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.

Choose the best answer. If necessary, use the paper you were given.
Which of the following is equivalent to 12x +8?
  • A. 4(3x+2)
  • B. 4(3x+8)
  • C. 4(3x+2x)
  • D. 20x
Correct Answer & Rationale
Correct Answer: A

To determine the equivalent expression for \(12x + 8\), we can factor out the greatest common factor, which is 4. Option A, \(4(3x + 2)\), simplifies to \(12x + 8\) when distributed, making it equivalent to the original expression. Option B, \(4(3x + 8)\), simplifies to \(12x + 32\), which is not equivalent. Option C, \(4(3x + 2x)\), simplifies to \(4(5x)\) or \(20x\), which is also not equivalent. Option D, \(20x\), does not match the original expression either. Thus, only option A is correct.

Other Related Questions

In triangle ABC above, AC ||DE. If AD = 2x - 1 and AC = 3x - 1 , what is the value of x ?
Question image
  • A. 3
  • B. 4
  • C. 5
  • D. 6
Correct Answer & Rationale
Correct Answer: A

In triangle ABC, since AC is parallel to DE, the segments AD and AC are proportional. This relationship can be expressed as AD = AC. Substituting the expressions gives us the equation: 2x - 1 = 3x - 1. Solving for x, we simplify to 2x - 3x = -1 + 1, leading to -x = 0, or x = 3. Option B (4), C (5), and D (6) do not satisfy the equation derived from the parallel lines, making them incorrect. Only x = 3 maintains the equality, confirming the proportional relationship in the triangle.
The sum of n and the product 3 times n is 12. What is the value of n?
  • A. 2
  • B. 3
  • C. 4
  • D. 4 ½
Correct Answer & Rationale
Correct Answer: B

To solve the equation formed by the problem statement, we express it as \( n + 3n = 12 \), which simplifies to \( 4n = 12 \). Dividing both sides by 4 gives \( n = 3 \). Option A (2) does not satisfy the equation, as substituting it results in \( 2 + 6 = 8 \), which is incorrect. Option C (4) leads to \( 4 + 12 = 16 \), also incorrect. Option D (4 ½) results in \( 4.5 + 13.5 = 18 \), which is too high. Thus, only \( n = 3 \) fulfills the original equation, confirming its validity.
During a sale, the regular price of a pair of running shoes is reduced by 20 percent. $64.00, what is the regular price of the running shoes?
  • A. $48.00
  • B. $51.20
  • C. $76.80
  • D. $80.00
Correct Answer & Rationale
Correct Answer: D

To find the regular price of the running shoes, we need to determine what amount, when reduced by 20%, equals $64.00. This can be calculated using the formula: Sale Price = Regular Price × (1 - Discount Rate). Here, the discount rate is 20%, or 0.20. Therefore, the equation becomes $64.00 = Regular Price × 0.80. Solving for Regular Price gives us $64.00 / 0.80 = $80.00. Option A ($48.00) is incorrect because it suggests a much larger discount than 20%. Option B ($51.20) miscalculates the reduction, indicating a 36% discount. Option C ($76.80) inaccurately reflects a smaller discount, resulting in an incorrect sale price. Thus, only option D correctly represents the regular price before the 20% reduction.
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.