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PM 11
Final Exam Review 4
1. Determine the equation of the quadratic function to the right:
2. Determine the zeroes of the quadratic function:
y  2 x 2  7 x  4 by factoring
3. Write the equation of the parabola with a vertex (2,3), opens down, with a yintercept of -5
4. Find the two numbers whose is 10 and whose product is a maximum. Show the
product as a function of x. Complete the square.
5. The equation of the inverse of y = 2x – 3 is:
6. Graph y   x  1  4 and its inverse. Label
2
7. Determine an equation of the graph
8. Find the equation of the cubic function has zeroes of -5, -3, and 2 and a y-intercept
of -15.
9. Graph y = x – 3 and its reciprocal. Label
1
, x  2
x 4
Given f(x) = 4x + 1 and g(x) = 2x – 4, determine g(f(3))
Given f(x) = 3x + 4 and g(x) = x 2  1 , find g(f(x))
Solve 4 x 2  5 x  2  x 2  2 x
14. Solve x3  2 x 2  x  2  0 by factoring
When 2 x3  x 2  kx  4 is divided by x + 1, the remainder is 4. Find the value of k
Solve x 3  4 x  7  0 by graphing
Solve 2x 2  3x  5  0 , then graph the solution
3
x
2
Solve x  x  3 x  2  0
19. Solve 
x x2
10. Graph and label y 
11.
12.
13.
15.
16.
17.
18.
20. Solve
2x 1 1  x
2
21. Solve
x 3  x 1
22. Solve x + 2y = 5
1
y x
3
23. Solve y   x 2  2 by graphing
24. Solve 2x + 3y = 8
25. Solve 2 x  3  x  6
y = 2x – 1
4x – y = 9
26. An aerobics studio charges a flat yearly fee plus a per-month charge. Alice was
charged a total of $340 for 4 months. Denise was charged $445 for 7 months.
Determine the a) yearly fee and b) the monthly charge
27. Solve y  2 x  3
x y 5
28. Find the missing angles
51°
x
y
47°
29. Find the missing angles
a
280°
b
30. Find the value of x
20
x
12
31. Find the values of x and y
10
y
66°
x
32. Find the values of x and y
y
47°
x
52°
33. Find the value of OP
15
8
P
O
34. Graph and label  x  3   y  1  4
2
2
35. Give the co-ordinates of the intersection point(s) of  x  3   y  1  13
2
2
and x + y = 7
36. Write the equation of the circle with a centre of (0,3) and a radius of
17
37. Determine the shortest distance from A(-4,5) and the line y = 3x – 2
38. OP = 5 cm, the radius is 4 cm, and OPB = 40°. Find the length of chord AB
O
40°
P
A
B
39. Determine the shortest distance from the origin to the line x – 2y = 4
40. Verify that x + 3y = 10 is tangent to x 2  y 2  10
41) Solve 4 cos 2   1  0 , for 0    360
42) Find the principle angle and the reference angle for the following
a) 700° b) (-125°) c) 640°
43) P( 2 ,-5) is on the terminal arm of angle  , in standard position. Find the exact
values of the six trig ratios
Answer Key:
 1 
2)   , 4 
 2 
1) y   x  2   3
2
5) y 
3) y  2  x  2   3
2
4) the numbers are 5 and 5
x3
2
6)
7) f ( x)   x  2  x  1
2
9)
1
 x  5 x  3 x  2 
2
10)
 1

13) x   , 2 
 3

16) x = { 2.59 }
12) 9 x 2  24 x  17
11) g(f(3)) = 22
15) k = { -3 }
17) x  1 or
x 
14) x  2, 1,1
5
2
-1
18) x  3 or 0  x  2
22) (3,1)
8) y 
5
2
19) X = {-3,2 }
23) { (-3,-7),(1,1) }
20) x = { 4 }
5 
24)  ,1 25) x = { 3, -3 }
2 
21) x = { 1 }
26) $200;$35
27)
28) x = 47°, y = 82°
30) x = { 8 }
31) x = 10cm, y = 57°
33) OP = 17
34)
36) x 2   y  3  17
2
29) a = 80°, b = 40°
32) x = 52°, y = 99°
35) { (6,1), (5,2) }
37) 5.87 units
38) AB = 4.76 units
39) 1.82 units
1
40) The radius has a slope of 3 and the line has a slope of  . The point of tangency is
3
(1,3)
41) 60,120, 240,300
42) a) 240°, 60° b) 235°, 55°
43) sin   
5
3 3
, cos  
c) 280°, 100°
2
5
3 3
3 3
2
, tan   
, sec  
, csc   
, cot   
5
5
3 3
2
2