TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers

Question 1

A rectangular garden has a length that is 5 feet longer than its width, w. The area of the garden is 104 square feet. Which of the following equations can be used to find the width of the garden?

Accepted Answer

w(w + 5) = 104

Answer

The area of a rectangle is calculated by multiplying its length by its width. In this scenario, the width is 'w' and the length is 'w + 5'. Therefore, the equation representing the area is w multiplied by (w + 5), which equals 104.

Question 2

If f(x) = 3x^2 - 4x + 1, what is the value of f(-2)?

Accepted Answer

21

Answer

To evaluate f(-2), substitute -2 for every x in the function: f(-2) = 3(-2)^2 - 4(-2) + 1. This simplifies to 3(4) + 8 + 1, which is 12 + 8 + 1 = 21.

Question 3

Which of the following is equivalent to the expression (2x - 3)(x + 4)?

Accepted Answer

2x^2 + 5x - 12

Answer

To expand the expression, use the FOIL method (First, Outer, Inner, Last). First: (2x)(x) = 2x^2. Outer: (2x)(4) = 8x. Inner: (-3)(x) = -3x. Last: (-3)(4) = -12. Combine the like terms (8x - 3x = 5x) to get the final expression: 2x^2 + 5x - 12.

Question 4

A cell phone plan costs $20 per month plus $0.15 for each text message sent. Which function can be used to find the total monthly cost, C(t), for sending 't' text messages?

Accepted Answer

C(t) = 20 + 0.15t

Answer

The total cost is the sum of the fixed monthly fee and the variable cost based on the number of text messages. The fixed fee is $20. The variable cost is $0.15 multiplied by the number of texts, 't'. Therefore, the function is C(t) = 20 + 0.15t.

Question 5

If 4(x - 2) + 5x = 3(x + 4), what is the value of x?

Accepted Answer

x = 10/3

Answer

First, distribute the numbers outside the parentheses: 4x - 8 + 5x = 3x + 12. Combine like terms on the left side: 9x - 8 = 3x + 12. Subtract 3x from both sides: 6x - 8 = 12. Add 8 to both sides: 6x = 20. Finally, divide by 6: x = 20/6, which simplifies to 10/3.

TSI Practice Test

TSI Practice Test

TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers