.(a) In a class of 80 students,\(\frac{3}{4}\) study Biology and \(\frac{3}{5}\) study Physics.
If each student studies at least one of the subjects: (i) draw a Venn diagram to represent this information
(ii) how many students study both subjects
(iii) find the fraction of the class that study Biology but not Physics.
(b) Johnson and Jocatol Ltd. owned a business office with floor measuring 15m by 8 m which was to be carpeted.
The cost of carpeting was Gh¢ 890.00 per square metre. If a total of GH 216,120.00 was spent on painting and carpeting, how much was the cost of painting?
(a) Copy and complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 19 | -2 | 26 |
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
(c) On the same axes, draw the graph of y = 2x + 3.
(d) Use the graph to find the: (i) roots of the equation 2x-3r-5 0; (i) range of values of x for which 2x\(^2\) -x - 2<0.
.(a) In APQR, ∠PQR= 90°. If its area is 216cm\(^2\) and |PQ|:|QR| is 3:4, find |PR|.
(b) The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?
In the diagram, \(\overline{PQ//RS}\) is a trapezium with QR//PS. U and T are points on \(\overline{PS}\) such that \(\overline{|PU|}\) = 5 cm,
\(\overline{|QU|}\) = 12 cm and ∠PUQ= ∠STR =90°. If the area of PQR = 20 cm\(^2\),
calculate, correct to the nearest whole number, the:
(a) perimeter; (b) area; of the trapezium
(a) A cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to: (i) two significant figures, the distance between the two farms, (ii) the nearest degree, the bearing of Manu's farm from Dogbe's.
(b) A ladder 10 m long leaned against a vertical wall xm high. The distance between the wall and the foot of the ladder is 2 m longer than the height of the wall.
Calculate the value of x
