Credit Revision Chapters 5 - 8 Pythagoras and Trig Right-angled Triangles.

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Presentation transcript:

Credit Revision Chapters 5 - 8

Pythagoras and Trig Right-angled Triangles

E.g. Find the length of each missing side. (to 1 dp) 5cm 3cm a 8cm 10cm c a 2 = a 2 = a =  34 = c 2 = c 2 = 36 6c =  36 =

Ex Find the length of each missing side. (to 1 dp) x 12cm 18cm 6cm y 4cm x 2 = x 2 = x =  180 = y 2 = y 2 = y =  52 =

E.g.Find the missing values hyp SOH CAH TOA 35º x 4m   opp adj opp hyp adj SOH CAH TOA  5 y° 14 

Problem 1Find x opp hyp adj SOH CAH TOA  93m x° 20m 

Problem 2 Find x hyp SOH CAH TOA  7 cm 37° x cm  adj opp

Problem 3 Ship A leaves the harbour and sails North at 15km/h Ship B leaves the harbour and sails East at 30km/h. After 3 hours how far apart are the two ships? hyp 2 = b 2 + c 2 AB 2 = x 2 = x 2 = x =  = 100.6km H A B 45km 90km

Problem 4Find the Perimeter 42  16m 6m x y opp hyp adj SOH CAH TOA   y 2 = y =  100 y = 10 P = P = 64.6m

Factorising Remember the three cases?

Factorise each of the following fully 1.18x – 12y2.4x 2 – 363.2x x (3x – 2y)4(x 2 – 9)2(x 2 + 5x + 6) 4(x  3)(x + 3) STEP 1 – COMMON FACTOR STEP 2 – DIFFERENCE OF TWO SQUARES STEP 3 – TWO BRACKETS 2(x + 2)(x + 3)

1.12x – 14y2.4x 2 – 6x3.15a 2 b + 12a 3 b 2(6x – 7y)(2x – 3)2x E.g.STEP 1 – COMMON FACTORS 3a 2 b(5 + 3a) 1.20x – 15y2.13y 2 – 7y3.12m 2 n – 8mn 2 5(4x – 3y)(13y – 7)y ExSTEP 1 – COMMON FACTORS 4mn(3m – 2n)

1.100 – y 2 2.4x 2 – 9y 2 3.2a 2 – 18 (10 + y)(10 – y)(2x – 3)(2x + 3y) E.g.STEP 2 – DIFFERENCE OF TWO SQUARES 2(a 2 – 9) 2(a + 3)(a – 3) 1.x 2 – 492.m 2 – 81n 2 3.ax 2 – ay 2 (x + 7)(x – 7)(m – 9n)(m + 9n) ExSTEP 2 – DIFFERENCE OF TWO SQUARES a(x 2 – y 2 ) a(x – y)(x + y)

1.x 2 + 8x x 2 – 3x – 403.a 2 – 7a + 10 (x + 6)(x + 2)– +(x 8)(x 5) E.g.STEP 3 – TWO BRACKETS (a 5)(a 2) – – 1.x 2 + 9x x 2 + 2x – 243.a 2 – 5a – 24 (x + 6)(x + 3)– +(x 4)(x 6) ExSTEP 3 – TWO BRACKETS (a 3)(a 8) + –

Factorise each of the following fully 1.4x – 6y2.x 2 – 93.x 2 + 8x x 2  85.y 2  2y  y y 2(2x – 3y)(x – 3)(x + 3)(x + 5)(x + 3) 2(x 2  4) 2(x + 2)(x – 2) (y  6)(y + 4) 4y(2y + 5)

Factorise each of the following fully 7.4x 2 – 498.5x 2 – 5009.x 2 - 9x x 2 y  y y 2  3y  xy x 2 y 3 (2x – 7)(2x + 7)5(x 2 – 100) (x - 8)(x - 1) y(x 2  y 2 ) y(x + y)(x – y) 3(y 2  y  20) 2xy 2 (7 + 10xy) 5(x – 10)(x + 10) 3(y  5)(y + 4)

Factorise each of the following fully 13.2ax 2 – 72a14.81 – 25h x x x 2 y + 12y a a y 2 + x 2 2a(x 2 – 36) 4(x 2 – 3x  10) 3y(x 2 + 4y 2 )2(a 2 + 6a + 5) (9 – 5h)(9 + 5h) 2(a + 5)(a + 1) 2a(x – 6)(x + 6) 4(x – 5)(x + 2)

Try and Factorise each of the following 19.2x x x x a 2  26a y 2  17y + 8 (2x + 3)(x + 4) 2x x 4 3 x 6 2 x 3 4 (3x + 2)(x + 4) 3x x 1 8 x 8 1 x 2 4 (3a  2)(a  8) 3a a a a (2y  1)(y  8) 2y y y y y y -8

Try and Factorise each of the following 23.3x x  x 2  15x  a a y y + 10 (3x  2)(x + 5) 3x x x x x x -2 5 (2x + 1)(x  8) 2x x x x 1 -8 (2a + 5)(2a + 3) 4a a a a 5 3 (6y + 5)(y + 2) 3y 2y 5 2 3y 2y 2 5 6y y 5 2 2a 5 3

Try and Factorise each of the following 27.6x 2 + x  x x  x 2  17x y y + 21 (3x  4)(2x + 3) 3x 2x x 2x -4 3 (5x  1)(2x + 3) 5x 2x x 2x 3 (6x  5)(x  2) 3x 2x -10 6x x (y + 7)(y + 3) y y 7 3

Solving Inequations Remember negative multipliers

E.g. 1E.g. 2 4x + x > x > 15 x > 3 4x - 2 > 13 - x 2x - 3  6x x - 6x  x  28 x  -7

Question 1Question 2 5x - 3x < x < 8 x < 4 5x + 2 < 3x x - 1  4x x - 4x  x  21 x  7

Question 3Question 4 5x + 20 > 3x + 6 5x - 3x > x > -14 x > -14 / 2 5(x + 4) > 3(x + 2) x > -7 3(x - 5) < -4(1 - x) 3x - 15 < x 3x - 4x < x < 11 x > 11 / -1 x > -11

Question 5Question 6 9x - 4  3x x - 3x  x  14 x  14 / 6 9x - 4  3(x + 2) + 4 x  7 / 3 3(2 - 5x) > x x > x -15x + 7x > x > 19 x < 19 / -8 9x - 4  3x + 10 x < -2 3 / 8

Question 7Question 8 5x - 10 = -3x x + 3x = x = -2 x = -2 / 8 5(x - 2) = -3(x + 4) x = -1 / 4 3(x + 4) < -4(5 - 2x) 3x +12 < x 3x - 8x < x < -32 x > -32 / -5 x > 6 2 / 5