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# GCSE: Consecutive Numbers

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Meet our team of inspirational teachers Get help from 80+ teachers and hundreds of thousands of student written documents 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. ## Algebra Basics

So to sum up, remember balance the x numbers with its kind and the normal numbers with its kind, note, that the letter could be anything, not just x, but even y or m etc. I will give more examples such as the question, 12X +9= 4X -8 Now I allow the time for you to work it out, it should take less then a two minutes work out. Now I will reveal the answer 12X - 4X= -8-9 8X=-17 X=17/8 Now for Mixed fraction the answer is 2 1/8 Because 8 times 2=16 16+1=17 so therefore in mixed fraction the answer is 2 1/8 The equation may also be balanced by a device called a variable.

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3. ## Portfolio: Continued Fractions

Graph 1. The value of the terms versus the term numbers. As n increases does the difference between the value of a term and the value of the term before decrease. This towards a specific value, and since we know that the sequence is the Fibonacci sequence we also know that the specific value the terms is moving towards is the golden ratio. When looking for the exact value of, for example, the 200th term problems arise. Mostly because of the fact that it is hard and takes a lot of time to count to the 200th term by hand,

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4. ## Continued Fractions

We can then conclude that as n increases tn�tn+1. From this, we can now deduce a formula for tn+1 in terms of tn: We can also conclude that if tn�tn+1, then tn-tn+1 will equal to zero. Any term (the nth term) can be determined using the above general formula (formula 1), but it requires having to calculate all the values up to that term. For example, the 200th term can be found but we would have to find all the values up to the 199th term. This is time-consuming and instead of having to do this, we can find a new general formula: (we can assume that tn=tn+1 when n is a large value)

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5. ## A baker's dozen

I can now use a formula to work a formula for this sequence. 2a = 1 a = 0.5 3a + b = 1 1.5 + b = 1 b = -0.5 a + b + c = 0 0.5 - 0.5 + c = 0 c = 0 an + bn + c 0.5n2 - 0.5n I have now found a formula which can be used to work out the number of switches required for any number of buns.

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6. ## Dehumanisation and the Holocaust.

The Viennese anti- Semitic picture paper depicts the Jew as a world-devouring vampire. They are dehumanising the Jews by describing the as "world- devouring vampires" whereas they are completely human and are not at all vampires. They have never done anything wrong to any Gentiles and aren't doing anything wrong, just believing something different to everyone but this does not mean they are world- devouring vampires. This made such atrocities 'easier' to commit as an image of a world- devouring vampire is being put into their heads, instead of normal human beings. The picture of a railway straight track going directly through the arch of a building represents a factory, mechanical, going straight in and straight out, they don't have a choice of where they are going.

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7. ## Orson Welles in Citizen Kane.

The majority of shots of Susan are medium or close-up shots; in fact almost all of the close-up shots in the entire film are of Susan. These close shots, especially when taken in moderate to high key lighting, give Susan an air of youthfulness, vulnerability and emphasize her meekness. Compared to Kane, who enters the scene in shadows and is almost always shot in the long-range, Susan comes across as being fragile, small and weak.

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8. ## Number Grid Investigation.

* Calculate the difference between these numbers. I did this, 12 x 23 = 276 13 x 22 = 286 286 - 276 = 10 The difference between them was 10 I decided to try it with A 3x3 box surrounding the numbers; 12 13 14 22 23 24 12 x 34 = 408 14 x 32 = 448 448 - 408 = 40 The difference between them was 40 I also tried this with A 4x4 box, and A 5x5 box: (4x4) 12 x 45 = 540 15 x 42 = 630 630 - 540 = 90 (5x5)

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9. ## 2D & 3D Sequences.

1 2 3 4 5 6 7 8 No. Of cubes 1 5 13 25 41 61 85 113 I am going to use this next method to see if I can work out some sort of pattern: Sequence Calculations Answer 1 =1 1 2 2(1)+3 5 3 2(1+3)+5 13 4 2(1+3+5)+7 25 5 2(1+3+5+7)+9 41 6 2(1+3+5+7+9)+11 61 7 2(1+3+5+7+9+11)+13 85 8 2(1+3+5+7+9+11+13)+15 113 9 2(1+3+5+7+9+11+13+15) +17 145 What I am doing above is shown with the aid of a diagram below; If we take sequence 3: 2(1+3)+5=13 2(1 squares)

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10. ## Towers of Hanoi.

(See fig. 1) 5 discs To try and make things slightly easier for myself I decided to use the first 15 moves I had used for 4 discs and then proceed from there. This method was effective and led me to find that the smallest number of moves was 31. (See fig. 2) Results and Formulas Number of discs Number of moves 1 1 2 3 3 7 4 15 5 31 When placing all the results into a table I noticed that if you take a certain number of moves for example 3 and then double it you end up with 6.

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11. ## Binary Explained.

