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PM 11
Final Exam Review 1
1. Graph and label y  2  x  1  7
2
1
and 4
3
3. Write the equation of the parabola with a vertex of (-2,4) and passing through (1,7)
2. Write the quadratic equation with roots of 
4. Determine the zeroes for y  2 x 2  7 x  3
5. Change y  x 2  6 x  7 to the form y  a  x  p   q
2
6. A rectangular lot is bordered on one side by a stream and on the other sides by a
total of 200m of fencing. The area of the lot is a maximum. Show the area as a function
of side length x. Complete the square. Determine the area.
7. Graph the inverse of y = 2x + 3
8. Determine the inverse of y   x  1  3
2
9. Write an equation of the function
1
1
11. y  2
2x  3
x  16
2
12. Given f  x   x  1 and g  x   2 x  4 , find g(f(2))
10. Graph and label y 
13. Given f(x) = 3x+1 and g(x) = 2x-6, find f(g(x))
14. Determine the domain and range of y  x 4  3x 2  1
15. Determine the equation of the function with zeroes of 0, 4, and -1 and passing
through (2,-6)
16. Solve x3  4 x  2  0 by graphing
17. For what value(s) of k does x 2  kx  2  0 have 2 equal real roots
18. Solve x3  x 2  5 x  2  0 by factoring
19. Solve  x  2 x 1 x  5  0
21. Solve
x  5  x 1
23. x + 3y = 7 by graphing
X–y=3
20. Solve
1
x
5


x x 1 x
22. Solve 2 x  5  x  1
24. 2x + 3y = 8
3x – y = 1
25. Solve y  x 2  1
y=x+3
26. Solve x – y – z = 1
2x + y + z = 14
X + y + 2z = 10
x3
27. Solve y  2
y  3x  2
28. Solve ∆ABC if  C=90°, AC = 10.1,BC = 7.5
29. Solve for x
12
x
36
30. Solve for each variable
30°
60°
w
y x
z
31. Solve for x.
x
10
32. Solve for x and y
y
x
66°
33. Graph and label  x  2   y 2  4
2
34. Find the co-ordinates of the intersection of  x  1  y 2  4 and x – 3y = 3
2
35. Given the circle described by  x  2    y  1  10 . Find the equation of the tangent
2
2
to the circle at the point P(-5,0)
36. A line is drawn through the origin at 50° to positive x-axis. The point O is 10cm
from the origin. With centre O, a circle is drawn with radius of 8cm. This circle
intersects the x-axis at A and B Calculate the length of chord AB
37. Determine the shortest distance between the origin and the line graphed by
4x + 5y = 20
38. Verify that figure ABCD is a rectangle if A(0,0), B(1,3), C(4,2), and D(3,-1)
39. Given, that angle  is in standard position, with its terminal arm in QIII, has
2
. Find exact values for the other 5 trig ratios
sin   
7
40. Determine the exact values for a) cos 135° b) csc 330° c) tan (-60°)
41. Solve sin 2   sin   0 , for 0    360
42. Solve 4 cos 2   3 , for 0    360
Answer Key:
4) zeroes are
1
and 3
2
8) y   x  3  1
10)
3) y 
2) 3x 2  11x  4  0
1)
5) y   x  3  2
2
6) 5000m2
9) y   x  3 x  1 x  2
1
2
 x  2  4
3
7)
11)
12) g(f(2)) = 6
15) y 
13) 6x – 17
1
x  x  4  x  1
2
R   y  3.25
19) x  2 or 1  x  5 20) x = { 2 }
 4
22) x  6, 
 3
21) x = { 4 }
}
16) x 2.21,0.54,1.68 17) k  2 2
 3  5 3  5 
,
18) x  2,

2
2 

26) (5,3,1)
14) D = {
23) (4,1)
24) (1,2)
25) {(2,5),(-1,2) }
27)
Shade the triangle
28)
A  37, B  53, AB  12.58
29) x  12 2
30) x = 120°, y = 240°, z = 30°, and w = 60°
31) x  5 2
32) x = 48° and y = 66°
34) { (3,0), (--0.6,-1.2) }
35) 3x + y + 15 = 0
37) 3.15 units
39) cos   
40) a) 
1
2
36) Chord AB = 4.61 units
38) AB  AD, AB CD
3
2
7
7
3
, csc   
, tan  
,sec   
, cot  
2
2
7
3
3
b) -2 c)  3
41) 0°, 90°, 189°
42) 30°, 150°, 210°, 330°
33)