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# GCSE: Miscellaneous

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• Marked by Teachers essays 3
1. ## GCSE Maths questions

• Develop your confidence and skills in GCSE Maths using our free interactive questions with teacher feedback to guide you at every stage.
• Level: GCSE
• Questions: 75
2. ## Frogs Investigation - look at your results and try to find a formula which gives the least number of moves needed for any number of discs x .It may help if you can count the number of hops and slides separately .

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8- Conclusion: Number of hops=4 Number of slides=4 Total number of moves=8 Question 2: Now try with 3 discs of each colour .Can You complete it in 15 moves ? Step 1-A3 slides to the right Step 2-B1 hops to the left Step 3-B2 slides to the left Step 4 -A3 hops to the right Step 5-A2 hops to the right Step 6-A1 slides to the right Step 7 -B1 hops to the left Step 8 -B2 hops to the left Step 9 -B3 hops

• Word count: 1371
3. ## 222 and all that!

4 Digit Numbers 1. Make all the combinations using the four digits. 2. Add the combinations together. 3. Add the four numbers together. 4. Divide ? the combinations divided by ? the four numbers and the answer will always be 6666. Examples 1234 1243 1324 1342 1423 1432 2134 2143 2314 2341 2413 2431 3124 3142 3214 3241 3412 3421 4123 4132 4213 4231 4312 4321 Adding the numbers on the previous page gives 66660 and 1 + 2 + 3 + 4 = 10, so 66660 � 10 = 6666.

• Word count: 1402
4. ## The Towers of Hanoi

Next I will try four discs, but first I will predict how many moves I can do it in. Here are the results I have had so far: o One disc = One move o Two discs = Three moves o Three discs = Seven moves The first thing I notice is that for each extra disc you can find the number of moves by doubling the number needed for the previous disc and the adding one. ==> ( 1 x 2 ) + 1 = 3 ==> ( 3 x 2 ) + 1 = 7 So for four discs I predict I will take 15 moves as that would be the next result in the pattern.

• Word count: 1017
5. ## GCSE module 5 AQA Mathematics

I am going to try and work out the formula by at first seeing what would happen if n was 1: 1 2 11 12 So the final outcome would be: 1x12=12 2x11= 22 22-12= 10 This can be proved with other 2 x 2 boxes. For example: 34 35 44 45 34 x 45= 1530 44 x 35= 1540 15- 1530 = 10 Equation. To find n and prove that any number can be selected and its 2 x 2 box can be calculated I can use this method which I have developed in to a formula so any number can be found.

• Word count: 1035
6. ## Trays. The first square I will investigate is a 24cm x 24cm square. My prediction is that the shopkeepers statement will also be true for a square of this size.

My prediction is that the shopkeeper's statement will also be true for a square of this size. If the width of the sides is represented by W then we have: So the volume of the tray = w(24cm - 2w)(24cm - 2w) Results Table Width of Side (cm) Length of base (cm) Volume (cm3) Area of Side (cm2) Area of all sides(cm2) Area of base (cm2) 1 22 484 22 88 484 2 20 800 40 160 400 3 18 972 54 216 324 4 16 1024 64 256 256 5 14 980 70 280 196 6 12 864 72 288 144 7 10 700 70 280 100 8 8 512 64 256 64 9 6 324

• Word count: 1718