South Carolina EOCEP Algebra 1

Simplify the expression (3x^4)(5x^3).

• A15x^12
• B15x^7
• C8x^7
• D15x^1

Simplify the expression (24y^8) / (6y^2) for y ≠ 0.

• A4y^6
• B4y^4
• C18y^6
• D4y^10

Which expression is equivalent to (2a^3 * b^-2)^4?

• A8a^7 / b^6
• B16a^12 / b^8
• C16a^7 / b^2
• D8a^12 / b^8

Simplify ((x^-3 * y^5) / (x^2 * y^-1))^-2.

• Ax^10 / y^12
• Bx^2 / y^8
• Cy^12 / x^10
• Dx^10 * y^12

Rewrite x^(5/3) in radical form.

• A∛(x^5)
• B∜(x^3)
• C5 * ∛(x)
• D3 * ∜(x)

Evaluate the expression 27^(2/3) + 16^(3/4).

• A17
• B25
• C14
• D35

Simplify the radical expression √(72).

• A6√2
• B12√2
• C36√2
• D2√6

Simplify 3√(20) - 2√(45) + √(80).

• A4√5
• B5√5
• C0
• D6√5

What is the product (2√3)(√15) in simplest radical form?

• A6√5
• B2√45
• C10√3
• D30

Simplify the quotient √(54x^5) / √(6x) assuming x > 0.

• A3x^2
• B9x^4
• C3x^4
• D9x^2

What is the sum of (4x^2 - 3x + 7) and (2x^2 + 5x - 4)?

• A6x^2 + 2x + 3
• B6x^4 + 2x^2 + 3
• C6x^2 + 8x + 11
• D2x^2 - 8x + 11

Subtract (3x^2 - 5x + 2) from (7x^2 + 2x - 6).

• A4x^2 + 7x - 8
• B4x^2 - 3x - 4
• C10x^2 - 3x - 4
• D4x^2 - 7x - 8

Expand and simplify (3x - 4)(2x + 5).

• A6x^2 + 7x - 20
• B6x^2 - 7x - 20
• C6x^2 + 23x - 20
• D5x^2 + 7x + 1

What is the expanded form of (2x - 5)^2?

• A4x^2 - 20x + 25
• B4x^2 - 25
• C4x^2 + 25
• D4x^2 - 10x + 25

A moving company charges C(x) = 95 + 1.4x dollars for a job of x miles, and it accepts only jobs between 10 and 300 miles. Which statement correctly identifies a limitation of this model in the real-world situation?

• AThe model should only be used for 10 ≤ x ≤ 300, because the company does not price jobs o…
• BThe model applies to every value of x, because a linear function is defined for all real…
• CThe model applies only to whole-number values of x that are greater than 95
• DThe model cannot be used at all, because a cost function must pass through the origin

Factor out the greatest common factor (GCF) from 12x^3 - 18x^2 + 6x.

• A6x(2x^2 - 3x + 1)
• B6(2x^3 - 3x^2 + x)
• C3x(4x^2 - 6x + 2)
• D2x(6x^2 - 9x + 3)

Factor completely: x^2 - 9x + 20.

• A(x - 4)(x - 5)
• B(x - 2)(x - 10)
• C(x + 4)(x + 5)
• D(x - 1)(x - 20)

Factor completely: x^2 - 16y^2.

• A(x - 4y)(x + 4y)
• B(x - 4y)^2
• C(x - 8y)(x + 8y)
• D(x + 4y)^2

Factor completely: 3x^2 + 13x - 10.

• A(3x - 2)(x + 5)
• B(3x + 2)(x - 5)
• C(3x - 5)(x + 2)
• D(3x + 10)(x - 1)

Factor completely: 2x^3 - 8x.

• A2x(x - 2)(x + 2)
• B2x(x - 4)^2
• C2(x^2 - 4)
• Dx(2x - 4)(2x + 4)

A survey of 200 students recorded whether each student rides the bus and whether each plays a school sport. Of the 120 bus riders, 42 play a sport. Of the 80 students who do not ride the bus, 44 play a sport. Which statement about a possible association is best supported?

• AStudents who do not ride the bus appear more likely to play a sport, because 55% of them…
• BThere is no possible association, because both groups contain students who play a sport
• CBus riders appear more likely to play a sport, because 120 is greater than 80
• DExactly half of the surveyed students play a sport, so the two variables must be independ…

Which binomial is a factor of 6x^2 - 11x - 35?

• A2x - 7
• B3x - 5
• C2x + 7
• D6x - 5

Given f(x) = -3x^2 + 4x - 5, evaluate f(-2).

• A-25
• B-1
• C15
• D-9

If g(x) = 5 - 2x, for what value of x is g(x) = -11?

• A8
• B-8
• C3
• D-3

Simplify (5 + √3)(5 - √3).

• A22
• B28
• C25 - √3
• D22 + 10√3

A cell phone plan charges a flat fee of $35 per month plus $0.10 per gigabyte of data used over the limit. Which function models total monthly cost C(d) for using d gigabytes over the limit?

