### Tuesday, October 24, 2006

Year 13 Hints

1 a What is cos x? b What is sin x?

2 Find 3x first.

3 Use the appropriate identity to produce a quadratic in tan x.

4 See the examples before exercise 7D.

5 Multiply both the numerator and denominator by sin x.

6 Use the double angle formulas. Use the appropriate versions of cos 2x so that the ones cancel.

7 Factorise both the numerator and denominator.

8 Factorise and then write with a common denominator.

9 a You can't simplify fg(x).

b Swap x and y, then rearrange. c ditto!

10 This is a quadratic equation.

11 Is there an asymptote?

12 Remember: for an inverse to exist every value of y must have only one value of x.

### Sunday, June 18, 2006

## 9G2 Homework

## 9W3 Homework

Problems involving money

1. A drink and a box of popcorn together cost 90p.

Two drinks and a box of popcorn together cost £1.45.

What does a box of popcorn cost?

2. Six friends went to a Chinese restaurant.

The total cost for the set menu was £75.

How much would the set menu cost for eight people?

3. This is what a stationery shop charges for printing a book.

Print charges

3p per page

75p for the cover

Jan paid £4.35 for his book, including its cover.

How many pages were there in his book?

4. A supermarket sells biscuits in these packets:

15 biscuits for 56p

24 biscuits for 88p

36 biscuits for £1.33

Which packet is the best value for money?

1. A drink and a box of popcorn together cost 90p.

Two drinks and a box of popcorn together cost £1.45.

What does a box of popcorn cost?

2. Six friends went to a Chinese restaurant.

The total cost for the set menu was £75.

How much would the set menu cost for eight people?

3. This is what a stationery shop charges for printing a book.

Print charges

3p per page

75p for the cover

Jan paid £4.35 for his book, including its cover.

How many pages were there in his book?

4. A supermarket sells biscuits in these packets:

15 biscuits for 56p

24 biscuits for 88p

36 biscuits for £1.33

Which packet is the best value for money?

### Thursday, June 15, 2006

## 8W4 Homework

Numbers from digits

Using three of the four digits below make three-digit numbers e.g. 194, 714

1 The largest number is

2 The smallest even number is

3 The largest odd number is

4 The number nearest to 700 is

5 The number nearest to 800 is

6 The number nearest to 200 is

7 The number nearest to 300 is

8 The number nearest to 500 is

9 A number that can be exactly divided by three is

Using three of the four digits below make three-digit numbers e.g. 194, 714

**1 4 7 9**1 The largest number is

2 The smallest even number is

3 The largest odd number is

4 The number nearest to 700 is

5 The number nearest to 800 is

6 The number nearest to 200 is

7 The number nearest to 300 is

8 The number nearest to 500 is

9 A number that can be exactly divided by three is

### Friday, June 09, 2006

## Puzzle No.1

**If you have two sand-filled timers, one for 11 minutes and one for 7 minutes. How would you use them to time 15 minutes without wasting any time at the start?**

Thanks to Jon Millington

## 9W3 Homework

The mathematician Pierre de Fermat (1601-65) discovered that some prime numbers are the sum of two square numbers. For example

Investigate this for other prime numbers.

Investigate this for other prime numbers.