tsia2 math practice test

A placement test used in Texas to assess a student's readiness for college-level coursework in math, reading, and writing.

If the values of x and y are negative, which of the following values must be positive?
  • A. x²-y²
  • B. x/y
  • C. x+y
  • D. x-y
Correct Answer & Rationale
Correct Answer: B

When both x and y are negative, the quotient \( x/y \) results in a positive value. This is because dividing a negative number by another negative number yields a positive outcome. Option A, \( x^2 - y^2 \), can be either positive or negative depending on the magnitudes of x and y; thus, it is not guaranteed to be positive. Option C, \( x + y \), is the sum of two negative numbers, which will always be negative. Option D, \( x - y \), involves subtracting a negative (y) from another negative (x), which can also yield a negative or zero result, depending on their values. Only \( x/y \) is assuredly positive.

Other Related Questions

For what values of x does 5x ^ 2 + 4x - 4 = 0 ?
  • A. x = 1/5 and x = - 1
  • B. x = - 4/5 and x = 1
  • C. x = (- 2±6 * √(2))/5
  • D. x = (- 2±2 * √(6))/5
Correct Answer & Rationale
Correct Answer: D

To solve the quadratic equation \(5x^2 + 4x - 4 = 0\), one can apply the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 5\), \(b = 4\), and \(c = -4\). Calculating the discriminant gives \(b^2 - 4ac = 16 + 80 = 96\), leading to \(x = \frac{-4 \pm \sqrt{96}}{10} = \frac{-4 \pm 4\sqrt{6}}{10} = \frac{-2 \pm 2\sqrt{6}}{5}\), which matches option D. Option A provides incorrect roots not derived from the quadratic formula. Option B also presents incorrect values, failing to satisfy the equation. Option C miscalculates the discriminant, leading to an incorrect expression. Thus, D accurately reflects the solution to the equation.
Which equation is a correct way to calculate x?
  • A. sin x=5,000 /7,000
  • B. sin x= 7,000 /5,000
  • C. tan x= 5,000/7,000
  • D. tan x=7,000/5,000
Correct Answer & Rationale
Correct Answer: C

To solve for \( x \), the correct relationship involves the tangent function, as \( \tan \) is defined as the ratio of the opposite side to the adjacent side in a right triangle. Option C, \( \tan x = \frac{5,000}{7,000} \), accurately represents this ratio. Option A misapplies the sine function, which should represent the ratio of the opposite side to the hypotenuse, not the adjacent side. Similarly, option B incorrectly uses sine but with the sides reversed, leading to an inaccurate representation. Option D misuses tangent, suggesting the opposite and adjacent sides are swapped, which does not align with the definition of tangent. Thus, only option C correctly applies the tangent function to find \( x \).
If the function g is defined by g (x) = x/(x+1)', which of the following is true?
  • A. g (10) <g (20)
  • B. g (20) <g (10)
  • C. g(0) =1
  • D. g(1)=0
Correct Answer & Rationale
Correct Answer: A

To analyze the function \( g(x) = \frac{x}{x+1} \), we first observe its behavior as \( x \) increases. The function \( g(x) \) is a rational function that approaches 1 as \( x \) approaches infinity. For option A, evaluating \( g(10) \) and \( g(20) \): - \( g(10) = \frac{10}{11} \approx 0.909 \) - \( g(20) = \frac{20}{21} \approx 0.952 \) Since \( 0.909 < 0.952 \), option A is true. For option B, it incorrectly suggests \( g(20) < g(10) \), which contradicts the findings. Option C states \( g(0) = 1 \), but \( g(0) = 0 \), making this option false. Option D claims \( g(1) = 0 \), while \( g(1) = \frac{1}{2} \), which is also incorrect. Thus, only option A holds true.
How many cups of peanut butter must be used in order to make exactly enough peanut butter balls for the children at the party?
  • A. 10
  • B. 12
  • C. 18
  • D. 24
Correct Answer & Rationale
Correct Answer: C

To determine the number of cups of peanut butter needed for the peanut butter balls, one must consider the recipe's requirements and the number of children attending the party. Option C (18 cups) aligns with the recipe's proportion to yield the exact quantity necessary for all children. Option A (10 cups) is insufficient, likely resulting in fewer peanut butter balls than required. Option B (12 cups) may also fall short, leading to a shortage. Option D (24 cups) exceeds the needed amount, creating waste. Thus, C is the optimal choice, ensuring each child receives a peanut butter ball without excess or deficit.