MATH165 CO1 Math Exam Review

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Questions and Answers

What is the result of the expression $5 - 4[3 - 6(2 \cdot 3 - 12 \div 4)]$?

371
149
353 (correct)
241

Is the statement |a - b| = |b - a| true for any real numbers a and b?

Depends on a and b
False
Only true for integers
True (correct)

Are all integers considered rational numbers?

Yes (correct)
No
Only negative integers
Only positive integers

How can the expression $x^2 - y^2$ be factored?

(x - y)(x + y) (D) Signup and view all the answers

Is the binomial $a + 4b$ factorable?

No, it's already in simplest form (B) Signup and view all the answers

What is the complete solution of the inequality $x > 4$?

x > 4 (C) Signup and view all the answers

What type of relation is defined as a function?

A relation where each input has exactly one output (C) Signup and view all the answers

What is the value of $\sqrt{8x^3}$ simplified?

$2x^{3/2}$ (D) Signup and view all the answers

What is the critical value used in the inequality analysis?

-2 (A) Signup and view all the answers

Which of the following intervals contains positive values in the Table of Signs?

(−3/2, 0) (D) Signup and view all the answers

What does the set notation for the solution of the inequality include?

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What is the simplified form of the expression $\frac{1}{1 + \frac{1}{1 + 2 + x}}$?

$\frac{x + 3}{3 + x}$ (B) Signup and view all the answers

What is the domain of the function defined by the expression $\frac{1}{1 + \frac{1}{1 + 2 + x}}$?

$D = {x \in \mathbb{R}: x \neq -2, -3}$ (A) Signup and view all the answers

What is $f(1)$ for the function $f(x) = 3x^2 - x - 5$?

$-4$ (D) Signup and view all the answers

What is the result of $f(2)$ for $f(x) = 3x^2 - x - 5$?

$7$ (C) Signup and view all the answers

What is $g(-1)$ for the function $g(x) = 2 - 3x$?

$5$ (B) Signup and view all the answers

What is the correct expression for $f + g$ where $f(x) = 3x^2 - x - 5$ and $g(x) = 2 - 3x$?

$3x^2 - 4x - 3$ (C) Signup and view all the answers

What is the value of $(f imes g)(-1)$?

$-15$ (C) Signup and view all the answers

What is the value of $f(g(2))$?

$-5$ (D) Signup and view all the answers

What expression represents $(f - g)(1)$?

$-4$ (D) Signup and view all the answers

What is the fully factored form of the expression 10z³ - 15z² - 4z + 6?

(2z - 3)(5z² - 2) (C) Signup and view all the answers

Which expression represents the simplified form of 7(y² - 1) / (y(y + 1)(y + 8))?

−7(y − 1) / (y(y + 8)) (D) Signup and view all the answers

What is the domain for the expression resulting from the simplification of 7(y² - 1) / (y(y + 1)(y + 8))?

{y ∈ ℝ: y ≠ -1, 0, -8} (B) Signup and view all the answers

What is the result of this binomial expansion: (c³ + 4b²)³?

c⁹ + 12c⁶b² + 48c³b⁴ + 64b⁶ (D) Signup and view all the answers

Which factorization is correct for the expression 2a⁶ - 128?

2(a - 2)(a² + 2a + 4)(a + 2) (C) Signup and view all the answers

What is the final simplified result of the expression after factoring 10z³ - 15z² - 4z + 6?

(2z - 3)(5z² - 2) (B) Signup and view all the answers

In the expression 2z - 3, what is the meaning of the number 3?

The constant term (D) Signup and view all the answers

What is a common mistake made when factoring 10z³ - 15z² - 4z + 6?

Disregarding common factors (D) Signup and view all the answers

What is the critical value of the inequality $2x + 3 \geq 0$?

-3/2 (B) Signup and view all the answers

Which of the following is the correct interval notation for the solution of the inequality given?

[−2, −2) (B) Signup and view all the answers

In the Table of Signs, which sign corresponds to the interval $(−2, 0)$?

<ul> <li>(B)</li> </ul> Signup and view all the answers

What is the solution in set notation for the inequality $x + 2 \leq 0$?

{x ∈ ℝ: x ≤ -2} (B) Signup and view all the answers

What does the expression $3 > 2x + 3$ simplify to when solved for x?

x < -1 (A) Signup and view all the answers

What is the range of x values for which the expression $2x + 3$ results in negative output based on the Table of Signs?

(−∞, −2) (B) Signup and view all the answers

Which of the following statements correctly interprets the critical value $x = -2$ for the inequality $x + 2 \leq 0$?

It is a boundary point where the inequality changes from true to false. (A) Signup and view all the answers

What is the result of the inequality analysis for $2x + 3 \geq 0$?

x ≥ -3/2 (C) Signup and view all the answers

Flashcards

Expanding (𝑐³ + 4𝑏²)³

Using the binomial theorem to expand the expression (𝑐³ + 4𝑏²)³ results in 𝑐⁹ + 12𝑐⁶𝑏² + 48𝑐³𝑏⁴ + 64𝑏⁶.

Factoring 10𝑧³ − 15𝑧² − 4𝑧 + 6

Factoring this expression involves grouping terms to find a common factor. The result is (2z − 3)(5z² − 2).