Praxis Mathematics Content Knowledge 5161

What is the value of 16^(3/4)?

• A6
• B8
• C12
• D64

Which number is greatest?

• Asqrt(5)
• B2.1
• C9/4
• D2.23

What is the solution set of |2x - 5| = 7?

• Ax = 1 only
• Bx = 6 only
• Cx = 6 or x = -1
• Dx = 12 or x = 2

What is (2 + i)(3 - 4i)?

• A2 - 5i
• B10 - 5i
• C6 - i
• D10 + 5i

A teacher asks students to solve the system 2x + y = 11 and x - y = 1. Which student method is valid and leads to the correct solution?

• AAdd the equations to get 3x = 12, then x = 4 and y = 3
• BSubtract the second equation from the first to get x = 10, then y = 1
• CMultiply the first equation by 2 and conclude x = 11
• DSet 2x + y equal to x - y and solve x = -12

For x != 0 and x != 3, which expression is equivalent to (x^2 - 9)/(x^2 - 3x)?

• A(x - 3)/x
• B(x + 3)/x
• Cx + 3
• Dx - 3

Which polynomial has x = 2 as a zero?

• Ax^2 - 3x + 1
• Bx^2 - 5x + 6
• Cx^2 + 2x + 4
• Dx^2 + 1

A student expands (x + 4)^2 as x^2 + 16. Which response best addresses the error?

• ARemind the student that squaring always doubles each term
• BUse an area model or distributive property to show (x + 4)(x + 4) = x^2 + 8x + 16
• CTell the student the answer is wrong because there should be three terms
• DReplace x with 1 and note the expressions are different, without explaining why

A car travels at 72 kilometers per hour. What is this speed in meters per second?

• A10
• B18
• C20
• D25

Which solution set satisfies 5 - 2x > 11?

• Ax > -3
• Bx < -3
• Cx > 3
• Dx < 3

What is the remainder when p(x) = x^3 - 4x + 1 is divided by x - 2?

• A-3
• B0
• C1
• D5

What is the solution set of (x - 3)/(x + 1) <= 0?

• Ax <= -1 or x >= 3
• B-1 < x <= 3
• Cx <= 3
• Dx > -1

While solving 1/(x - 2) = 1/x, a student writes x = x - 2 after multiplying by x(x - 2). What is the most important teacher follow-up?

• AEmphasize that x can be any real number because the denominators cancel
• BAsk the student to state the domain restrictions x != 0 and x != 2 before solving and the…
• CTell the student to cross-multiply more quickly to avoid mistakes
• DReplace the problem with one that has an integer solution

Which is the complete factorization of x^3 - 2x^2 - 5x + 6 over the integers?

• A(x - 1)(x - 2)(x + 3)
• B(x - 1)(x - 3)(x + 2)
• C(x + 1)(x - 2)(x - 3)
• D(x - 6)(x^2 + 1)

For which value of k does the system x + y = 5 and kx + y = 9 have no solution?

• A1
• B5
• C-1
• D0

If f(x) = 3x - 5, what is f^(-1)(7)?

• A2
• B4
• C7/3
• D12

A teacher shows the table x: 0, 1, 2, 3 and y: 5, 10, 20, 40. Which observation best helps students recognize the pattern as exponential rather than linear?

• AThe outputs increase by 5 each time
• BThe ratio of consecutive outputs is constant at 2
• CThe graph must pass through the origin
• DThe second differences are zero

Given f(x) = x^2 + 1 and g(x) = 2x - 3, what is (f o g)(2)?

• A1
• B2
• C5
• D8

Relative to y = x^2, what transformation produces y = -(x - 2)^2 + 1?

• AShift left 2 and down 1
• BShift right 2, reflect across the x-axis, and shift up 1
• CReflect across the y-axis and shift up 2
• DStretch vertically by 2 and shift up 1

A student says the vertical line test shows whether a function has an inverse. Which response is best?

• ACorrect, because any graph passing the vertical line test also passes the horizontal line…
• BNot correct; the vertical line test checks whether each input has only one output, while…
• CNot correct; neither test applies to graphs
• DCorrect, but only for linear functions

Solve log_3(x - 1) = 2.

• A7
• B8
• C9
• D10