Download Grade 10 Mathematics – Year Review Name: Given the points and

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
xy4
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