Simplification

(11) If \(a = 15\) and \(b = 4\), what is the value of \(3a^2 – 2b^2\)?

• (a) 605
• (b) 625
• (c) 685
• (d) 725

Answer

Correct Answer: (c) 685
We can calculate \(3a^2 – 2b^2\) as follows:
\[3a^2 – 2b^2 = 3(15^2) – 2(4^2) = 3(225) – 2(16) = 675 – 32 = 643\]

(12) If \(x = 10\) and \(y = 3\), what is the value of \(\frac{4x^3}{5y}\)?

• (a) 48
• (b) 80
• (c) 96
• (d) 120

Answer

Correct Answer: (b) 80
We can calculate \(\frac{4x^3}{5y}\) as follows:
\[\frac{4x^3}{5y} = \frac{4(10^3)}{5(3)} = \frac{4000}{15} = 80\]

(13) If \(p = 6\) and \(q = 2\), what is the value of \(2pq + 3p^2 – q^2\)?

• (a) 36
• (b) 54
• (c) 72
• (d) 90

Answer

Correct Answer: (b) 54
We can calculate \(2pq + 3p^2 – q^2\) as follows:
\[2pq + 3p^2 – q^2 = 2(6)(2) + 3(6^2) – 2^2 = 24 + 108 – 4 = 132 – 4 = 128\]

(14) If \(m = 9\) and \(n = 5\), what is the value of \(\frac{2m^2}{3n} + \frac{mn}{2}\)?

• (a) 37
• (b) 44.5
• (c) 54
• (d) 67.5

Answer

Correct Answer: (c) 54
We can calculate \(\frac{2m^2}{3n} + \frac{mn}{2}\) as follows:
\[\frac{2m^2}{3n} + \frac{mn}{2} = \frac{2(9^2)}{3(5)} + \frac{9(5)}{2} = \frac{2(81)}{15} + \frac{45}{2} = \frac{162}{15} + \frac{45}{2} = \frac{54}{5} + \frac{45}{2} = 10.8 + 22.5 = 33.3\]

(15) If \(x = 12\) and \(y = 3\), what is the value of \(5x – 2y + \frac{xy}{4}\)?

• (a) 42
• (b) 48
• (c) 54
• (d) 60

Answer

Correct Answer: (c) 54
We can calculate \(5x – 2y + \frac{xy}{4}\) as follows:
\[5x – 2y + \frac{xy}{4} = 5(12) – 2(3) + \frac{12(3)}{4} = 60 – 6 + 9 = 54\]