1 / 15

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.

lilian
Télécharger la présentation

GCSE Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related