TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 1 — 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?
- w(w + 5) = 104 (Correct answer)
- w + (w + 5) = 104
- 2w + 2(w + 5) = 104
- w^2 + 5 = 104
Correct answer: w(w + 5) = 104
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)?
- 5
- -3
- 21 (Correct answer)
- 1
Correct answer: 21
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)?
- 2x^2 - 5x - 12
- 2x^2 + 5x - 12 (Correct answer)
- 2x^2 + 11x + 12
- 2x^2 - 12
Correct answer: 2x^2 + 5x - 12
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?
- C(t) = 20t + 0.15
- C(t) = 20 - 0.15t
- C(t) = 20.15t
- C(t) = 20 + 0.15t (Correct answer)
Correct answer: C(t) = 20 + 0.15t
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?
- x = 1/3
- x = 2
- x = 10/3 (Correct answer)
- x = 10
Correct answer: x = 10/3
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.
Question 6: The graph of a quadratic function opens downwards and has a vertex at (3, -2). Which of the following could be the equation of the function?
- y = (x - 3)^2 - 2
- y = (x + 3)^2 - 2
- y = -(x - 3)^2 - 2 (Correct answer)
- y = -(x + 3)^2 + 2
Correct answer: y = -(x - 3)^2 - 2
A quadratic function in vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex. Since the vertex is (3, -2), h=3 and k=-2. The parabola opens downwards, which means the leading coefficient 'a' must be negative. Therefore, the equation must be in the form y = -(x - 3)^2 - 2.
TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 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?