• Linear Graphs1

• Linear Graphs 2

• Simultaneous Equations - Elimination example 1

• Simultaneous Equations - Elimination example 2

• Simultaneous Equations - Elimination example 3

• Simultaneous Equations - Elimination example 4

• Simultaneous Equations - Elimination example 5

• Surds - Simplifying surds

• Circle Theorems

• Indices Song

• Scatter Graphs (Scatter Diagrams)

• Recurring Decimals

Hi, This is my maths revision page. Feel free to use it for revision. Lauren Diamond

• Mon December 10 - Maths Amnesty for Miss Morrish and Mr Colebrooks classes!!

B Brackets I Indices D Divide M Multiply A Addition S Subtraction

Simultaneous Equatons!!! Where two linear graphs cross, the x and y co-ordinates are the same. How to Solve Simultaneous Equations using Elimination: (1) Make sure the co-efficient of x or y are the same. (don't worry about negatives(step 1 only)) (2) If the signs are the same (positive and positive or negative and negative) subtract one from the other (bigger take away smaller) (3) If the signs are opposites (positive and negative and vice a versa) add equations together (4)Re-arrange to find the value of either x or y (whichever you have left) (5) substitute in the value you have found in step 4 to find the second value. e.g.) 3y + 2x = 6 5y - 2x = 10 the signs are different so you add 8y = 16 so 16 divided by 8 = 2 y = 2 the substitue it back in 3y + 2x = 6 3(2) + 2x = 6 6 + 2x = 6 minus 6 from each side 2x = 0 divide both sides by two x = 0 therefore x = 0 and y = 2 (0,2) e.g.2 ) 3x + y = 0 5x + 4y = 22 First make the coefficient of x and y the same so we will times the first equation by four so that the co-efficient of y is the same 12x + 4y = 0 5x + 4y = 22 the signs are the same so you subtarct 7x = -21 so -21 divided by 7 = -3 x = -3 the substitue it back in 3x + y = 0 3(-3) + y = 0 -9 + y = 0 add 9 to each side y = 9 divide both sides by two x = 0 therefore x = -3 and y = 9 (-3,9) QUADRATIC EQUATIONS!!! the general equation for a quadratic equation: y = ax(squared) + bx + c the quadratic formula -b (+or-) (the square root of) b (squared) -4ac x = ---------------------------------------------------------------- 2a

Linear Graphs!!! THE GENERAL EQUATION FOR A STRAIGHT LINE Y= MX+C the Y is the y axis the M is the gradient the X is the x axis the + can be be + or - the C is the y intercept the gradient is the steepness of the line Parallel lines have the same gradient Rise over Run Parallel & Perpendicular Lines Perpendicular lines croos at 90 degrees Gradients of perpendicular lines multiply to make -1 e.g.) y = 4x and y = -1/4x e.g.) 2 and -1/2 e.g.) -7 and 1/7 HISTOGRAMS!!! Histograms have no gaps between the bars. The area of the bars shows the frequency not the height. The width of the bars varies depending on the class width. The horizontal axis (x) has a continuous scale. The vertical axis (y) is always the frequency density. Histograms are different to bar charts because : Bar charts have gaps. The bars must be the same width. Discrete data = one or the other Continuous data = anything with no end e.g.) time To calculate Frequency Density: Frequency of class interval Frequency Density = -------------------------------------------- Width of class interval

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2BA2 Calculate using Fractional and negative indices. RULES: (1) 1 to the power of anything is 1 e.g.) 1 to the power of 5 is 1 1 to the power of 56 is 1 (2) Anything to the power of 1 is itself e.g.) 4 to the power of 1 is 4 73 to the power of 1 is 73 (3) Anything to the power of 0 is 1 e.g.) 4 to power of 0 is 1 73 to the power of 0 is 1 (4) When you multiply powers, you add them (only if the fist number is the same) e.g.) 4 to the power of 2 times 4 to the power of 5 is 4 to the power of 7 3 to the power of 3 times 3 to the power of 3 is 3 to the power of 6 If the numbers are different then this rule doesn't apply. e.g.) 3 to the power of 3 times 4 to the power of 3 is still 3 to the power of 3 times 4 to the power of 3 (5) When you divide powers you subtract them e.g.) 4 to the power of 5 divded by 4 to the power of 3 is 4 to the power of 2 3 to the power of 7 divided by 3 to the power of 3 is 3 to the power of 4 4 to the power of 5 divided by 4 to the power of 5 is 4 to the power of 5 (6) When you raise one power to another power you multiplly the powers e.g.) (4 to the power of 5) to the power of 2 = 4 to the power of 10 (5 to the power of 6) to the power of 4 = 5 to the power of 24 If there is a set of brackets you just multiply the powers. (7) Anything to the power of 1 over any number is the root of the number e.g.) a to the power of 1/2 = the square root of a a to the power of 1/3 = the cubed root of a a to the power of 1/n = the nth root of a (8) Anything to the power of -1 is its reciprocal e.g.) 4 to the power of -1 = 1 over 4 or a quarter 73 to the power of -1 = 1 over 73 or one 73rd (9) Anything to the power of -n is its reciprocal to the power of n e.g.) 4 to the power of -2 is 1 over 4 to the power of -2 = 1 over 16 3 to the power of -3 is 1 over 3 to the power of -3 = 1 over 27 5x to the power of -2 is 5 over x to the power of -2 5 to the power of -2 is 1 over 5 to the power of -2 = 1 over 25 (10) EXAMPLE 1 27 to the power of a third As the fraction has a third, the first step is to find the cube root 27 divided by 3 = 9 9 divided by 3 = 3 then, as two is the numerator, raise your answer to the power of two 3 squared is 9 Therefore your answer is 9! EXAMPLE 2 27 to the power of 4 thirds As the fraction has a third, the first step is to find the cube root 27 divided by 3 = 9 9 divided by 3 = 3 then, as 4 is the numerator, raise your answer to the power of 4 3 X 3 = 9 9 X 3 = 27 27 X 3 = 81 Therefore your answer is 81!

