If y = 243(4x + 5)-2, find \(\frac{dy}{dx}\) when x = 1
- A. \(\frac{-8}{3}\)
- B. \(\frac{3}{8}\)
- C. \(\frac{9}{8}\)
- D. -\(\frac{8}{9}\)
From the top of a vertical mast 150m high., two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60o and 45o respectively. Find the distance between the huts
- A. 150(1 + \(\sqrt{3}\))m
- B. 50(3 + \(\sqrt{3}\))m
- C. 150 \(\sqrt{3}\)m
- D. \(\frac{50}{\sqrt{3}}\)m
solve the equation cos x + sin x = \(\frac{1}{cos x – sinx}\) for values of such that 0 \(\leq\) x < 2\(\pi\)
- A. \(\frac{\pi}{2}\), \(\frac{3\pi}{2}\)
- B. \(\frac{\pi}{3}\), \(\frac{2\pi}{3}\)
- C. 0, \(\frac{\pi}{3}\)
- D. 0, \(\pi\)
The midpoint of the segment of the line y = 4x + 3 which lies between the x-ax 1 is and the y-ax 1 is
- A. (\(\frac{3}{2}\), \(\frac{3}{2}\))
- B. (\(\frac{2}{3}\), \(\frac{3}{2}\))
- C. (\(\frac{3}{8}\), \(\frac{3}{2}\))
- D. (-\(\frac{3}{8}\), \(\frac{3}{2}\))
If the distance between the points (x, 3) and (-x, 2) is 5. Find x
- A. 6.0
- B. 2.5
- C. \(\sqrt{6}\)
- D. \(\sqrt{3}\)
The locus of all points at a distance 8cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.
- A. 4\(\sqrt{3cm^2}\)
- B. 16\(\sqrt{3cm^2}\)
- C. 32cm2
- D. 64cm2
a cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimeters
- A. 12.5
- B. 25.0
- C. 45.0
- D. 50.00
Let = \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) p = \(\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix}\) Q = \(\begin{pmatrix} u & 4+u \\ -2v & v \end{pmatrix}\) be 2 x 2 matrices such that PQ = 1. Find (u, v)
- A. (-\(\frac{5}{2}\) - 1)
- B. (-\(\frac{5}{2}\) - \(\frac{3}{2}\))
- C. (-\(\frac{5}{6}\) - 1)
- D. (\(\frac{5}{2}\) - \(\frac{3}{2}\))
The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{pmatrix}\) in terms of x is
- A. -3x2 - 17
- B. -3x2 + 9x - 1
- C. 3x2 + 17
- D. 3x2 - 9x + 5
The binary operation \(\ast\) is defined by x \(\ast\) y = xy – y – x for all real values x and y. If x \(\ast\) 3 = 2\(\ast\) x, find x
- A. -1
- B. 4
- C. 1
- D. 5
The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p
\\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\)
- A. p
- B. q
- C. r
- D. s
The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.
- A. \(\frac{1}{4}\)
- B. \(\sqrt{\frac{3}{2}}\)
- C. \(\frac{1}{\sqrt{3}}\)
- D. \(\frac{1}{\sqrt{2}}\)
If p + 1, 2P – 10, 1 – 4p2are three consecutive terms of an arithmetic progression, find the possible values of p
- A. -4, 2
- B. -3, \(\frac{4}{11}\)
- C. -\(\frac{4}{11}\), 2
- D. 5, -3
If x is a positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\) > \(\frac{1}{4x}\)
- A. x > -\(\frac{1}{6}\)
- B. x > 0
- C. 0 < x < 4
- D. 0 < x < \(\frac{1}{6}\)
Express in partial fractions \(\frac{11x + 2}{6x^2 – x – 1}\)
- A. \(\frac{1}{3x - 1}\) + \(\frac{3}{2x + 1}\)
- B. \(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
- C. \(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
- D. \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
Divide 2x\(^{3}\) + 11x\(^2\) + 17x + 6 by 2x + 1.
- A. x2 + 5x + 6
- B. 2x2 + 5x - 6
- C. 2x2 + 5x + 6
- D. x2 - 5x + 6
Make \(\frac{a}{x}\) the subject of formula \(\frac{x + a}{x – a}\) = m
- A. \(\frac{m - 1}{m + 1}\)
- B. \(\frac{m + 1}{1 - m}\)
- C. \(\frac{m - 1}{1 + m}\)
- D. \(\frac{m + 1}{m - 1}\)
Solve for the equation \(\sqrt{x}\) – \(\sqrt{(x – 2)}\) – 1 = 0
- A. \(\frac{3}{2}\)
- B. \(\frac{2}{3}\)
- C. \(\frac{4}{9}\)
- D. \(\frac{9}{4}\)
Factorize r2 – r(2p + q) + 2pq
- A. (r - 2q)(2r - p)
- B. (r - p)(r + p0
- C. (r - q)(r - 2p)
- D. (2r - q)(r + p)
When the expression pm\(^2\) + qm + 1 is divided by (m – 1), it has a remainder is 2, and when divided by (m + 1), the remainder is 4. Find p and q respectively
- A. 2, -1
- B. -1, 2
- C. 3, -2
- D. -2, 3
A man is paid r naira per hour for normal work and double rate for overtime. if he does a 35-hour week which includes q hours of overtime, what is his weekly earning in naira?
- A. r(35 + q)
- B. q(35r - q)
- C. q(35 + r)
- D. r(35 + 2q)