PART ONE
a. Factorize: px - 2qx - 4qy + 2py
b. Given that the universal set U = {1,2,3,4,5,6,7,8,9,10}, P = {1,2,4,6,10} and Q = {2,3,6,9}. Show that (P ∪ Q)\(^I\) = P\(^I\) ∩ Q\(^I\).
a. The quantity y is partly constant and partly varies inversely as the square of x. Write down the relationship between x and y
b. The quantity y is partly constant and partly varies inversely as the square of x. When x = 1, y = 11, and when x = 2, y = 5. Find the value of y when x = 4
a. In the diagram above, PQSR and SRYZ are parallelograms, and PQYZ is a straight line. If |QY| = 2cm and |RS| = 3cm, find |PZ|
b. P and Q are two towns on the Earth's surface on latitude of 56°N. Their longitudes are 25°E and 95°E, respectively. Find the distance PQ along their parallel of latitude, correct to the nearest km. [Take radius of the earth as 6400 km and π = \(\frac{22}{7}\)]
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
