West Virginia General Summative Assessment Mathematics — Grade 8

What is the simplified value of \(\frac{4^7}{4^4}\)?

• A12
• B64
• C256
• D1024

Which expression is equivalent to \(5^{-3}\)?

• A-15
• B-125
• C\(\frac{1}{125}\)
• D\(\frac{1}{15}\)

What is the number 0.00048 written in scientific notation?

• A\(4.8 \times 10^{-5}\)
• B\(4.8 \times 10^{-4}\)
• C\(4.8 \times 10^4\)
• D\(48 \times 10^{-5}\)

Solve for \(x\): \(x^2 = 121\).

• A11
• B22
• C60.5
• D242

Solve for \(y\): \(y^3 = 64\).

• A4
• B8
• C16
• D21.33

A linear graph representing a proportional relationship passes through the origin \((0,0)\) and the point \((4, 12)\). What is the unit rate (slope) of this relationship?

• A\(\frac{1}{3}\)
• B3
• C8
• D48

Solve for \(x\): \(3x + 8 = 29\).

• A5
• B7
• C11
• D37

What are the slope and \(y\)-intercept of the linear equation \(y = -2x + 7\)?

• ASlope = 7, y-intercept = (0, -2)
• BSlope = -2, y-intercept = (0, 7)
• CSlope = 2, y-intercept = (0, -7)
• DSlope = -2, y-intercept = (0, -7)

Which set of ordered pairs represents a function?

• A\(\{(1, 2), (2, 4), (3, 6), (4, 8)\}\)
• B\(\{(2, 3), (2, 5), (4, 7), (5, 9)\}\)
• C\(\{(3, 1), (3, 4), (3, 7), (3, 9)\}\)
• D\(\{(5, 2), (5, 8), (6, 1), (7, 3)\}\)

Which equation represents a linear function?

• A\(y = x^2 + 3\)
• B\(y = 4x - 5\)
• C\(y = \frac{2}{x}\)
• D\(y = 3^x\)

A function is defined by \(f(x) = 5x - 3\). What is \(f(4)\)?

• A11
• B17
• C20
• D23

Maya pays a fixed monthly gym membership fee of $15 plus $5 per fitness class attended. The total cost is modeled by \(C = 5x + 15\), where \(x\) is the number of classes. What does the \(y\)-intercept of 15 represent in this context?

• AThe cost per fitness class
• BThe maximum number of classes Maya can attend
• CThe fixed monthly membership fee before attending any classes
• DThe total cost for attending 5 classes

Simplify the expression \(\frac{(2^3 \cdot 2^5)^2}{2^4}\).

• A256
• B1024
• C4096
• D16384

What is \((3.2 \times 10^5) + (4.5 \times 10^4)\) expressed in standard scientific notation?

• A\(7.7 \times 10^5\)
• B\(3.65 \times 10^5\)
• C\(3.65 \times 10^9\)
• D\(7.7 \times 10^4\)

The mass of a microscopic dust particle is approximately \(4 \times 10^{-9}\) kg. What is the combined total mass of \(6 \times 10^6\) dust particles?

• A\(2.4 \times 10^{-3}\) kg
• B\(2.4 \times 10^{-2}\) kg
• C\(24 \times 10^{-2}\) kg
• D\(2.4 \times 10^3\) kg

Solve for \(x\): \(5x - 7 = 2x + 14\).

• A\(x = 3\)
• B\(x = 7\)
• C\(x = 21\)
• D\(x = 3.5\)

Solve for \(x\): \(4(x - 3) + 2x = 3(x + 5)\).

• A\(x = 3\)
• B\(x = 7\)
• C\(x = 9\)
• D\(x = 27\)

How many solutions does the linear equation \(3(2x + 4) = 6x + 12\) have?

• ANo solution
• BExactly one solution (x = 0)
• CExactly two solutions
• DInfinitely many solutions

Which linear equation has no solution?

