a. The sum of three numbers is 81. The second number is twice the first. given that the third number is 6 more than the second, find the numbers.
b. Give me the points P(3, 5) and Q(-5, 7) on the Cartesian plane such that R (x, y) is the midpoint of PQ, find the equation of the line that passes through R and perpendicular to line PQ.
a. Copy and complete the tables of values of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 17 | -4 |
b. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 unit on the y-axis, draw the graph of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3.
ci. Use the graph to find: the roots of the equation \(2x^2 - x - 4\)
ii. Use the graph to find the: values of x for which y increases as x increases;
iii. Use the graph to find the: minimum point of y.
a. The table shows the height of teak trees harvested by a farmer: Find the median height.
| Height(m) | 3 | 4 | 5 | 6 | 7 | 8 |
| number of trees | 4 | 6 | 4 | 5 | 6 | 2 |
b. calculate and correct to one decimal place the: i. mean; ii. standard deviation.
a. In a town, Chief X resides 60 m away on a bearing of 057° from Palace P, while Chief Y resides on a bearing of 150° from the same Palace P. The residence of X and Y are 180 m apart. Illustrate the information in a diagram.
b. Find and correct to three significant figures, the: i. bearing of X from Y; ii. distance between P and Y.
a. Two regular polygons P and Q are such that the number of sides of P is twice the number of sides of Q. The difference between the exterior angle of P and Q is 45°.find the number of sides of p.
b. The area of a semi-circle is 32π \(cm^2\). Find, in terms of π, the circumference of the semi-circle.
