NBT Algebra and Functions 2

Question 1

Simplify: (3a²b)(4ab³)

Accepted Answer

12a³b⁴

Answer

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)).

Accepted Answer

17

Answer

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?

Accepted Answer

k = 6 or k = -6

Answer

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

Accepted Answer

x > 4

Answer

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?

Accepted Answer

x = 2 and x = 3

Answer

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.

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