• AC(d) = 0.10d + 35
• BC(d) = 35d + 0.10
• CC(d) = 35.10d
• DC(d) = 0.10(d + 35)

Researchers collected plant-height data from day 5 through day 40 after planting and fit the model ŷ = 0.8x + 12, where x is days after planting and ŷ is height in centimeters. Using the model to predict the height on day 20 is an example of which process, and what height does it predict?

• AInterpolation; 28 cm
• BExtrapolation; 28 cm
• CInterpolation; 20.8 cm
• DExtrapolation; 32 cm

A scatterplot of weekly hours of television watched (x) and reading test score (y) shows points falling from the upper left to the lower right in a fairly tight band. How is the association between the two variables best described?

• AA strong negative linear association
• BA strong positive linear association
• CA weak negative linear association
• DNo association

A gym's monthly charge is modeled by ŷ = 22x + 35, where x is the number of classes attended. What do the slope and the y-intercept mean in this context?

• AEach additional class adds $22 to the monthly charge, and $35 is the charge when no class…
• BEach additional class adds $35 to the monthly charge, and $22 is the charge when no class…
• CThe first class costs $22 and every class after that costs $35
• DThe monthly charge works out to $57 for every class attended

What is the range of the quadratic function f(x) = (x - 3)^2 + 4?

• Ay ≥ 4
• By ≥ 3
• Cy ≤ 4
• DAll real numbers

The height of a ball in feet after t seconds is modeled by h(t) = -16t^2 + 48t + 64. If the ball hits the ground at t = 4 seconds, what is the practical domain for this function?

• A0 ≤ t ≤ 4
• Bt ≥ 0
• C0 ≤ h ≤ 100
• DAll real numbers

What is the range of the exponential function f(x) = -2(3)^x + 5?

• Ay < 5
• By > 5
• Cy ≤ 5
• Dy > -2

What is the slope of the line passing through (-2, 5) and (4, -7)?

• A-2
• B2
• C-1/2
• D-1

What are the x-intercept and y-intercept of the line 3x - 4y = 12?

• Ax-intercept (4, 0), y-intercept (0, -3)
• Bx-intercept (-3, 0), y-intercept (0, 4)
• Cx-intercept (3, 0), y-intercept (0, -4)
• Dx-intercept (4, 0), y-intercept (0, 3)

Which is the equation in slope-intercept form of the line passing through (3, -1) with slope m = 4?

• Ay = 4x - 13
• By = 4x - 1
• Cy = 4x + 11
• Dy = 4x - 7

Which equation represents a line perpendicular to y = -2/5 x + 3 and passing through (4, 1)?

• Ay = 5/2 x - 9
• By = -2/5 x + 13/5
• Cy = -5/2 x + 11
• Dy = 5/2 x + 1

Line L1 passes through (1, 4) and (3, 10). Line L2 is parallel to L1 and passes through (-2, 1). What is the equation of L2?

• Ay = 3x + 7
• By = 3x + 1
• Cy = -3x - 5
• Dy = 1/3 x + 5/3

A plumber charges a flat service fee plus an hourly rate. A 2-hour job costs $150, and a 5-hour job costs $315. What is the hourly rate?

• A$55 per hour
• B$63 per hour
• C$75 per hour
• D$40 per hour

What is the vertex of the quadratic function f(x) = (x + 4)^2 - 9?

• A(-4, -9)
• B(4, -9)
• C(-4, 9)
• D(4, 9)

What is the equation of the axis of symmetry for g(x) = 2x^2 - 8x + 5?

• Ax = 2
• Bx = -2
• Cx = 4
• Dy = -3

What are the x-intercepts of the function f(x) = x^2 - 2x - 15?

• A(5, 0) and (-3, 0)
• B(-5, 0) and (3, 0)
• C(15, 0) and (-1, 0)
• D(5, 0) and (3, 0)

A quadratic function is given by f(x) = -x^2 + 6x - 5. Does this function have a maximum or minimum value, and what is that value?

• AMaximum value of 4
• BMinimum value of 4
• CMaximum value of 9
• DMinimum value of -5

Write f(x) = x^2 - 10x + 16 in vertex form by completing the square.

• Af(x) = (x - 5)^2 - 9
• Bf(x) = (x - 5)^2 + 16
• Cf(x) = (x - 10)^2 - 84
• Df(x) = (x - 5)^2 - 25

The height h in meters of a projectile after t seconds is given by h(t) = -5t^2 + 30t + 2. What is the maximum height reached by the projectile?

• A47 meters
• B3 meters
• C45 meters
• D92 meters

How does the graph of g(x) = 3(x - 2)^2 + 1 compare to parent graph f(x) = x^2?

• AStretched vertically by factor 3, shifted right 2, up 1
• BCompressed vertically by factor 3, shifted left 2, up 1
• CStretched vertically by factor 3, shifted left 2, down 1
• DStretched vertically by factor 3, shifted right 2, down 1