TCAP Algebra II End-of-Course Assessment

Which expression is the completely factored form of x^4 - 16 over the real numbers?

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

Simplify the polynomial sum: (3x^3 - 5x^2 + 2x - 7) + (2x^3 + 4x^2 - 6x + 3).

• A5x^3 - x^2 - 4x - 4
• B5x^3 + x^2 - 8x - 10
• C5x^3 - 9x^2 + 8x - 4
• D6x^3 - x^2 - 4x - 4

According to the Remainder Theorem, what is the remainder when P(x) = 2x^3 - 4x^2 + 3x - 5 is divided by x - 3?

• A12
• B17
• C22
• D31

Multiply the polynomials: (2x - 3)(x^2 + 4x - 5).

• A2x^3 + 5x^2 - 22x + 15
• B2x^3 + 11x^2 - 22x - 15
• C2x^3 + 5x^2 + 2x - 15
• D2x^3 + 8x^2 - 22x + 15

What is the end behavior of the graph of f(x) = -4x^5 + 3x^3 - 2x + 1?

• AAs x -> -infinity, f(x) -> -infinity and as x -> infinity, f(x) -> infinity
• BAs x -> -infinity, f(x) -> infinity and as x -> infinity, f(x) -> -infinity
• CAs x -> -infinity, f(x) -> infinity and as x -> infinity, f(x) -> infinity
• DAs x -> -infinity, f(x) -> -infinity and as x -> infinity, f(x) -> -infinity

What are the real zeros of the function f(x) = x^3 - 9x?

• Ax = 0, 9
• Bx = -3, 3
• Cx = -3, 0, 3
• Dx = 0, 3, 9

Simplify the rational expression: (x^2 - 9) / (x^2 + 5x + 6) for all valid values of x.

• A(x - 3) / (x + 2)
• B(x + 3) / (x + 2)
• C(x - 3) / (x - 2)
• D-9 / (5x + 6)

Simplify the radical expression sqrt(72x^5), assuming x >= 0.

• A6x * sqrt(2x)
• B6x^2 * sqrt(2x)
• C36x^2 * sqrt(2x)
• D12x^2 * sqrt(x)

Rewrite the expression (64x^6)^(2/3) in simplified exponential form.

• A8x^4
• B16x^3
• C16x^4
• D32x^4

Solve the radical equation: sqrt(2x + 5) = 5.

• Ax = 10
• Bx = 15
• Cx = 20
• Dx = 25

What is the domain of the rational function f(x) = (x + 4) / (x^2 - 16)?

• AAll real numbers except x = -4
• BAll real numbers except x = 4
• CAll real numbers except x = -4 and x = 4
• DAll real numbers

Multiply and simplify: [4x / (x + 3)] * [(x^2 - 9) / (2x^2)].

• A2(x - 3) / x
• B2(x + 3) / x
• C4(x - 3) / x^2
• D(2x - 6) / (x + 3)

Rationalize the denominator of 6 / sqrt(3).

• A3 * sqrt(3)
• B2 * sqrt(3)
• Csqrt(3)
• D6 * sqrt(3)

What is the logarithmic form of the exponential equation 3^4 = 81?

• Alog_4(81) = 3
• Blog_3(81) = 4
• Clog_81(3) = 4
• Dlog_3(4) = 81

Evaluate the expression log_2(32).

• A4
• B5
• C16
• D8

Expand the expression log_5(x^3 * y^2) using the properties of logarithms.

• A3 * log_5(x) + 2 * log_5(y)
• B6 * log_5(x * y)
• Clog_5(3x) + log_5(2y)
• D3 * log_5(x) * 2 * log_5(y)

Solve the exponential equation: 4^(x + 1) = 64.

• Ax = 1
• Bx = 2
• Cx = 3
• Dx = 15

An initial population of 500 bacteria triples every hour. Which function models the population P(t) after t hours?

• AP(t) = 500 + 3^t
• BP(t) = 500(3)^t
• CP(t) = 3(500)^t
• DP(t) = 1500^t

What is the exact value of ln(e^7)?

• A0
• B1
• C7
• De^7

Solve for x: log_3(2x - 1) = 2.

• Ax = 4
• Bx = 5
• Cx = 7
• Dx = 9

What is the exact value of sin(pi / 6)?

• A1/2
• Bsqrt(2)/2
• Csqrt(3)/2
• D1

Convert 120 degrees to radians in terms of pi.

• Api / 3
• B2pi / 3
• C3pi / 4
• D5pi / 6

What is the amplitude of the trigonometric function f(x) = -3 * cos(2x) + 4?

