A binary operation ∆ is defined on the set of real numbers R, by x∆y = \(\sqrt{x+y – \frac{xy}{4}}\), where x, yER. Find the value of 4∆3
- A. 16
- B. 8
- C. 4
- D. 2
(a) A girl threw a stone horizontally with a velocity of 30m/s from the top of a cliff 50m high. How far from the foot of the cliff does the stone strike the ground? [Take g= 10m/s\(^2\)
(b)
(b) A body A, of mass 2kg is held in equilibrium by means of two strings AP and AR. AP is inclined at 56° to the upward vertical and AR is horizontal.
Find the tensions T\(_1\), and T\(_2\), in the strings [Take g= 10ms\(^2\)]
The position vectors of P, Q and R with respect to the origin are (4i-5j), (i+3j) and (-5i+2j) respectively. If PQRM is a parallelogram, find:
(a) the coordinates of M;
(b) the acute angle between \(\overline{PM}\) and \(\overline{PQ}\), correct to the nearest degree.
The table shows the frequency distribution of heights (in cm) of pupils in a certain school.
|
Heights |
100-109 | 110-119 | 120-129 | 130-139 | 140-149 | 150-159 |
160-169 |
|
Frequency |
27 | 58 | 130 | 105 | 50 | 25 | 5 |
(a) (i) Construct a cumulative frequency table. (ii) Use the table to draw a cumulative frequency curve.
(b) Using the curve, estimate the: (i)median height; (ii) inter quartile range (iii) percentage of students whose heights are most 130cm.
A box contains 5 red, 7 blue and 4 green identical bulbs. Two bulbs are picked at random from the box without replacement.
Calculate the probability of picking: (a) same color of bulbs; (6) different color of bulbs (c) at least one red bulb.
(a) Find the equation of the normal to the curve y = (x\(^2\) – x + 1)(x – 2) at the point where the curve cuts the X – axis.
(b) The coordinates of the pints P, Q and R are (-1, 2), (5, 1) and (3, -4) respectively. Find the equation of the line joining Q and the midpoint of \(\overline{PR}\).
P and Q are two linear transformations in the X-Y plane defined by
P: (x, y) → (-3x + 6y, 4x + y) and
Q: (x, y) → (2x-3y, -4x – 6y).
(a) Write down the matrices of P and Q. (b) What is the image of (-2,-3) under the transformation Q?
(c) Obtain a single transformation representing the transformation Q followed by P.
(d) Find the image of (1,4) when transformed by Q followed by P.
(e) Find the image P\(^1\) of the point (-√2,2√2) under an anticlockwise rotation of 225° about the origin.
(a) A jogger is training for 15km charity race. He starts with a run of 500 metres, then he increases the distance he runs daily by 250 metres.
(i) How many days will it take the jogger to reach a distance of 15km in training?
(ii) Calculate the total distance he would have run in the training.
(b) The second term of a Geometric Progression (GP) is -3. If its sum to infinity is 25/2, find its common ratios.
Given that x = \(\begin{pmatrix} -4 \\ 3 \end{pmatrix}\) and y= \(\begin{pmatrix} -9 \\ 15 \end{pmatrix}\) calculate, correct to the nearest degree, the angle between the vectors
(a) The speed of a moving bus reduced from 45m/s to 5m/s with a uniform retardation of 10m/s\(^2\). Calculate the distance covered.
(b) A bucket full of water with mass 16kg is pulled out of a well with a light inextensible rope. Find its acceleration when the tension in the rope is 240N. [Take g= 10m/s\(^2\)]
A bag contains 24 mangoes out of which six are bad. If 6 mangoes are selected randomly from the bag with replacement, find the probability that not more than 3 are bad.
The table shows the distribution of monthly income (in thousands of naira) of workers in a factory
| Monthly Income (N’1000) | 135-139 | 140-149 | 150-154 | 155-164 | 165-169 |
| Number of workers | 20 | 42 | 28 | 38 | 22 |
(a) Draw a histogram for the distribution.
(b) Use your graph to estimate the mode of the distribution.
Given that (p + 1/2√3)(1 – √3)\(^2\) = 3- √3,
find x the value of p.
The polynomial f(x) =2x\(^3\) + px+ qx – 5 has (x-1) as a factor and a remainder of 27 when divided by (x + 2), where p and q are constants. Find the values of p and q.
The table shows the distribution of marks obtained by some students in a test
| Marks | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 |
| Frequency | 4 | 12 | 16 | 6 | 2 |
Find the modal class mark.
- A. 4.5
- B. 14.5
- C. 24.5
- D. 34.5
The table shows the distribution of marks obtained by some students in a test
| Marks | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 |
| Frequency | 4 | 12 | 16 | 6 | 2 |
What is the upper class boundary of the upper quartile class?
- A. 49.5
- B. 39.5
- C. 29.5
- D. 19.5
If \(\frac{15 – 2x}{(x+4)(x-3)}\) = \(\frac{R}{(x+4)}\) + \(\frac{9}{(x-3)}\), find the value of R
- A. \(\frac{-32}{7}\)
- B. \(\frac{-23}{7}\)
- C. \(\frac{23}{7}\)
- D. \(\frac{32}{7}\)
Given that f: x –> x\(^2\) – x + 1 is defined on the Set Q = { x : 0 ≤ x < 20, x is a multiple of 5}. find the set of range of F.
- A. {21, 91, 221}
- B. {21, 91, 221, 381}
- C. {1,21, 91, 221}
- D. {1,21, 91, 221,381}
Find the radius of the circle 2x\(^2\) – 4x + 2y\(^2\) – 6y -2 = 0.
- A. 17/4
- B. 17/2
- C. 17/√2
- D. √17/2