21. If given two points A(3, 12) and B(5, 22) on a x-y plane. Find the equation of the straight line with intercept at 2.
- A. y = 5x + 2
- B. y = 5x + 3
- C. y = 12x + 2
- D. y = 22x + 3
22. If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n.
- A. m = 0, n = 4
- B. m = 4, n = 0
- C. m = 2, n = 2
- D. m = -2, n = 4
23. If \(\begin{vmatrix} 2 ~~~ -4 \\ x ~~~ 9 \end{vmatrix} = 58\), find the value of x.
- A. 10
- B. 30
- C. 14
- D. 28
24. If \(y = 6x^3 + 2x^{-2} – x^{-3}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
- A.
\(\frac{\mathrm d y}{\mathrm d x} = 15x^2 – 4x^{-2} – 3x^{-2}\) - B.
\(\frac{\mathrm d y}{\mathrm d x} = 6x + 4x^{-1} – 3x^{-4}\) - C.
\(\frac{\mathrm d y}{\mathrm d x} = 18x^2 – 4x^{-3} + 3x^{-4}\) - D.
\(\frac{\mathrm d y}{\mathrm d x} = 12x^2 + 4x^{-1} – 3x^{-2}\)
25. \(\frac{d}{dx} [\log (4x^3 – 2x)]\) is equal to
- A.
\(\frac{12x – 2}{4x^2}\) - B.
\(\frac{43x^2 – 2x}{7x}\) - C.
\(\frac{4x^2 – 2}{7x + 6}\) - D.
\(\frac{12x^2 – 2}{4x^3 – 2x}\)
26. If \(f(x) = 3x^3 + 4x^2 + x – 8\), what is the value of f(-2)?
- A. -24
- B. 30
- C. -18
- D. -50
27.
Solve for x in \(\frac{4x – 6}{3} \leq \frac{3 + 2x}{2}\)
- A. \(x \leq 1\frac{1}{2}\)
- B. \(x \leq \frac{21}{2}\)
- C. \(x \geq \frac{21}{2}\)
- D. \(x \geq 1\frac{1}{2}\)
28. Solve the inequality: -7 \(\leq\) 9 – 8x < 16 – x
- A. -1 \(\leq\) x \(\leq\) 2
- B. -1 \(\leq\) x < 2
- C. -1 < x < 2
- D. -1 < x \(\leq\) 2
29. The nth term of a sequence is given by 2\(^{2n – 1}\). Find the sum of the first four terms.
- A. 74
- B. 32
- C. 42
- D.170
30. Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)
- A.\(4\frac{1}{2}\)
- B.\(3\frac{1}{2}\)
- C.\(7\frac{1}{2}\)
- D.\(5\frac{1}{4}\)
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