Download final exam review problems

Intermediate Algebra final exam review problems
1. Evaluate:
√
(b) − −64
(a) −52 − 8/2
(c)
√
3
−64
(d) −64−1/2
2. If f (x) = 4 − 3x + x2 , find the function value f (−5).
3. Rewrite as a root:
5. Simplify:
x3/4
4. Rewrite with a fractional exponent:
(Assume any variables represent positive numbers)
(a)
√
20x6
(b)
16x4 y 2
81y −2 z 8
7. Simplify:
√
3
(c) Multiply & simplify:
27a6 b10
4
(Assume any variables represent positive numbers)
8. Solve x2 + 6x + 2 = 0 using the method of completing the square.
10. Simplify: (2+3i)2 , where i =
√
x+2 x−3=0
11. Solve for x:
2
1
3
x+4 = x−5
4
3
−1.
n(n − 2) = 24
14. Solve for x:
13. Solve for y:
y 2 − 6y + 25 = 0
x=
15. Solve for x:
5<
√
12. Solve for n:
1
1+x
16. Solve the absolute value inequality
for x:
|x − 500| < 2
8 − 2x
≤7
3
17. Use subsitution and/or elimination methods to solve the system


2x − 3y + z = −1 











5y − 3z = 1






−3y + 4z = 6






y5
√ √ √
3 5 10 − 2 15
!− 3
9. Solve for x:
√
18. Factorize completely: 3x3 + 12x2 − 3x − 12
20. Multiply & simplify:
19.Subtract & simplify:
(4x3 − 6x + 4) − (3x2 − 6x + 2)
21. Divide and simplify:
x2 + 5x − 14
x−2
÷ 2
2
x −9
x + x − 12
22. Subtract and simplify:
23. Simplify:
4
3x+3h
−
h
(2x − y)(4x2 + 2xy + y 2 )
x2
2
5
− 2
+ x − 6 x + 4x + 3
4
3x
24. A line passes through the points (x, y) = (50, 10) and (86, 30).
(a) Calculate the slope of this line
(b) Find an equation for the line
(c) A point (58, y) is on the line. Find the value of y.
25. Calculate the slope of the line with
equation
26. Find the x and y coordinates of the
vertex of the parabola
2x − 3y = 24
y=
1
(x − 50)2 − 2007
100
27–28. Graph each linear equation & inequality:
27.
y + 3 = − 34 (x − 2)
29. Use long division to simplify:
28.
2x2 + 4x − 7
x+3
30. Graph the parabola y = −x2 +3x+4
3x − 4y ≥ 12