Year 10 Homework Sheet Straight Line Graphs I

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1 Year 10 Homework Sheet Straight Line Graphs I Equation Gradient Y intercept Example: y = 2x + 3 G = 2 Y intercept = 3 1. y = 2x + 3 G = Y intercept = 2. y = 3x + 4 G = Y intercept = 3. y = x + 5 G = Y intercept = 4. y = 7x - 3 G = Y intercept = 5. y = 9x + 18 G = Y intercept = 6. y = -3x -7 G = Y intercept = 7. y = -5x + 9 G = Y intercept = 8. y = -10x + 13 G = Y intercept = 9. y = ½ x + 8 G = Y intercept = 10. y = ¾ x -11 G = Y intercept = 11. y = ¼ x 19 G = Y intercept = 12. y = 17x + 99 G = Y intercept = Example: y = x G = 4 Y intercept = y = 8 +2x G = Y intercept = 2. y = 10-3x G = Y intercept = 3. y = x G = Y intercept = 4. y = x G = Y intercept = 5. y = 8 0.5x G = Y intercept = 6. y = 12-9x G = Y intercept = 7. y = -2-5x G = Y intercept = 8. y = -8 7x G = Y intercept = 9. y = 12-2x G = Y intercept = 10. y = x G = Y intercept = 11. y = 18-19x G = Y intercept = 12. y = x G = Y intercept = Example: y - 3 = 4x G = 4 Y intercept = 3 1. y + 4 = 5x G = Y intercept = 2. y + 7 = 6x G = Y intercept = 3. y + 11 = 12x G = Y intercept = 4. y + 14 = 15x G = Y intercept = 5. y + 19 = 19x G = Y intercept = 6. y + 27 = 21x G = Y intercept = 7. y - 4 = -5x G = Y intercept = 8. y - 1 = 7x G = Y intercept = 9. y - 12 = -15x G = Y intercept = 10. y - 9 = -11x G = Y intercept = 11. y - 7 = 6x G = Y intercept = 12. y - 5 = -4x G = Y intercept =

2 Year 10 Homework Sheet Gradients I Find the gradient between each of these pairs of points. Gradient = (y 2 y 1 ) (x 2 x 1 ) Coordinate Gradient Example: (1,4) and (2,5) G = ( 5 4 ) ( 2 1 ) = 1 1 = 2 1. (1,3) and (2,7) G = ( 7 3 ) ( 2 1 ) = = 2. (1,1) and (3,9) G = 3. (2,2) and (3,5) G = 4. (2,1) and (2,5) G = 5. (0,0) and (2,8) G = 6. (0,0) and (3,12) G = 7. (0,0) and (4,16) G = 8. (2,4) and (4,8) G = 9. (1,3) and (4,12) G = 10. (-1,-2) and (1,4) G = 11. (-1,-1) and (3,11) G = 12. (1,6) and (7,18) G = Example: (1,1) and (5,2) G = ( 2 1 ) ( 5 1 ) = 1 4 = ¼ 1. (0,0) and (3,1) G = 2. (0,0) and (6,3) G = 3. (0,0) and (12,2) G = 4. (0,0) and (8,2) G = 5. (1,1) and (3,2) G = 6. (2,1) and (5,2) G = 7. (3,6) and (11,8) G = 8. (2,0) and (6,2) G = 9. (4,0) and (7,1) G = 10. (0,2) and (7,3) G = 11. (0,6) and (10,8) G = 12. (1,7) and (4,8) G = Example: (3,3) and (1,7) G = ( 7 3 ) ( 1 3 ) = 4-2 = (3,3) and (1,9) G = 2. (1,1) and (0,3) G = 3. (2,2) and (1,5) G = 4. (0,0) and (-2,8) G = 5. (0,0) and (-1,5) G = 6. (-1,0) and (-2,4) G = 7. (-2,0) and (-3,8) G = 8. (-2,0) and (-4,4) G = 9. (-3,0) and (-5,10) G = 10. (-5,0) and (-6,9) G = 11. (-2,-2) and (-5,10) G = 12. (3,-3) and (2,3) G =