• A\(4x + 9 = 4x + 9\)
• B\(4x + 9 = 4x - 2\)
• C\(4x + 9 = 2x + 9\)
• D\(4x + 9 = 0\)

What is the slope of the line passing through the points \((-3, 4)\) and \((5, -12)\)?

• A-2
• B2
• C\(-\frac{1}{2}\)
• D\(\frac{1}{2}\)

A line passes through \((0, 4)\) and \((3, 10)\). What is the equation of this line in slope-intercept form?

• A\(y = 4x + 2\)
• B\(y = 2x + 4\)
• C\(y = 3x + 4\)
• D\(y = 2x + 10\)

Function A is defined by \(y = 6x + 2\). Function B is represented by a line passing through \((1, 5)\) and \((4, 26)\). Which statement correctly compares their rates of change?

• AFunction A has a greater rate of change because 6 > 5.
• BFunction B has a greater rate of change because 7 > 6.
• CBoth functions have equal rates of change.
• DFunction A has a greater rate of change because its y-intercept is higher.

Solve the system of equations by substitution: \(y = 2x + 1\) \(3x + y = 16\)

• A\((2, 5)\)
• B\((3, 7)\)
• C\((5, 11)\)
• D\((4, 9)\)

Solve the system of linear equations using elimination: \(2x + 3y = 12\) \(5x - 3y = 9\)

• A\((3, 2)\)
• B\((2, 3)\)
• C\((1, 4)\)
• D\((4, 1)\)

A theater sold adult tickets for $10 each and child tickets for $6 each. A total of 150 tickets were sold for $1,180. How many adult tickets (\(a\)) and child tickets (\(c\)) were sold?

• A70 adult tickets and 80 child tickets
• B80 adult tickets and 70 child tickets
• C60 adult tickets and 90 child tickets
• D90 adult tickets and 60 child tickets

Two lines \(y = 3x - 4\) and \(y = -x + 8\) are graphed on the coordinate plane. At which point do the two lines intersect?

• A\((2, 2)\)
• B\((3, 5)\)
• C\((4, 8)\)
• D\((1, -1)\)

What is the relationship between the graphs of the system of equations \(y = 4x + 3\) and \(2y - 8x = 10\)?

• AIntersect at a single point (0, 3)
• BCoincident lines with infinitely many solutions
• CParallel lines with no solution
• DPerpendicular lines intersecting at (1, 7)

A cell phone plan charges a flat fee of $30 per month plus $0.05 per text message sent. Which equation models the total monthly cost \(C\) for sending \(t\) text messages?

• A\(C = 30t + 0.05\)
• B\(C = 0.05t + 30\)
• C\(C = 35t\)
• D\(C = 0.05(t + 30)\)

A cyclist rides up a steep hill at a steady slow pace, rests at the top for 5 minutes, and then rides down the other side at a fast steady speed. Which best describes the graph of distance versus time?

• AA line sloping upward moderately, a flat horizontal line, then a line sloping upward stee…
• BA line sloping upward, a line sloping downward, then a horizontal line
• CA horizontal line, a line sloping upward, then a line sloping downward
• DA line sloping downward, a horizontal line, then a line sloping downward

Which table of values represents a non-linear function?

• Ax: (1, 2, 3, 4), y: (3, 6, 9, 12)
• Bx: (1, 2, 3, 4), y: (2, 5, 10, 17)
• Cx: (1, 2, 3, 4), y: (10, 8, 6, 4)
• Dx: (1, 2, 3, 4), y: (-1, 1, 3, 5)

Which statement correctly compares the functions \(y = 4x\) and \(y = 4x + 5\)?

• A\(y = 4x\) is proportional because its \(y\)-intercept is 0, while \(y = 4x + 5\) is non-…
• B\(y = 4x + 5\) is proportional because it has an added constant.
• CBoth equations represent proportional relationships because they have the same slope.
• DNeither equation represents a linear function.

