a. A pack of 52 playing cards is shuffled, and a card is drawn at random. Calculate the probability that it is either a five or a red nine.
[Hint: There are 4 fives and 2 red nines in a pack of 52 cards]
b. P, Q, and R are points in the same horizontal plane. The bearing of Q from P is 150º, and the bearing of R from Q is 060º. If |PQ| = 5 m and |QR| = 3 m, find the bearing of R from P, correct to the nearest degree.
The frequency table shows the marks scored by 32 students in a test.
| Marks scored | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Number of students | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 3 | 2 | 1 |
a(i) Find the mean of the marks
(ii) Find the median of the marks
(iii) Find the mode of the marks
b. Percentage of those who scored at least 8 marks
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
