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]
a. The table shows the scores of 2000 candidates in an entrance examination into a private secondary school.
| % mark | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 | 51 - 60 | 61 - 70 | 71 - 80 | 81-90 |
| Number of pupils | 68 | 184 | 294 | 402 | 480 | 310 | 164 | 98 |
Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.
bi. Use the curve to estimate the cut-off mark if 300 candidates are to be offered admission.
bii. Use your curve to estimate the probability that a candidate picked at random scored at least 45%
a. A box contains 5 blue balls, 3 black balls, and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining: two red balls
b. A box contains 5 blue balls, 3 black balls, and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining: two blue balls or two black balls
c. A box contains 5 blue balls, 3 black balls, and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining: one black ball and one red ball in any order