Evaluate the numeric expression \(\sqrt{36} + \sqrt[3]{125} - 2^3\).

• A3
• B7
• C11
• D19

Light travels at approximately \(3.0 \times 10^8\) meters per second. If the average distance from Earth to the Sun is \(1.5 \times 10^{11}\) meters, approximately how many seconds does it take for light to travel from the Sun to Earth?

• A50 seconds
• B500 seconds
• C5,000 seconds
• D\(4.5 \times 10^{19}\) seconds

Solve for \(x\): \(\frac{2}{3}(6x - 9) + 5 = \frac{1}{4}(12x + 16)\).

• A\(x = 3\)
• B\(x = 5\)
• C\(x = 7\)
• D\(x = 9\)

Marcus buys 3 notebooks and 2 pens for $14. The next week, at the same store prices, he buys 6 notebooks and 4 pens for $28. How many valid price solutions exist for the cost of one notebook and one pen?

• ANo solution
• BExactly one unique price combination
• CExactly two price combinations
• DInfinitely many possible price combinations

Company A charges a base fee of $40 plus $15 per hour for lawn care. Company B models its total charge using \(C = 20h + 25\), where \(h\) represents hours. For how many hours of service will both companies charge the exact same total cost?

• A2 hours
• B3 hours
• C4 hours
• D5 hours

Simplify the expression \(\left( \frac{3a^4 b^{-2}}{a^{-2} b^3} \right)^2\) using positive exponents only.

• A\(\frac{6 a^8}{b^2}\)
• B\(\frac{9 a^{12}}{b^{10}}\)
• C\(\frac{9 a^4}{b^2}\)
• D\(\frac{6 a^{12}}{b^5}\)

The area \(A\) of a square picture frame is given by \(A = s^2\), where \(s\) is side length. If the side length doubles from 3 inches to 6 inches, how does the area change, and why is this function non-linear?

• AArea doubles from 9 to 18 sq in; it is linear because rate of change is constant.
• BArea increases by 9 sq in; it is linear because sides are equal.
• CArea quadruples from 9 to 36 sq in; it is non-linear because rate of change is not consta…
• DArea increases by 36 sq in; it is non-linear because initial value is 0.

Solve the system of equations: \(\frac{1}{2}x + \frac{1}{3}y = 4\) \(x - y = 3\)

• A\((4, 1)\)
• B\((6, 3)\)
• C\((8, 5)\)
• D\((3, 0)\)

Water Tank A contains 500 gallons of water and drains at a constant rate of 15 gallons per minute. Water Tank B contains 200 gallons of water and is filled at a constant rate of 10 gallons per minute. After how many minutes will both tanks contain the exact same volume of water?

• A8 minutes
• B10 minutes
• C12 minutes
• D15 minutes

Point \(P\) has coordinates \((3, -4)\). What are the coordinates of \(P'\) after a translation of 5 units left and 2 units up?

• A\((8, -2)\)
• B\((-2, -2)\)
• C\((-2, -6)\)
• D\((8, -6)\)

Point \(A\) is located at \((-4, 7)\). What are the coordinates of \(A'\) after reflecting across the \(x\)-axis?

• A\((4, 7)\)
• B\((-4, -7)\)
• C\((4, -7)\)
• D\((7, -4)\)

A right triangle has leg lengths of 6 cm and 8 cm. What is the length of its hypotenuse?

• A10 cm
• B14 cm
• C48 cm
• D100 cm

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

• A8 inches
• B12 inches
• C14 inches
• D18 inches

What is the volume of a cylinder with a radius of 3 cm and a height of 10 cm? (Use \(\pi \approx 3.14\))

• A94.2 cm³
• B188.4 cm³
• C282.6 cm³
• D847.8 cm³

A cone has a radius of 6 cm and a height of 9 cm. What is its volume in terms of \(\pi\)?

• A\(36\pi\) cm³
• B\(108\pi\) cm³
• C\(324\pi\) cm³
• D\(972\pi\) cm³