x + 2y = 12. Which equation represents a line parallel to it?

  1. y = −2x + 7 Correct answer.
  2. y = 0.5x + 7
  3. y = −0.5x + 7
  4. y = 2x + 7

Explanation

Rewrite 4x + 2y = 12 as y = −2x + 6, so the slope is −2. Parallel lines have equal slopes, so y = −2x + 7 is parallel.

Question 38Mathematics content standards (Grade 8) - domain weights not enumerated in source

A line passes through the point (−2, 5) and is perpendicular to a line with slope 1/3. What is the equation of the line?

  1. y = 3x + 11
  2. y = −3x + 5
  3. y = −3x − 1 Correct answer.
  4. y = (1/3)x + 17/3

Explanation

A perpendicular line has slope −3, the negative reciprocal of 1/3. Using point-slope form: y − 5 = −3(x + 2), which simplifies to y = −3x − 1.

Question 39Mathematics content standards (Grade 8) - domain weights not enumerated in source

Which expression is equivalent to (x⁵)(x⁻²)?

  1. x⁻¹⁰
  2. x³ Correct answer.
  3. x⁻³
  4. x⁷

Explanation

When multiplying powers with the same base, add the exponents: 5 + (−2) = 3, so the product is x³.

Question 40Mathematics content standards (Grade 8) - domain weights not enumerated in source

The number 0.000 000 45 is written in scientific notation. Which expression is correct?

  1. 45 × 10⁻⁸
  2. 4.5 × 10⁻⁷ Correct answer.
  3. 4.5 × 10⁷
  4. 4.5 × 10⁻⁶

Explanation

Scientific notation requires a coefficient between 1 and 10. Moving the decimal 7 places right to get 4.5 means the exponent is −7.

Question 41Mathematics content standards (Grade 8) - domain weights not enumerated in source

A sequence begins 2, 6, 18, 54, ... and continues with the same pattern. Which expression gives the nth term?

  1. 2n + 4
  2. 2 · 3ⁿ
  3. 3 · 2ⁿ⁻¹
  4. 2 · 3ⁿ⁻¹ Correct answer.

Explanation

Each term is 3 times the previous term and the first term is 2, so this is a geometric sequence. The nth term is a₁ · rⁿ⁻¹ = 2 · 3ⁿ⁻¹.

Question 42Mathematics content standards (Grade 8) - domain weights not enumerated in source

A scatter plot compares the age of a used car in years with its selling price in dollars. The data show a linear association with a correlation coefficient of r = −0.91. Which conclusion is best supported?

  1. There is no relationship between age and selling price.
  2. Older cars tend to sell for less, and the linear pattern is strong. Correct answer.
  3. Older cars tend to sell for more, and the linear pattern is strong.
  4. Older cars tend to sell for less, but the linear pattern is weak.

Explanation

The negative sign of r indicates that as age increases, price tends to decrease. A value of −0.91 is close to −1, so the linear association is strong.

Question 43Mathematics content standards (Grade 8) - domain weights not enumerated in source

Two-way tables often describe data with two categorical variables. A table shows 40 students who play a sport and 60 who do not; of the 40 athletes, 30 also play an instrument. What is the relative frequency of playing an instrument among athletes?

  1. 0.50
  2. 0.30
  3. 0.75 Correct answer.
  4. 0.40

Explanation

A relative frequency within a row is found by dividing the row count by the row total. Here 30 ÷ 40 = 0.75, so 75% of athletes also play an instrument.

Question 44Mathematics content standards (Grade 8) - domain weights not enumerated in source

A trend line for a data set is y = 2.5x + 12, where x is the number of months a gym member has belonged and y is the number of visits per month. What does the slope represent?

  1. A new member makes about 12 visits per month.
  2. Each additional month is associated with about 2.5 more visits per month. Correct answer.
  3. Each additional visit is associated with 2.5 more months of membership.
  4. The total number of visits after 2.5 months.

Explanation

In a linear model y = mx + b, the slope m gives the predicted change in y for each one-unit increase in x. Here each extra month predicts about 2.5 additional visits per month.

Question 45Mathematics content standards (Grade 8) - domain weights not enumerated in source

A cube has a volume of 512 cubic inches. What is the total surface area of the cube?

  1. 512 square inches
  2. 384 square inches Correct answer.
  3. 64 square inches
  4. 96 square inches

Explanation

The edge length is the cube root of 512, which is 8 inches. Each of the 6 faces has area 8² = 64, so the total surface area is 6 × 64 = 384 square inches.

Question 46Mathematics content standards (Grade 8) - domain weights not enumerated in source

A sphere has a radius of 6 centimeters. Using π ≈ 3.14, what is the volume of the sphere?

  1. 904.32 cubic centimeters Correct answer.
  2. 216 cubic centimeters
  3. 452.16 cubic centimeters
  4. 288 cubic centimeters

Explanation

The volume of a sphere is V = (4/3)πr³. Substituting gives (4/3)(3.14)(216) = 904.32 cubic centimeters.

Question 47Mathematics content standards (Grade 8) - domain weights not enumerated in source

A cone has a volume of 100π cubic centimeters and a height of 12 centimeters. What is the radius of its base?

  1. 5 centimeters Correct answer.
  2. 10 centimeters
  3. √(25/π) centimeters
  4. 25 centimeters

Explanation

Using V = (1/3)πr²h, substitute: 100π = (1/3)πr²(12) = 4πr². Dividing by 4π gives r² = 25, so r = 5 centimeters.

Question 48Mathematics content standards (Grade 8) - domain weights not enumerated in source

A system of equations is shown: y = 2x + 1 and 4x − 2y = −2. How many solutions does the system have?

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

Explanation

Substitute y = 2x + 1 into the second equation: 4x − 2(2x + 1) = −2 becomes 4x − 4x − 2 = −2, or −2 = −2. This is always true, so the equations describe the same line and every point on it is a solution.

Question 49Mathematics content standards (Grade 8) - domain weights not enumerated in source

The function f(x) = x² is transformed to g(x) = (x − 4)² + 3. Which statement describes the graph of g?

  1. It is the graph of f shifted 4 units left and 3 units up.
  2. It is the graph of f shifted 4 units right and 3 units down.
  3. It is the graph of f shifted 3 units right and 4 units up.
  4. It is the graph of f shifted 4 units right and 3 units up. Correct answer.

Explanation

Replacing x with (x − 4) shifts the graph 4 units to the right, and adding 3 outside the square shifts it 3 units up.

Question 50Mathematics content standards (Grade 8) - domain weights not enumerated in source

A right triangle has legs of length 9 centimeters and 12 centimeters. A second triangle similar to the first has a hypotenuse of 30 centimeters. What is the area of the second triangle?

  1. 108 square centimeters
  2. 432 square centimeters
  3. 54 square centimeters
  4. 216 square centimeters Correct answer.

Explanation

The first hypotenuse is √(81 + 144) = 15, so the scale factor is 30 ÷ 15 = 2. The first area is (1/2)(9)(12) = 54, and areas scale by the square of the factor, so the second area is 54 × 4 = 216 square centimeters.