Below is a table to explain how the decimal equivalent would be written. This is how binary works. Because the binary system has a base of two, this means that each place number is a power of two. The table below shows the system. Table 1 If we look at the table and take the furthest column to the right and work our way the left, we see that: 2 to the power of 0 is = 1 2 to the power of 1 is = 2 (2x1 = 2) 2 to the power of 2 is = 4 (2x2 = 4)

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12. ## This coursework will be to investigate to see how many squares would be needed to make any cross-shape build up in this way.

4 4 No of squares: 1 5 13 25 41 61 1st Diff: 4 8 12 16 20 2nd Diff: 4 4 4 4 To find the 1st and 2nd difference, I used a table and then the diagram above to check if I was right about my suggested answers. First of all, for the 1st difference, I took the number of squares for shape number 2 and subtracted that with the number of squares I got for the first shape, which then gave me the 1st difference.

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13. ## How does the use of numbers, statistics, graphs, and other quantitative instruments affect perceptions of the validity of knowledge claims in the human sciences?

These studies on the human race are divided into many categories mainly called human sciences. These studies are called sciences because the use of numbers in collecting data and analysing them are essential to prove certain events. In todays society numbers became really important because it is an element that is essential in our life, starting from the money that we use to buy our daily needs to knowing how to count. Whenever humans encounter numbers in magazines they tend to believein them. Any quantitative instrument is believed in todays society because it is known that most of the quantitative instruments that are available are very precise.

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14. ## In this course work I have been asked to find out how many squares will be needed to make up a certain pattern according to its sequence.

5 8 4 3 5 8 13 12 4 4 13 12 25 16 4 5 25 16 41 20 4 6 41 20 61 24 4 7 61 24 85 28 4 8 85 28 113 32 4 9 113 32 14 5 36 4 10 145 36 181 40 4 11 181 40 221 44 4 12 221 44 265 4 Table showing my results. I have achieved these results in the table I have shown above. I got these results from the drawings I have drawn.

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15. ## Nth Term - Finding and verifying a formula for the nth term of a sequence.

So the formula will be 3�n + something (You can complete this something later on) This is because, if the step length is the same for all the terms in the sequence, the formula will be of the format: step � n + something For the sequence above, the rule 3�n + something would give the values 3�1 + something = 3 + something 3�2 + something = 6 + something 3�3 + something = 9 + something 3�4 + something = 12 + something 3�5 + something = 15 + something You then compare these values with the ones in the actual sequence - it should be obvious that the value of the something is +2 So the formula for the nth term is 3n + 2 That's Easy Enough!

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16. ## Maths Statistics Dice Investigation

6 No' time thrown 9 8 8 9 9 7 From the table above it shows that if the game was played for real it would make a small profit of �5 for every �50 that came in. There is still a 1/6 chance of winning but the prize money has been reduces so that for every 6 pounds that I took I would be paying out �5 so I would statistically be making a profit of �1 for every 6 throws that took place From the previous results that I received I think that I should increase the amount of events that can take place.

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17. ## Maths Coursework &#150; N Lines

10 crossovers 14 16 6 lines 1 2 3 4 5 6 7 8 9 10 13 14 11 12 16 17 18 19 20 regions 15 crossovers 12 open regions 10 closed regions 20 21 22 This is what I predicted 7 lines 1 2 3 4 5 6 11 13 14 10 15 7 8 9 17 18 19 20 29 21 22 21 Crossovers 29 regions 16 25 14 open regions 15 closed regions 23

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18. ## To see if three horizontal rectangle numbers e.g. &#147;12,13,14&#148; &#150; have the same result when you multiply the middle number by 2 and add the 1st and last number together.

when we write as it's shortest form i.e.: ( + ( = (2 ( ( 2= (2 Formula: Middle number multiplied by 2 = (First number) + (Last number) Case.2: To see if "Case.1" applies for horizontal and diagonal rectangles. Testing: Conclusion: The original formula (Case.1)

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19. ## Trimino Maths Coursework

The table below shows the highest number o the trimino and the number of possible triminos. I began by taking the difference of the number of combinations, as shown above. As you can see, I had to take three differences before the differences were constant. This meant that the formula I wanted had to contain a cubic function. During my research prior to this investigation, I discovered the formula: ax3 + bx2 + cx + d = y I believed I could use this formula to help me discover a formula to link the highest number with the number of possible combinations.

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20. ## Consecutive Sums

You can not make every number as a lot of numbers in the eight times table can not be made such as 8,16,32,40,56,64,80,88,96 so not every number can be made. C) 1 CON NUMBERS 2 CON NUMBERS 3 CON NUMBERS 4 CON NUMBERS 5 CON NUMBERS 1 0 + 1 2 3 1+2 0+1+2 4 5 2+3 6 1+2+3 0+1+2+3 7 3+4 8 ** ** ** ** ** 9 4+5 2+3+4 10 1+2+3+4 11 5+6 0+1+2+3+4+5 12 3+4+5 13 6+7 14 2+3+4+5 15 7+8 4+5+6 1+2+3+4+5 16 ** ** ** ** ** 17 8+9 18 5+6+7 3+4+5+6 19 9+10

• Word count: 666