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

(a ^ 9 * b ^ 12)/(a ^ 3 * b) =
  • A. a ^ 3 * b ^ 11
  • B. a ^ 6 * b ^ 12
  • C. a ^ 3 * b ^ 12
  • D. a ^ 6 * b ^ 11
Correct Answer & Rationale
Correct Answer: D

To simplify the expression \((a^9 * b^{12})/(a^3 * b)\), apply the laws of exponents. For the \(a\) terms, subtract the exponents: \(9 - 3 = 6\), giving \(a^6\). For the \(b\) terms, also subtract the exponents: \(12 - 1 = 11\), resulting in \(b^{11}\). Thus, the simplified expression is \(a^6 * b^{11}\). Option A is incorrect because it miscalculates the exponent of \(b\). Option B incorrectly maintains the exponent of \(b\) at 12. Option C fails to adjust the exponent of \(a\) correctly. Only option D accurately reflects the simplification.
Doreen bought a dress priced at $89 and a skirt priced at $36. She paid a total of $135 for the dress and the skirt, including sales tax. What was the sales tax rate?
  • A. 6%
  • B. 7%
  • C. 8%
  • D. 9%
Correct Answer & Rationale
Correct Answer: C

To determine the sales tax rate, first calculate the total cost of the dress and skirt without tax: $89 + $36 = $125. Doreen paid $135, which means the sales tax was $135 - $125 = $10. To find the sales tax rate, divide the tax amount by the pre-tax total: $10 / $125 = 0.08, or 8%. Option A (6%) is incorrect as it would result in a lower tax amount. Option B (7%) also yields a tax amount that is too low. Option D (9%) would produce a tax amount exceeding $10, making it incorrect. Thus, the only option that accurately reflects the calculated sales tax rate is 8%.
Which of the following is NOT a factor of x^4 +x^3?
  • A. X
  • B. X + 1
  • C. X^3
  • D. X^4
Correct Answer & Rationale
Correct Answer: D

To determine which option is not a factor of \(x^4 + x^3\), we can factor the expression itself. Factoring out the greatest common factor, we have \(x^3(x + 1)\). - **Option A: X** is a factor since \(x\) is part of \(x^3\). - **Option B: X + 1** is a factor as it is the remaining term after factoring \(x^3\). - **Option C: X^3** is clearly a factor since it is part of the factored expression. **Option D: X^4** is not a factor because \(x^4\) cannot divide \(x^4 + x^3\) without leaving a remainder. Thus, it does not fit into the factorization.
The average of 4 numbers is 9. If one of the numbers is 7, what is the sum of the other 3 numbers?
  • A. 2
  • B. 12
  • C. 29
  • D. 36
Correct Answer & Rationale
Correct Answer: C

To find the sum of the other three numbers, start by calculating the total sum of all four numbers. Since the average is 9, multiply this by 4, yielding a total of 36. Given that one of the numbers is 7, subtract this from the total: 36 - 7 = 29. Therefore, the sum of the other three numbers is 29. Option A (2) is too low, as it does not account for the total sum needed. Option B (12) underestimates the remaining numbers. Option D (36) mistakenly includes the known number, rather than calculating the sum of the others.