NBT Algebra and Functions 2 — Questions and Answers
Question 1: Simplify: (3a²b)(4ab³)
- 12a³b⁴ (Correct answer)
- 7a³b⁴
- 12a²b³
- 7a²b³
Correct answer: 12a³b⁴
Multiply the coefficients: 3 × 4 = 12. Add the exponents for like bases: a²⁺¹ = a³ and b¹⁺³ = b⁴. The result is 12a³b⁴.
Question 2: If f(x) = 3x - 1 and g(x) = x + 4, find f(g(2)).
- 17 (Correct answer)
- 15
- 9
- 11
Correct answer: 17
First find g(2) = 2 + 4 = 6. Then f(6) = 3(6) - 1 = 17. Composite functions are evaluated from the inside out.
Question 3: For which value of k does the equation x² + kx + 9 = 0 have equal roots?
- k = 3 or k = -3
- k = 6 or k = -6 (Correct answer)
- k = 9
- k = 18
Correct answer: k = 6 or k = -6
For equal roots, the discriminant must be zero: b² - 4ac = 0. So k² - 4(1)(9) = 0, giving k² = 36, therefore k = ±6.
Question 4: Solve the inequality: 2x - 5 > 3
- x > 4 (Correct answer)
- x > 1
- x < 4
- x > -1
Correct answer: x > 4
Add 5 to both sides: 2x > 8. Then divide by 2: x > 4. The inequality sign stays the same since we divided by a positive number.
Question 5: What are the roots of x² - 5x + 6 = 0?
- x = 1 and x = 6
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = -1 and x = -6
Correct answer: x = 2 and x = 3
Factorise: (x - 2)(x - 3) = 0. Setting each factor to zero gives x = 2 and x = 3. We can verify: 2 + 3 = 5 and 2 × 3 = 6.
Question 6: If f(x) = x² - 4x, what is the axis of symmetry of the parabola?
- x = 4
- x = -2
- x = 2 (Correct answer)
- x = -4
Correct answer: x = 2
The axis of symmetry for y = ax² + bx + c is x = -b/(2a). Here a = 1 and b = -4, so x = -(-4)/(2×1) = 4/2 = 2.
NBT Algebra and Functions 2
Simplify: (3a²b)(4ab³)