1. Find two numbers whose ratio is 3 and such that two sevenths of the larger is 15 more than one half the smaller.

2. Determine the factors of the lowest common multiple of and

3. Find to two decimal places the value of

when and

4. Solve the equations:

5. Solve any 3 of these equations:

5. (a)

5. (b)

5. (c)

5. (d)

6. The sum of two numbers is 13, and the sum of their cubes is 910. Find the smaller number, correct to the second decimal place.

7. The sum of 9 terms of an arithmetical progression is 46; the sum of the first 5 terms is 25. Find the common difference.

8. Explain the terms, and prove that if four numbers are in proportion, they are in proportion by alternation, by inversion, and by composition. Find x when

9. Find the value of x in each of these equations:

9. (a)

9. (b)