a) Given that m = tan 30º and n = tan 45º, simplify, without using calculator, \(\frac{ m - n}{mn}\), leaving the answer in the form p + \(\sqrt{q}\)
b) There are 20 women in a bus. 15 of them wear glasses and 10 wear wristwatches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and wristwatches.
The graph shows the relation of the form y = mx\(^2\) + nx + r, where m, n and r are constants.
Using the graph:
(a) state the scale used on both axes; (b) find the values of m, n and r; (c) find the gradient of the line through P and Q; (d) state the range of values of x for which y > Q.
(a) A man purchased 180 copies of a book at N250.00 each. He sold y copies at N300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price.
If he made a profit of N7,125.00, find the value of y.
(b) A trader bought x bags of rice at a cost C = 24x + 103 and sold them at a price, S = \(\frac{x^2}{20} - 33x\).
Find the expression for the profit (i) If 20 bags of rice were sold,
(ii) calculate the percentage profit.
| Item | food & drinks | fuel | rent | building project | education | savings |
| Percentage% | 35 | 7.5 | 1.0 | 15 | 17.5 | x |
The table shows the monthly expenditure (in percentages) of Mr. Okafor's salary.
(a) Calculate the percentage of Mr. Okafor's salary that was put into savings.
(b) Illustrate the information on a pie chart.
(c) If Mr. Okafor's annual gross salary is $28,800.00 and he pays tax of 12%.
Calculate; (i) his monthly tax; (ii) the amount saved each month.
(a) Copy and complete the table of values for y = 3Sinx + 7Cosx for 0°
| xº | 0 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 |
| y | 7.0 | 4.2 | -0.9 |
(b) Using a scale of 2cm to 20° on the x-axis and 2cm to 2 units on the y-axis, draw the graph of y = 3Sinx + 7Cosx for 0°
(c) Using the graph, find the;
(i) value of y when x= 150°,
(i) range of values of x for which y > 0.
