Olympiad Maths Trainer 4. Solve these questions. Show your working clearly. Each question carries 4 marks.

1. Use a simple method to calculate each of the following.

(a) 376 + 285 + 124 + 715

(b) 81 + 79 + 82 + 83 + 88

(c) 173 + 123 + 877 +327

(d) 169 + 171 + 173 + 172 + 167

2. Complete each number pattern

(a) 2, 4, 6, 8, …, …. , …., ….

(b) 1, 4, 9, 16, … , …. , …

(c) 1, 1, 2, 3, 5, … , … , … , …,

(d) 2, 1, 4, 3, 6, 5, … , …

3. Determine whether each of the following sequences has a common difference. Find the common difference if there is. State the first and last terms of each sequence.

(a) 5, 10, 15, 20, 25, 30, 35

(b) 1, 4, 7, 10, 13, 16, 19

(c) 1, 4, 9, 16, 25, 36, 49

(d) 2, 4, 6, 8, 10, 12, 14

4. If a * b  = (a + b) /2, evaluate

(a) 3 * 7

(b) 4 * (8 *4)

5. There is a total 660 passenger on two ships. 30 passengers alight from ship A and 70 passengers board on ship B. As a result, the number of passenger on the two ships becomes the same. How many passengers are there on each ship at first?

6. A car and bicycle depart from town A and town B respectively at the same time.

The bicycles moves at 35 km/h and the car moves at 75 km/h. How far is town B from town A if the car cathces up with the bicycle three hours later?