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.

Which of the following could be the function graphed above?
  • A. f(x)=x+1
  • B. f(x)=x-1
  • C. f(x)=|x|+1
  • D. f(x)=x-1
Correct Answer & Rationale
Correct Answer: C

Option C, \( f(x) = |x| + 1 \), accurately represents a V-shaped graph that opens upwards, with its vertex at (0, 1). This aligns with the characteristics of the graph shown. Option A, \( f(x) = x + 1 \), is a linear function with a slope of 1, resulting in a straight line, which does not match the V-shape. Option B, \( f(x) = x - 1 \), is another linear function with a slope of 1, also producing a straight line that does not fit the graph. Option D, \( f(x) = x - 1 \), is identical to Option B and shares the same linear characteristics, further confirming it cannot represent the V-shaped graph.

Other Related Questions

Which of the following is a factor of x ^ 3 * y ^ 3 + x * y ^ 5 ?
  • A. x ^ 3 - y ^ 3
  • B. x ^ 3 + y ^ 3
  • C. x ^ 2 + y ^ 2
  • D. x + y
Correct Answer & Rationale
Correct Answer: C

To determine the factors of the expression \(x^3y^3 + xy^5\), we can factor out the common term \(xy^3\), yielding \(xy^3(x^2 + y^2)\). Option A, \(x^3 - y^3\), represents a difference of cubes and does not apply here. Option B, \(x^3 + y^3\), is a sum of cubes, which is not a factor of the given expression. Option D, \(x + y\), does not appear in the factorization derived from the original expression. Thus, \(x^2 + y^2\) is the only viable factor, confirming its role in the factorization of the expression.
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.
If the combined amount of donations collected by Kevin, Fran, and Brooke exceeded the amount Lamar collected by $250, what was the total amount of donations collected by all five club members?
  • A. $500
  • B. $1,200
  • C. $2,500
  • D. $3,200
Correct Answer & Rationale
Correct Answer: C

To determine the total amount of donations collected by all five club members, we start with the information that the combined donations of Kevin, Fran, and Brooke exceeded Lamar's by $250. If we denote Lamar's donations as \( L \), then the amount collected by Kevin, Fran, and Brooke is \( L + 250 \). Thus, the total donations from all five members can be expressed as \( L + (L + 250) = 2L + 250 \). To find a plausible total, we consider the options. - A: $500 is too low, as it doesn't allow for both \( L \) and the excess amount. - B: $1,200 also falls short since it would imply \( L \) is negative. - D: $3,200 would require \( L \) to be too high, exceeding reasonable donation limits. C: $2,500 fits perfectly, allowing \( L \) to be $1,125, which is a feasible figure. Therefore, the total amount is logically $2,500.
The average of 5 numbers is 11. Which of the following must be true?
  • A. The range of the 5 numbers is 55.
  • B. The sum of the 5 numbers is 55.
  • C. The median of 5 numbers is 11.
  • D. The mode of 5 numbers is 11.
Correct Answer & Rationale
Correct Answer: B

To find the average of 5 numbers, you sum them and divide by 5. If the average is 11, the total sum must be 5 times 11, which equals 55. Thus, option B is true. Option A is incorrect; the range is the difference between the highest and lowest numbers, which can vary regardless of the average. Option C is also not necessarily true; the median, or middle value, can differ from the average depending on the distribution of the numbers. Option D is incorrect; the mode, or most frequently occurring number, does not have to be the same as the average.