Question 1: \[ \text{What is the factorization of } x^2 – 9? \] \[ \text{(a) } (x+3)(x-3), \quad \text{(b) } (x-9)(x+9), \quad \text{(c) } (x-3)^2, \quad \text{(d) } (x+9)(x-9) \] Answer: A Question 2: \[ \text{Which of the following is a factor of } x^2 – 5x + 6? \] \[ \text{(a) } (x-1), \quad … Read more

Question 1: \[ \text{If } P(x) = x^3 – 4x^2 + 3x + 5, \text{ what is } P(2)? \] \[ \text{(a) } 1, \quad \text{(b) } 3, \quad \text{(c) } 5, \quad \text{(d) } 7 \] Answer: C Question 2: \[ \text{Which of the following is a polynomial?} \] \[ \text{(a) } x^2 + … Read more

Question 1: \[ \text{If } \log_2 8 = x, \text{ what is the value of } x? \] \[ \text{(a) } 2, \quad \text{(b) } 3, \quad \text{(c) } 4, \quad \text{(d) } 5 \] Answer: B Question 2: \[ \text{If } \log_5 (25) = x, \text{ then } x \text{ is:} \] \[ \text{(a) … Read more

Question 1: \[ \text{Which of the following is the general form of an exponential function?} \] \[ \text{(a) } f(x) = ax^b, \quad \text{(b) } f(x) = a^x, \quad \text{(c) } f(x) = x^a, \quad \text{(d) } f(x) = a + bx \] Answer: B Question 2: \[ \text{What is the value of } f(x) … Read more

Question 1: \[ \text{If } 2^x = 32, \text{ then what is the value of } x? \] \[ \text{(a) } 4, \quad \text{(b) } 5, \quad \text{(c) } 6, \quad \text{(d) } 3 \] Answer: B Question 2: \[ \text{Simplify: } \frac{a^7}{a^4}. \] \[ \text{(a) } a^3, \quad \text{(b) } a^{11}, \quad \text{(c) } … Read more

Question 1: \[ \text{Solve the inequality: } |x – 3| < 5. \] \[ \text{(a) } -2 < x < 8, \quad \text{(b) } x < -2 \text{ or } x > 8, \quad \text{(c) } x \geq -2, \quad \text{(d) } x \leq 8 \] Answer: A Question 2: \[ \text{Solve: } |2x + … Read more

Question 1: \[ \text{Solve the inequality: } 3x – 5 > 7. \] \[ \text{(a) } x > 4, \quad \text{(b) } x > \frac{4}{3}, \quad \text{(c) } x > 3, \quad \text{(d) } x > \frac{5}{3} \] Answer: A Question 2: \[ \text{Which of the following is the solution set for } 2x + … Read more

\[ \textbf{Question 1:} \] \[ \text{What is the slope of the line } 2x – 3y = 6? \] \[ \text{(a) } \frac{2}{3}, \quad \text{(b) } -\frac{2}{3}, \quad \text{(c) } \frac{3}{2}, \quad \text{(d) } -\frac{3}{2} \] Answer: B Step by Step Solution \[ \textbf{Solution:} \] \[ \text{Rearrange the equation into slope-intercept form } y = … Read more

Question 1: \[ \text{What is the solution to the equation } 2x + 5 = 15 \text{?} \] \[ \text{(a) } x = 10, \quad \text{(b) } x = 5, \quad \text{(c) } x = -5, \quad \text{(d) } x = 2 \] Answer: B Question 2: \[ \text{Solve for } x: \quad 3x – … Read more

Question 1: \[ \text{Which of the following is an integral domain but not a field?} \] \[ \text{(a) } \mathbb{Z}, \quad \text{(b) } \mathbb{Q}, \quad \text{(c) } \mathbb{R}, \quad \text{(d) } \mathbb{C} \] Answer: A Question 2: \[ \text{Let } R \text{ be a commutative ring with unity. If } R \text{ has no zero … Read more

Question 1: \[ \text{If } a^2 + b^2 = 29 \text{ and } ab = 10, \text{ then find } (a+b)^2. \] \[ \text{(a) } 39, \quad \text{(b) } 49, \quad \text{(c) } 59, \quad \text{(d) } 69 \] Answer: B Step by Step Solution Solution: Using the identity: \[ (a+b)^2 = a^2 + b^2 … Read more

Question 1: \[ \text{If } a^2 – b^2 = 15 \text{ and } a – b = 3, \text{ then } a + b = ? \] \[ \text{(a) } 5, \quad \text{(b) } 8, \quad \text{(c) } 6, \quad \text{(d) } 9 \] Answer: C Step by Step Solution Solution: Using the identity: \[ … Read more