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GCSE Mathematics

GCSE Mathematics. 8 Week Revision Course Mark Hanson. 1 Algebra 2 Simultaneous Equations 3 Indices/Standard Form 4 Trigonometry/ Pythagoras. 5 Graphs/trial and improvement 6 Probability/Data Handling 7 Geometry 8 Number Patterns 9 You decide!. Weekly Topics. GCSE Mathematics.

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GCSE Mathematics

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  1. GCSE Mathematics 8 Week Revision Course Mark Hanson

  2. 1 Algebra 2 Simultaneous Equations 3 Indices/Standard Form 4 Trigonometry/ Pythagoras 5 Graphs/trial and improvement 6 Probability/Data Handling 7 Geometry 8 Number Patterns 9 You decide! Weekly Topics

  3. GCSE Mathematics Algebra

  4. Evaluating Expressions • Substitute given values into the expressions. • Be careful of negative and double negative values • Always apply BODMAS rules • Brackets, Order, Division, Multiplication, Addition, Subtraction

  5. 2a+5b+3c 2x3 + 5x(-1) +3x2=7 6a-7b 6x3 - 7x(-1) = 18 - -7=25 4b - 2c 4x(-1) - 2x2= -8 2a2 - 3b2 2xaxa - 3xbxb 2x3x3 -3x(-1)x(-1) =15 (5-3b)c (5 - 3x(-1))x2 =8x2 =16 Examples, using a=3, b=-1, c=2

  6. Removing Brackets • For single brackets, remember to multiply EACH TERM in the brackets by the number AND sign immediately outside the brackets. • If there is no number, then this implies it is 1. • E.g. 3-(4+x) is the same as 3-1(4+x)

  7. 3(a+b) =3a + 3b 5(2a-5c) =10a-25c 4(2a-3b)-5(a-6b) =8a-12b-5a+30b =3a+18b 6c-(3a+2b-5c) =6c-3a-3b+5c =11c-3a-3b 4(5a-b)-2(3a-b-c) =20a- 4b-6a+2b+2c =14a-2b+2c Remove the brackets

  8. Removing Brackets • For double brackets, remember FOIL • First (A+b)(C+d)=AxC • Outside (A+b)(c+D)=AxD • Inside (a+B)(C+d)=BxC • Last (a+B)(c+D)=BxD

  9. (X+3)(X+2) FX x X=X2 OX x 2=2X I3 x X=3X L3 x 2=6 X2+ 2X + 3X +6 X2+ 5x + 6 (X-7)(X+1) X2+ X - 7X -7 X2- 6X-7 (X-4)(X-5) X2- 5X - 4X +20 X2 - 9X +20 (2x+3) 2=(2x+3)(2x+3) 4X2 + 12X + 9 Remove The Brackets

  10. Factorising Expressions • This is the reverse of removing brackets: Brackets are added to the expression. • The term outside the bracket must divide into ALL the terms in the original expression

  11. 15x3 + 17x2 + 19x x(15x2 + 17x + 19) 25wx3 + 15w2 x2 + 35w3 x 5wx(5 x2 + 3wx + 7w2) Factorise the following: • 6x + 8y • 2(3x+4y) • 12xy - 15xz • 3x(4y - 5z) • 8x+16xy+24xz • 8x(1 + 2y +3z)

  12. Factorising Quadratics • Note that: • (x + a) (x + b) = x2 + (a+b)x + ab • The number by the x is the sum of the numbers in brackets • The constant is the product of the numbers in brackets

  13. x2 + 5x +6 sum = 5 product =6 (x+2)(x+3) x2 - 4x + 3 Sum = - 4 product = 3 (x-3)(x-1) x2 + 2x - 3 sum =2 product = - 3 (x+3)(x-1) x2 - 2x - 3 Sum = -2 product = -3 (x-3)(x+1) Factorising Quadratics

  14. Equations • Two golden rules: • 1) Aim to get letters on one side, numbers on the other • 2) Whatever you do to one side of the equation, do the same to the other side

  15. x + 7 = 10 x + 7- 7= 10- 7 x = 3 2x - 1 = 11 2x - 1+ 1 = 11+ 1 2x = 12 x = 6 2x+7 = 5x - 26 7 = 3x - 26 33 = 3x x = 11 6x + 10 = 24x + 19 10 = 18x + 19 -9 = 18x x = - 0.5 Solve for x

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