GCSE: Miscellaneous
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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

OPPOSITE CORNERS
3 star(s) (1 x 12) = 22  12 = 10 Example 2: 25 26 35 36 (35 x 26)  (25 x 36) = 910  900 = 10 Example 3: 63 64 73 74 (73 x 64)  (63  74) = 4672  4662 = 10 So, from the above examples I can see that the difference is 10, now I will find out the general case algebraically. GENERAL CASE: n n + 1 n + 10 n + 11 (n + 10)(n + 1)
 Word count: 2281

opposite corners
3 star(s)I am multiplying the top left number by the bottom right and multiplying the top right by the bottom left in order to find the differences of the two products. 12 13 22 23 12x23= 276 13x22= 286 Difference= 286 276= 10 I am doing more than one example in order to check the accuracy of my work, if my work is not accurate the pattern will not be and I will therefore not be able to find a formula.
 Word count: 10875

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 1A3 slides to the right Step 2B1 hops to the left Step 3B2 slides to the left Step 4 A3 hops to the right Step 5A2 hops to the right Step 6A1 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

Algebra Story
They had chips, cocktail sausages, chicken wings, and a cake. They wanted some party mix of peanuts and candy corn. The peanuts sold for 2 dollars a pound, in which they bought 7 pounds of it. They need to get Y pounds of candy corn selling at 4 dollars a pound. The total weight of the mix is 11 pounds. They could not find any candy corn at any of the local stores. They went to Byerly's, Target, Mackenthun's, and Walgreen's. Then they tried Costco and Sam's Club, but still they were no where to be found.
 Word count: 505

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

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

Rational Zeros Portfolio Assignment
In Part 2, we will be more closely examining the smallest positive roots of several functions. We will also take a look at how these functions relate to each other and try to correlate which changes in a function bring about certain changes in their graphs and in their roots. In Part 3, we will more formally and accurately try to find the established relationship between the rational root of the equation to the leading coefficients of a and the constant term d. We will accomplish this simply by rewriting and rearranging formulas to discover this relationship.
 Word count: 2769

Linear Systems
Equivalent systems Systems of equations that have the same solution. Linear Systems was mostly founded by Carl Friedrich Gauss. He was a German scientist and mathematician who excelled in mathematics. Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. Gauss earned a scholarship and in college, he independently rediscovered several important theorems; his breakthrough occurred in 1796 when he was able to show that any regular polygon, each of whose odd factors are distinct Fermat primes, can be constructed by ruler and compass alone, thereby adding to work started by classical Greek mathematicians.
 Word count: 504

Equible Shapes
Using the height I can then calculate the area of each triangle. By multiplying the number of triangles, of which there are the same amount as of sides, by the area of each, I can discover the total area of the shape. I can then calculate the perimeter by multiplying the side length, x, but the number of sides, n. I will use a hexagon as an example: x is the side length of the hexagon. It is also the base of the triangles the hexagon is made up of: As a hexagon has six sides, I can work out the angles that are at the bottom by taking 2 away from the number of sides, so 4, and multiplying this by 90: a = 90 (n  2)
 Word count: 672

Pythagorian Triples
Area = 0.5 x 19 x 180 = 1710cm� Perimeter = 19cm+180cm+181cm = 380cm I will now add all of my results into a table so I can see them more clearly and see if there are any trends and rules. Term Number Side A Side B Side C Area (cm�) Perimeter (cm) 1 3 4 5 6 12 2 5 12 13 30 30 3 7 24 25 84 56 4 9 40 41 180 90 5 11 60 61 330 132 6 13 84 85 546 182 7 15 112 113 840 240 8 17 144 145 1224
 Word count: 3187

maxi products
I will try now in fractional numbers if I can get a number higher than 36. (6 1/3,5 2/3)=12 > 6 1/3+5 2/3 > 6 1/3x5 2/3=35.88 (6 2/5,6 3/5)=12 > 6 2/5+6 3/5 > 6 2/5x6 3/5=35.84 (6 2/7,5 5/7)=12 > 6 2/7+5 5/7 > 6 2/7x5 5/7=35.92 (2dp) (6 2/9,5 7/9)=12 > 6 2/9+5 7/9 > 6 2/9x5 7/9=35.95 (2dp) I have found that 6 and 6 are the two numbers which added together make 12 and when multiplied together make 36 which is the highest possible answer which is retrieved when two numbers added together equal 12 are multiplied.
 Word count: 10642

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 2212= 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

Stair Totals coursework
3 T= 3+ 4+ 5+ 13+ 14+ 23 T= 62 n= 4 T= 4+ 5+ 6+ 14+ 15+ 24 T= 68 n= 5 T= 5+ 6+ 7+ 15+ 16+ 25 T= 74 I will now draw a table because it is at a glance data, which means that it is quick and easy to look at, and furthermore drawing a table will help me find the nth term later on. n 1 2 3 4 5 T 50 56 62 68 74 +6 +6 +6 +6 +6 Observations From the table I have noticed a few trends which are as follows; 1.
 Word count: 3591

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