Math 1010-2 Practice Midterm 2
1. Simplify the following expressions:
(a)
(b)
(c)
(d)
(e)
2y −1 z −3
4yz −3
x2 + xy − 2y 2
x2 + 3xy + 2y 2
¶
µ
(3r)3
10t4
µ
¶
9r
(2t)2
r
x2
5
√
2x
√
√
x− 2
2. Find the following product by any method you choose:
(x2 − 5x − 2)(x2 − 2)
3. Factor the following polynomials:
(a) 8y 2 − 18x4
(b) x2 − 5x + 6
(c) 4x2 + 5x − 6
4. Solve the following equations:
1
1
−
=0
x+1 x−1
1
1
(b)
+
=1
x+1 x−1
x−1
(c)
=x
x−1
√
√
(d) x + 5 − x = 1
(a)
(e) x2 + 2x + 4 = −1
5. Perform the following division by any method you choose:
x3 − 4x + 7
x−1
6. Evaluate the following expressions:
(a) 4−2
1
(b) 4 2
1
(c) (−4) 2
7. Find the vertex of the parabola given by f (x) = x2 − 6x + 3.
8. Write the equation of the parabola with vertex (1, 1) and y-intercept −2.
9. A tennis ball is tossed vertically upward from a height of 5 feet according to the height equation
h = −16t2 + 21t + 5, where h is the height of the tennis ball in feet and t is the time in seconds.
(a) After how many seconds is the height 11 feet?
(b) After how many seconds does the tennis ball hit the ground?
(c) What is the maximum height of the ball?
The problems of the real midterm will not necessarily come from this practice problem list.
The real midterm will have less problems.