Given that p = \(\begin{pmatrix} m + 1 & m – 1 \\ m + 4 & m – 8 \end{pmatrix}\) and |p| = – 34, find the value of m.
- A. 5
- B. 4
- C. 3
- D. 2
If p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), find a vector, r such that 2p – 3r = q
- A. \(\begin{pmatrix} -2ย \\ 3ย \end{pmatrix}\)
- B. \(\begin{pmatrix} -26ย \\ 11ย \end{pmatrix}\)
- C. \(\begin{pmatrix} 2ย \\ 3ย \end{pmatrix}\)
- D. \(\begin{pmatrix} 6ย \\ -9ย \end{pmatrix}\)
Solve 2\(^{2x}\) – 5(2\(^x\)) + 4 = 0
- A. x = 0 and 2
- B. x = 1 and 2
- C. x = 0 and 1
- D. x = 2 and 4
If f(x) = \(\frac{2 – x}{x}\), x โ 0, find the inverse of f.
- A. \(\frac{2}{x - 1}\), xย โ 1
- B. \(\frac{2}{x+1}\), xย โ -1
- C. \(\frac{2}{1-x}\), xย โ 1
- D. \(\frac{x}{2 + x}\), xย โ -2
Evaluate: \(\frac{cos^2 300ยบ – 4sin^2 120ยบ}{tan^2 135ยบ}\)
- A. -2\(\frac{3}{4}\)
- B. -3\(\frac{3}{4}\)
- C. -2\(\frac{1}{4}\)
- D. -3\(\frac{1}{4}\)
If log\(_2^x\) = 2, evaluate log\(_x^{128}\).
- A. 7
- B. 2
- C. \(\frac{7}{2}\)
- D. \(\frac{2}{7}\)
If 5x + 7 \(\equiv\) P(x + 3) + Q(x – 1), find the value of p
- A. 3
- B. 2
- C. 1
- D. 0
If h(x) = x\(^2\) + px + 2 is divided by (x + 3), the remainder is 5, find p
- A. 4
- B. 3
- C. 2
- D. 1
If the n\(^{th}\) term of a linear sequence (A.P) is (5n – 2), find the sum of the first 12 terms of the sequence.
- A. 120
- B. 183
- C. 366
- D. 732
A binary operation * is defined on the set of real numbers, R by x * y = \(\frac{y^2 – x^2}{2xy}\), x, y โ 0, where x and y are real numbers. Evaluate -3 * 2
- A. \(\frac{5}{12}\)
- B. \(\frac{13}{12}\)
- C. -\(\frac{5}{12}\)
- D. -\(\frac{13}{12}\)
\(\sqrt{x}\) – \(\frac{6}{\sqrt{x}}\) = 1, find the value of x
- A. 36
- B. 16
- C. 9
- D. 25
Given that f: x โ \(\sqrt{x}\) and g : x โ 25 – x\(^2\), find the value of f o g(3)
- A. 4
- B. 3
- C. 2
- D. 1
If \(\frac{5}{\sqrt{2}}\) – \(\frac{\sqrt{8}}{8}\) = m\(\sqrt{2}\), find the value of m
- A. \(\frac{12}{5}\)
- B. \(\frac{9}{4}\)
- C. \(\frac{7}{3}\)
- D. \(\frac{5}{2}\)
(a) A see-saw pivoted at the middle is kept in balance by weights of Richard, John and Philip such that only Richard whose mass is 60 kg sits on one side. If they sit at distances 2 m , 3 m , and 4 m respectively from the pivot and Philip is 15 kg, find the mass of John.
(bi) A body of mass 12 kg rests on a rough plane inclined at an angle of 30ยบ to the horizontal. The coefficient of friction between the body and the plane is \(\frac{2}{3}\). A force of magnitude P Newton acts on the body along the inclined plane. Find the value of P, if the body is at the point of moving:
down the plane;
[Take \(g = 10 ms ^{-2}\)]
(bii) A body of mass 12 kg rests on a rough plane inclined at an angle of 30ยบ to the horizontal. The coefficient of friction between the body and the plane is \(\frac{2}{3}\). A force of magnitude P Newton acts on the body along the inclined plane. Find the value of P, if the body is at the point of moving:
up the plane;
[Take \(g = 10 ms ^{-2}\)]
(a) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
acceleration of the particle;
(b) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
magnitude of the force F ;
(c) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
magnitude of the velocity of the particle after 8 seconds , correct to three decimal places.
(ai) A bag contains 16 identical balls of which 4 are green. A boy picks a ball at random from the bag and replaces it. If this is repeated 5 times, what is the probability that he:
did not pick a green ball;
(aii) A bag contains 16 identical balls of which 4 are green. A boy picks a ball at random from the bag and replaces it. If this is repeated 5 times, what is the probability that he:
picked a green ball at least three times?
(b) The deviations from a mean of values from a set of data are \(-2, ( m – 1), ( m ^2 + 1), -1, 2, (2 m – 1)\) and \(-2\). Find the possible values of \(m\) .
(a) The table shows the distribution of marks scored by some candidates in an examination.
| Marks | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 | 81 – 90 |
91 – 100 |
| Num of candidates | 5 | 39 | 14 | 40 | 57 | 25 | 11 | 8 | 1 |
Construct a cumulative frequency table for the distribution.
(b) The table shows the distribution of marks scored by some candidates in an examination.
| Marks | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 | 81 – 90 |
91 – 100 |
| Num of candidates | 5 | 39 | 14 | 40 | 57 | 25 | 11 | 8 | 1 |
Draw a cumulative frequency curve for the distribution.
(ci) Use the curve to estimate the:
number of candidates who scored marks between 24 and 58 ;
(cii) Use the curve to estimate the:
lowest mark for distinction, if 12% of the candidates passed with distinction.
(a) Express \(\frac{8x^2 + 8x + 9}{(x – 1)(2x + 3)^2}\) in partial fractions.
(b) The coordinates of the centre and circumference of a circle are (-2, 5) and 6ฯ units respectively. Find the equation of the circle.
(ai) A quadratic polynomial, g (x) has (2x + 1) as a factor. If g (x) is divided by (x – 1) and (x – 2), the remainder are -6 and -5 respectively. Find;
g (x);
(aii) A quadratic polynomial, g (x) has (2x + 1) as a factor. If g (x) is divided by (x – 1) and (x – 2), the remainder are -6 and -5 respectively. Find;
the zeros of g (x).
(b) Find the third term when (\(\frac{x}{2}-1\))\(^8\)is expanded in descending powers of \(x\).
(a) Find the derivative of \(4x-\frac{7}{x^2}\)with respect to \(x\), from first principle.
(b) Given that tan \(P =\frac{3}{x – 1}\) and tan \(Q\) =\frac{2}{x + 1}\), find tan \(( P – Q )\)
P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\) = 8i + 3j and \(\overline{MO}\) = 14i – 5j, find \(\overline{MP}\) .