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 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
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
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.
9G2 Homework
Consider the formula
When n=1, P=17, which is a prime number.
Investigate for other values of n.
When n=1, P=17, which is a prime number.
Investigate for other values of n.
