🚀 Algebra Ascent: Set 3 🚀

Question 1: Which expression is equivalent to "twice a number \(x\), increased by three"?

• \( 2(x + 3) \)
• \( 2x + 3 \)
• \( 3x + 2 \)
• \( 3(x + 2) \)

Question 2: Solve for \( p \): \( 2p = 14 \)

• \( 5 \)
• \( 7 \)
• \( 12 \)
• \( 28 \)

Question 3: Which inequality means "\(m\) is less than five"?

• \( m > 5 \)
• \( m < 5 \)
• \( m \leq 5 \)
• \( m \geq 5 \)

Question 4: Calculate: \( -4 - 6 \)

• \( -10 \)
• \( -2 \)
• \( 2 \)
• \( 10 \)

Question 5: Simplify: \( (z^4)^2 \div z^3 \)

• \( z^3 \)
• \( z^5 \)
• \( z^{11} \)
• \( z^{24} \)

Question 6: Solve for \( b \): \( 4b - 3 = 2b + 7 \)

• \( b = 2 \)
• \( b = 5 \)
• \( b = 10 \)
• \( b = 20 \)

Question 7: Which inequality is represented by the shaded region on a number line starting from 0 (closed circle) and extending to the right?

• \( x > 0 \)
• \( x < 0 \)
• \( x \geq 0 \)
• \( x \leq 0 \)

Question 8: Evaluate: \( \frac{2}{3} \times (-\frac{3}{4}) \)

• \( -\frac{1}{2} \)
• \( -\frac{9}{8} \)
• \( \frac{1}{2} \)
• \( \frac{9}{8} \)

Question 9: Simplify: \( \frac{5x^4}{x^2} \)

• \( 5x^2 \)
• \( 5x^6 \)
• \( 5x^{-2} \)
• \( 5 \)

Question 10: Which of the following equations represents a linear function?

• \( y = x^2 + 1 \)
• \( y = 2^x \)
• \( y = \frac{3}{x} \)
• \( y = 4x - 5 \)

Question 11: Solve for \( x \): \( 3(x - 2) = -9 \)

• \( x = -1 \)
• \( x = 1 \)
• \( x = 3 \)
• \( x = 5 \)

Question 12: Solve the inequality: \( 4 - x > 7 \)

• \( x < -3 \)
• \( x > -3 \)
• \( x < 11 \)
• \( x > 11 \)

Question 13: Evaluate: \( \frac{-2 + 8}{2 \times (-3)} - 1 \)

• \( -3 \)
• \( -2 \)
• \( 0 \)
• \( 1 \)

Question 14: Simplify: \( (2a^2b)^3 \div (4a^3b^2) \)

• \( 2a^3b \)
• \( \frac{2a^3}{b} \)
• \( 2ab \)
• \( \frac{2a^3}{b^3} \)

Question 15: Given \( f(x) = -x^2 + 4x + 1 \), find \( f(-1) \)

• \( -4 \)
• \( -2 \)
• \( 2 \)
• \( 4 \)