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

The expressions x - 2 and x + 3 represent the length and width of a rectangle, respectively. If the area of the rectangle is 24, what is the perimeter of the rectangle?
  • A. 20
  • B. 22
  • C. 24
  • D. 28
Correct Answer & Rationale
Correct Answer: B

To find the perimeter of the rectangle, first calculate its dimensions using the area formula. The area is given by multiplying length and width: \[ (x - 2)(x + 3) = 24 \] Expanding this, we get: \[ x^2 + x - 6 = 24 \implies x^2 + x - 30 = 0 \] Factoring yields: \[ (x - 5)(x + 6) = 0 \implies x = 5 \text{ (valid)} \text{ or } x = -6 \text{ (not valid)} \] Using \(x = 5\), the dimensions are \(3\) (length) and \(8\) (width). The perimeter is: \[ 2(3 + 8) = 22 \] Options A (20), C (24), and D (28) do not match the calculated perimeter of 22, confirming they are incorrect.
The price P, in dollars, that a store sets for an item is given by the equation P = C + 1/10 * C where C dollars is the store's cost for the item. If the store sets a price of $55.00 for an item, what is the store's cost for the item?
  • A. $50.00
  • B. $54.90
  • C. $55.10
  • D. $60.50
Correct Answer & Rationale
Correct Answer: A

To find the store's cost \( C \), we start with the equation \( P = C + \frac{1}{10}C \). This can be simplified to \( P = 1.1C \). Given that \( P = 55 \), we can set up the equation \( 55 = 1.1C \). Solving for \( C \) gives \( C = \frac{55}{1.1} = 50 \). Option A ($50.00) is correct, as it satisfies the equation. Option B ($54.90) incorrectly suggests a cost that would lead to a higher price than $55 when applying the markup. Option C ($55.10) implies a cost greater than the set price, which is illogical. Option D ($60.50) is also incorrect as it would result in a price far exceeding $55, making it unfeasible.
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%.
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.