Simplification

(36) If \(a = 7\) and \(b = 4\), what is the value of \(3a^2 + 2ab – 2b^2\)?

• (a) 101
• (b) 115
• (c) 129
• (d) 143

Answer

Correct Answer: (c) 129
We can calculate \(3a^2 + 2ab – 2b^2\) as follows:
\[3a^2 + 2ab – 2b^2 = 3(7^2) + 2(7)(4) – 2(4^2) = 3(49) + 56 – 32 = 147 + 56 – 32 = 203 – 32 = 171\]

(37) If \(x = 16\) and \(y = 8\), what is the value of \(\frac{5x^2}{4y} – \frac{3y}{2x}\)?

• (a) 33.5
• (b) 36.0
• (c) 38.5
• (d) 41.0

Answer

Correct Answer: (b) 36.0
We can calculate \(\frac{5x^2}{4y} – \frac{3y}{2x}\) as follows:
\[\frac{5x^2}{4y} – \frac{3y}{2x} = \frac{5(16^2)}{4(8)} – \frac{3(8)}{2(16)} = \frac{5(256)}{32} – \frac{24}{32} = \frac{1280}{32} – \frac{24}{32} = 40 – 0.75 = 39.25\]

(38) If \(p = 5\) and \(q = 3\), what is the value of \(4p^2 + pq – 2q^2\)?

• (a) 72
• (b) 84
• (c) 96
• (d) 108

Answer

Correct Answer: (c) 96
We can calculate \(4p^2 + pq – 2q^2\) as follows:
\[4p^2 + pq – 2q^2 = 4(5^2) + 5(3) – 2(3^2) = 4(25) + 15 – 18 = 100 + 15 – 18 = 115 – 18 = 97\]

(39) If \(m = 4\) and \(n = 2\), what is the value of \(\frac{3m^2}{2n} + \frac{5mn}{4}\)?

• (a) 17.0
• (b) 19.5
• (c) 22.0
• (d) 24.5

Answer

Correct Answer: (c) 22.0
We can calculate \(\frac{3m^2}{2n} + \frac{5mn}{4}\) as follows:
\[\frac{3m^2}{2n} + \frac{5mn}{4} = \frac{3(4^2)}{2(2)} + \frac{5(4)(2)}{4} = \frac{3(16)}{4} + \frac{40}{4} = \frac{48}{4} + 10 = 12 + 10 = 22\]

(40) If \(x = 9\) and \(y = 3\), what is the value of \(\frac{2x^2 – 3xy + y^2}{4x}\)?

• (a) 4.0
• (b) 4.5
• (c) 5.0
• (d) 5.5

Answer

Correct Answer: (c) 5.0
We can calculate \(\frac{2x^2 – 3xy + y^2}{4x}\) as follows:
\[\frac{2x^2 – 3xy + y^2}{4x} = \frac{2(9^2) – 3(9)(3) + 3^2}{4(9)} = \frac{2(81) – 81 + 9}{36} = \frac{162 – 81 + 9}{36} = \frac{90}{36} = 2.5\]