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Grade 10 Mathematics – Year Review Name: __________________________ 1. Given the points A(0,1) and B(1,2) determine the following: a. Distance between A and b. Slope of AB c. Midpoint of AB B. 2. From the graph, write the equation of the line. Equation: _______________________ 3. State the slope and y-intercept of each line a. y (x 2)2 3 slope: ________ y-intercept: ________x – intercept:________ b. 3x 3 2 y 4 slope: ________ y-intercept: ________x – intercept:________ Write the coordinate of the x and y intercepts of each of the following. 4. 3x 2 y 12 5. x 2 y 3 0 1 3 6. x y 2 5 10 8. y 3 10. 1 x 2 y 3 2 7. 0.2x 0.3y 1.2 9. x 3 1 11. y x 2 5 Determine if the point given is a solution of the equation. 12. 2,0 ; 3x y 6 13. 5, 1 ; 1 3 14. ( 6, 4) ; x y 1 3 4 xy4 15. 1, 2 ; 2 x y 4 0 Find k so that the given point will be a solution of the equation. 16. 2,k ; 3 x 2 y 8 17. k 1,7 ; 18. 3k,1; 6 x y 12 19. k,2k ; y 2 x 1 4x 3y 5 Find the slope of each line described by the given information. 20. y 2x 3 21. (-3, 5) and (6, 4) 23. x = 5 24. A vertical line 22. (-2,0) and (-2,-8) 25. 2 x 3 y Graph the line through the given point with the given slope in the diagram below. A) B) C) D) E) 1 2 3, 2 ; 4 3, 1 ; no slope 4,5;0 2,5 ; 1,0 ; 2 5 A line has a given slope, y-intercept, or contains the indicated point(s). Write an equation, in standard form, of each line. 27. (3,2),m 3 5 26. (1,6),m 6 5 3 28. m ,b 8 8 29. m 3,b 7 3 30. 2,3, 0,4 31. The line having an x-intercept of 4 and a slope of 1/3 32. 0,6,(10,0) 33. 7,3, line is horizontal 34. The line having an x-intercept of -2 and a y-intercept of 3. 35. The line having an x-intercept of 3 and y-intercept of 10. Find an equation in STANDARD FORM given the following information. 36. Through (5, 7) and parallel to x 4 y 5. 37. Through (6, 3) and parallel to line through (2,1) and (5,-3). 38. Through (-2,1) and parallel to y=5. 39. Through (-3,2) and parallel to 2 x 5 y 4. 40. Through (6, -10) and perpendicular to y x . 41. Through (8,0) and perpendicular to the line through (-1,4) and (5,2). 42. Through (-3,-8) and perpendicular to x 5. 43. The x-intercept is 3 and it is perpendicular to the line through (5,1) and (-2,3). 44. Perpendicular to AB at point B, given A:(-3, 5) and B:(6,-2). 45. Graph the following lines to solve the system of equations. State the solution. 3x 2y 11 y x 1 46. Solve the following system of equations using elimination. 3 2 x 2y 2 3 3x 2y 6 47. Solve the following system of equations using substitution method: 3y 9 12x 2x 4y 6 0 48. The points (3,10) and (x,2) lie on a line that is parallel to 2x 4y 8 . Find the value of x. 49. Given two points A(6,2) and point B(8,y), determine the value(s) of y so that the length of [AB] is 10 units. 50. The midpoint of [AB] is M(2,3). Determine the coordinates of point A if B has the coordinates B(6,5). 51. Given two points A(4,2) and D (x,10) , determine the value(s) of x if the length of AD is 2 5 units. 3 52. A man cycles 50km between two towns in 3 hours. He rides slow at 4km/h for the 4 first part of the journey and rides fast at 12km/h for the remaining part. How long was he riding fast? 53. Graph the equation 3 x 2y 6 0 on the grid below. 2