3 Year 10 Homework Sheet Quadratics I Factorise the quadratic expressions Quadratic Factorised Form Example: x 2 + 6x + 8 = ( x + 4) ( x + 2 ) x 2 + 4x + 3 = ( + ) ( + ) x 2 + 5x + 4 = ( + ) ( + ) x 2 + 8x + 7 = ( + ) ( + ) x x + 20 = ( + ) ( + ) x x + 24 = ( + ) ( + ) x 2 + 9x + 14 = ( + ) ( + ) x x + 24 = ( + ) ( + ) x x + 16 = ( + ) ( + ) x 2 + 6x + 9 = ( + ) ( + ) x x + 40 = ( + ) ( + ) x x + 50 = ( + ) ( + ) x x + 32 = ( + ) ( + ) x 2 + 8x + 16 = ( + ) ( + ) x x + 18 = ( + ) ( + ) x x + 22 = ( + ) ( + ) x x + 28 = ( + ) ( + ) x x + 30 = ( + ) ( + ) x x + 19 = ( + ) ( + ) Example: x 2-7x + 10 = ( x - 5 ) ( x - 2 ) x 2-7x + 6 = ( - ) ( - ) x 2-10x + 21 = ( - ) ( - ) x 2-9x + 14 = ( - ) ( - ) x 2-8x + 15 = ( - ) ( - ) x 2-5x + 4 = ( - ) ( - ) x 2-8x + 7 = ( - ) ( - ) x 2-10x + 16 = ( - ) ( - ) x 2-13x + 30 = ( - ) ( - ) x 2-17x + 70 = ( - ) ( - ) x 2-12x + 27 = ( - ) ( - ) x 2-18x + 77 = ( - ) ( - ) x 2-11x + 30 = ( - ) ( - ) x 2-32x + 31 = ( - ) ( - ) x 2-13x + 36 = ( - ) ( - ) x 2-21x + 38 = ( - ) ( - ) x 2-11x + 18 = ( - ) ( - ) x 2-9x + 20 = ( - ) ( - ) x 2-10x + 21 = ( - ) ( - )

4 Year 10 Homework Sheet Quadratics II Factorise the quadratic expressions Quadratic Factorised Form Example: x 2 + 6x + 9 = ( x + 3) 2 x 2 + 4x + 4 = ( + ) 2 x x + 25 = ( + ) 2 x 2 + 8x + 16 = ( + ) 2 x x + 36 = ( + ) 2 x x + 49 = ( + ) 2 x x = ( + ) 2 x x = ( + ) 2 x x + 64 = ( + ) 2 x 2-6x + 9 = ( - ) 2 x 2-12x + 36 = ( - ) 2 x 2-18x + 81 = ( - ) 2 x 2-22x = ( - ) 2 x 2-2x + 1 = ( - ) 2 x 2-24x = ( - ) 2 x 2-34x = ( - ) 2 x 2-40x = ( - ) 2 x 2-60x = ( - ) 2 x 2-8x + 16 = ( - ) 2 Example: x 2-9 = ( x + 3 ) ( x - 3 ) x 2 49 = ( + ) ( - ) x 2 64 = ( + ) ( - ) x 2 16 = ( + ) ( - ) x 2 49 = ( + ) ( - ) x = ( + ) ( - ) x = ( + ) ( - ) x = ( + ) ( - ) x 2 4 = ( + ) ( - ) x 2 16 = ( + ) ( - ) x 2 81 = ( + ) ( - ) x = ( + ) ( - ) x = ( + ) ( - ) x = ( + ) ( - ) x = ( + ) ( - ) 4x 2 9 = ( 2x + ) ( 2x - ) 9x 2 49 = ( 3x + ) ( 3x - ) 100x 2 81 = ( + ) ( - ) 16x 2 25 = ( + ) ( - )

