PART TWO
ai Using mathematical tables, find: 2sin63.35º
ii Using mathematical tables, find: log cos 44.74º
iii Find the value of k given that log k - log(k - 2) = log 5
b) Use logarithm tables to evaluate: \(\frac{3.68^2 \times 6.705}{\sqrt{0.3581}}\)
a. Given that p = x + ym\(^3\), find m in terms of p, x, and y
b. Using the method of completing the square method, find the roots of the quadratic equation x\(^2\) - 6x + 7 = 0 to 1 decimal place.
c. The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it. Find the two numbers.
a. Copy and complete the table for the relation y = 2cos2x - 1
| x | 0º | 30º | 60º | 90º | 120º | 150º | 180º |
| y = 2cos 2x - 1 | 1.0 | 0 | 1.0 |
b. Using a scale of 2cm = 30º on the x - axis and 2cm = 1 unit on the y - axis, draw the graph of y = 2cos2x - 1 for 0º ≤ x ≤ 180º
c. On the same axes, draw the graph of y = \(\frac{1}{180}\)(x - 360)
d. Use your graphs to find the values of x for which 2cos2x + \(\frac{1}{2}\) = 0
a. Using a ruler and a pair of compasses only, construct triangle ABC with |AB| = 7.5cm, |BC| = 8.1cm, and < ABC = 105º
b. Locate a point D on \(\overline{BC}\) such that |BD| : |DC| is 3:2
c. Through D, construct a line L perpendicular to \(\overline{BC}\)
d. If the line L meets \(\overline{AC}\) at P, measure |BP|
ai. A man travels from a village X on a bearing of 060º to a village Y, which is 20 km away. From Y, he travels to a village Z, on a bearing of 195º. If Z is directly east of X, calculate, correct to three significant figures, the distance of Y from Z
ii. A man travels from a village X on a bearing of 060º to a village Y, which is 20 km away. From Y, he travels to a village Z, on a bearing of 195º. If Z is directly east of X, calculate, correct to three significant figures, the distance of Z from X
bi. An aircraft flies due south from an airfield on latitude 36ºN, longitude 138ºE to an airfield on latitude 36°S, longitude 138ºE. Calculate the distance travelled, correct to three significant figures.
ii. An aircraft flies due south from an airfield on latitude 36ºN, longitude 138ºE to an airfield on latitude 36ºS, longitude 138ºE. If the speed of the aircraft is 800 km per hour, calculate the time taken, correct to the nearest hour. [Take π = \(\frac{22}{7}\), R = 6400 km]