• A-3
• B2
• C3
• D4

What is the period of the function f(x) = sin(4x)?

• Api / 4
• Bpi / 2
• Cpi
• D2pi

If theta is an acute angle in Quadrant I and cos(theta) = 3/5, what is sin(theta)?

• A4/5
• B3/4
• C5/4
• D2/5

A dataset has a mean of mu = 75 and a standard deviation of sigma = 5. What is the z-score of a data value x = 85?

• A1
• B2
• C2.5
• D10

According to the Empirical Rule (68-95-99.7 rule) for a normal distribution, approximately what percentage of data falls within 1 standard deviation of the mean?

• A50%
• B68%
• C95%
• D99.7%

A researcher selects every 10th student entering a school building to complete a survey. What sampling method is being used?

• ASimple random sampling
• BSystematic sampling
• CStratified sampling
• DConvenience sampling

A political survey reports that 54% of voters support a candidate, with a margin of error of +- 3%. What is the resulting confidence interval for voter support?

• A51% to 57%
• B50% to 58%
• C52% to 56%
• D53% to 55%

Which study design assigns subjects randomly to a treatment group or a control group to measure the effect of a new medication?

• AObservational study
• BSample survey
• CRandomized experiment
• DCase study

Divide 2x^3 - 3x^2 - 11x + 6 by x - 3. What is the quotient?

• A2x^2 + 3x - 2
• B2x^2 - 9x + 16
• C2x^2 + 3x + 2
• D2x^2 - 3x - 2

Factor the polynomial 8x^3 - 27 completely.

• A(2x - 3)(4x^2 - 6x + 9)
• B(2x - 3)(4x^2 + 6x + 9)
• C(2x + 3)(4x^2 - 6x + 9)
• D(2x - 3)^3

What are the complex roots of the polynomial equation x^2 - 6x + 13 = 0?

• A3 +- 4i
• B3 +- 2i
• C-3 +- 2i
• D6 +- 2i

Factor x^3 + 3x^2 - 4x - 12 completely.

• A(x - 2)(x + 2)(x + 3)
• B(x - 4)(x + 1)(x + 3)
• C(x^2 + 4)(x + 3)
• D(x - 3)(x + 2)^2

A polynomial function P(x) of degree 3 has real coefficients and zeros at x = 4 and x = 2i. Which polynomial represents P(x)?

• Ax^3 - 4x^2 - 4x + 16
• Bx^3 - 4x^2 + 4x - 16
• Cx^3 + 4x^2 + 4x + 16
• Dx^3 - 2x^2 + 4x - 8

According to the Rational Root Theorem, which of the following is a possible rational zero of P(x) = 3x^3 + 5x^2 - 2x - 8?

• A3/2
• B4/3
• C5/3
• D3

The graph of f(x) = (x - 1)^2 * (x + 3)^3 * (x - 5) touches the x-axis without crossing it at which x-value?

• Ax = -3
• Bx = 1
• Cx = 5
• Dx = -1

The parent function f(x) = x^3 is shifted right by 2 units, vertically stretched by a factor of 3, and shifted up by 5 units. What is the equation of the transformed function g(x)?

• Ag(x) = 3(x + 2)^3 + 5
• Bg(x) = 3(x - 2)^3 + 5
• Cg(x) = (1/3)(x - 2)^3 + 5
• Dg(x) = 3(x - 5)^3 + 2

Solve the polynomial inequality: x^2 - 4x - 12 < 0.

• A(-infinity, -2) U (6, infinity)
• B(-2, 6)
• C[-6, 2]
• D(2, 6)

What is the third term in the expansion of (2x - 3)^4?

• A96x^3
• B-216x^2
• C216x^2
• D-96x

A cubic function f(x) = x^3 - 3x^2 - 9x + 5 has critical points where f'(x) = 0. At which x-value does f(x) attain its relative maximum?

• Ax = 3
• Bx = -1
• Cx = 1
• Dx = -3

How many total complex zeros (including real, non-real, and repeated zeros) does the polynomial P(x) = 5x^6 - 2x^4 + x^3 - 7 have?

• A4
• B5
• C6
• D7

Simplify: 3 / (x - 2) + 5 / (x + 4).

• A(8x + 2) / (x^2 + 2x - 8)
• B8 / (2x + 2)
• C(8x + 22) / (x^2 + 2x - 8)
• D(8x + 2) / (x^2 - 8)

Solve the rational equation: x / (x - 3) + 3 / (x + 3) = 18 / (x^2 - 9).

• Ax = 3 and x = -9
• Bx = -9 only
• Cx = 3 only
• DNo real solutions