5 Year 10 Homework Sheet Quadratics III Factorise the quadratic expressions Quadratic Factorised Form Example: x 2-6x - 7 = ( x 7 ) ( x + 1 ) x 2 x 12 = ( x ) ( x + ) x 2 x - 6 = ( x ) ( x + ) x 2 2x 8 = ( x ) ( x + ) x 2 3x 10 = ( x ) ( x + ) x 2 2x 80 = ( x ) ( x + ) x 2 2x 35 = ( x ) ( x + ) x 2 3x 4 = ( x ) ( x + ) x 2 3x 28 = ( x ) ( x + ) x 2 5x 6 = ( x ) ( x + ) x 2 5x 14 = ( x ) ( x + ) x 2 6x 16 = ( x ) ( x + ) x 2 6x 27 = ( x ) ( x + ) x 2 10x 11 = ( x ) ( x + ) x 2 12x 28 = ( x ) ( x + ) x 2 4x 60 = ( x ) ( x + ) x 2 4x 140 = ( x ) ( x + ) x 2 4x 32 = ( x ) ( x + ) x 2 x 110 = ( x ) ( x + ) Example: x 2 + x 12 = ( x + 4 ) ( x - 3 ) x 2 + x 2 = ( x ) ( x + ) x 2 + x 6 = ( x ) ( x + ) x 2 + 2x 8 = ( x ) ( x + ) x 2 + 3x 10 = ( x ) ( x + ) x 2 + 2x 80 = ( x ) ( x + ) x 2 + x 20 = ( x ) ( x + ) x 2 + x 30 = ( x ) ( x + ) x 2 + 2x 48 = ( x ) ( x + ) x 2 + x 42 = ( x ) ( x + ) x 2 + x 56 = ( x ) ( x + ) x 2 + 2x 63 = ( x ) ( x + ) x 2 + 3x 70 = ( x ) ( x + ) x 2 + 8x 9 = ( x ) ( x + ) x 2 + 9x 10 = ( x ) ( x + ) x x 11 = ( x ) ( x + ) x x 14 = ( x ) ( x + ) x 2 + 7x 30 = ( x ) ( x + ) x x 45 = ( x ) ( x + )

6 Year 10 Homework Sheet Angles in Regular Polygons I Question: What are the Method + Answer interior and exterior angles? 12 sides Exterior = = Ext = sides Exterior = 6 sides Exterior = 10 sides Exterior = 20 sides Exterior = 40 sides Exterior = 60 sides Exterior = 120 sides Exterior = Question: How many sides? Method + Answer Exterior = = 36 sides Exterior = 12 Exterior = 20 Exterior = 30 Exterior = 60 Exterior = 120 Exterior = 90 Exterior = 3 Question: How many sides? Method + Answer 135 Exterior = = = 8 sides 135 Exterior = Exterior = 90 Exterior = 120 Exterior = 140 Exterior = 150 Exterior = 179 Exterior =

7 Year 10 Homework Sheet Mean from Discrete Data Question 1 Answers to Q1 1 7 Which is the modal score? Calculate the mean: Totals: 50 Question 2 Answers to Q2 Which is the median score? Calculate the mean: Totals: Question 3 Answers to Q3 Which is the modal score? Calculate the mean: Totals: Question 4 Answers to Q4 Which is the median score? Calculate the mean: Totals: Question 5 Answers to Q5 Which is the modal score? Calculate the mean: Totals:

8 Year 10 Homework Sheet Straight Line Graphs II Find the equation of the line from the information given. Gradient Y intercept Equation G = 2 Y intercept = 3 Example: y = 2x + 3 G = 3 Y intercept = 1 1. y = G = 4 Y intercept = 4 2. y = G = 5 Y intercept = 5 3. y = G = -2 Y intercept = 0 4. y = G = -5 Y intercept = 2 5. y = G = 7 Y intercept = 3 6. y = G = 1 Y intercept = y = G = 3 Y intercept = 7 8. y = G = 2 Y intercept = 4 9. y = G = 6 Y intercept = y = G = 8 Y intercept = y = G = -3 Y intercept = y = Use: (y y 1 ) = Gradient times (x x 1 ) G = 4 Through (2,2) Example: (y-2) =4(x-2) y 2 = 4x 8 y = 4x - 6 G = 3 Through (1,1) 1. G = 2 Through (0,2) 2. G = 1 Through (1,3) 3. G = 2 Through (4,1) 4. G = 3 Through (3,3) 5. G = 4 Through (1,5) 6. G = 3 Through (6,2) 7. G = 2 Through (2,4) 8. G = 1 Through (1,10) 9. G = 3 Through (3,0) 10. G = 2 Through (5,4) 11. G = 4 Through (10,3) 12. Name:

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