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If it's: 1 2 3 4 then round down but if its: 5 6 7 8 9 then round up e.g.) 362.7 = 363 e.g.) 389.26 = 389.3 or = 389 e.g.) 6872.726 = 6872.73 or = 6872.7 or = 6873

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Surds are any number that isn't a square root!!!

Circle Theorems help you find missing angles in circles. They are: 1) Angles in a semi sircle 2)Angles at tangents 3) Cyclic quadrilaterals 4)Tangent lengths 5)Bisecting tangents 6)Alternate segment theory 7)Agles in a quadrilateral where 1 corner is the center 8)Angles in the same segment Plus a bonus theory: Isosceles Triangles To see the diagrams about how these theorems work click on the tab above labled "helpful diagrams".

T ranslation --------> Vector ---------> Scale Factor (S.F) E nlargement ---------> Center of Enlargements (C.O.E) -------> Center of rotation (C.O.R) R otation --------> Angle --------> Direction R eflection ----------> Mirror line Y ou now know everything you need to know about transformations The point (0,0) is called he origin Congruent: Congruent means that they are the same size but can be rottated, translated or reflected. The angles are always identical. Similar: Similar means that are the same shape, different size. All the sides are in the same ratio. Rotation: A rotation occurs when an object is turned around a fixed point. To describe a rotation we need to know 3 things: 1. The angle of rotation e.g.) 1/2 turn = 180 degrees 1/4 turn = 90 degrees 3/4 turn = 270 degrees 2. The center of roation The point of rotation 3. The direction of rotation e.g.) clockwise or anti-clockwise

SOHCAHTOA Sitting On Hard Concrete Always Hurts The Outer Areas O A O S H C H T A Sine Cosine Tangent O = opposite H = Hypotenuse A = Adjacent

To calculate pythagoras theorem in 2D do: * = squared # = square root To find the longest side ( the hypotenuse) a* + b* = c* then # To find the shorter side/s c* - b* = a* then # To calculate Pythagoras theorem in 3D do: a* + b* + c* = d* then #

Vectors tell you how to move a shape. if the co-ordinate was (3,2) and the vector was : /5\ \4/ the you do: /5\ ----> the x axis how far to move the-----> \4/ ----> the y axis new co-ordinate is (8,6) remember: the top tells you how far to move it left or right if negative then left if positive then right the bottom tells you how far to move it up or down if negative then down if positive then up

F = Fractions D = Decimals P = Percentages '-, = divide From(F/D/P) to (F/D/P) D ---------> P X100 P ---------> D '-,100 D ---------> F e.g.) 0.723 = 723 / 1000 0.52698 = 52698 / 100000 F ---------> D top '-, bottom e.g) 18/25 = 25 '-, 18 = 0.72 P ---------> F Put it over 100 then simplify if neccesary F ---------> P turn into decimal then X100

Reciprocals = the inverse 6/8 = 8/6 1/4 = 4/1 12 = 1/12

THE FIRST 1000 PRIME NUMBERS 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873 7877 7879 7883 7901 7907 7919

Rational numbers have an end and can be written as a fraction!!! Any whole number can be written as a fraction and are therefore rational. Irrational numbers go on forvever and have no end and they cant be written as a fraction!!!

ADD & SUBTRACT - - = + -+ = - ++= + +- = -

π = 3.1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198

This has a huge list of diagrams to help you with circle theorems.

Diagrams to help you with correlation.

Angles in a semi circle The angle not touching the diameter equal 90 degrees.

Angles at tangents Where the radius meets the tangent is 90 degrees.

Cyclic quadrilaterals Opposite angles add up to 180 degrees.

Tangent lengths When tangents cross at a common point, the distance to the circle is always equal.

Bisecting tangents The line joining a point to the center bisects the angle between the tangents.

Alternate segment theory The angle between a tangent & a chord through the point of contact is equal to the angle in the alternate segment.

Inscribed angles The angle at the center is twice the angle at the circumference

Angles in the same segment Angles that are in the same segment are equal.