Exam1 review College Algebra
Solve the equation.
1) t2 - 9t = -14
2)
10m(m + 3) = 13m - 3
Solve the equation by using the square root property.
3) (3z - 18)2 + 58 = 40
Solve the quadratic equation by completing the square and applying the square root property.
4) y2 + 34 = 10y
Solve the equation by using the quadratic formula.
5) 8x(x - 2) = 5
6)
(2w - 1)(w - 2) = -4
Use the discriminant to determine the type and number of solutions.
7) 4x2 + 3x + 2 = 0
Solve the equation.
8) y2 + 10y - 5 = (y + 3)(y - 1)
Solve the problem.
9) An open box is formed from a rectangular piece of cardboard that is 6 in. longer than it is wide, by
removing squares of side 2 in. from each corner and folding up the sides. If the volume of the
carton is then 80 in3 , what were the dimensions of the original piece of cardboard?
10) A
model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in
feet is given by
h(t) = -16t2 + 112t + 20 (t = seconds after launch).
After how many seconds does the object reach its maximum height?
Solve the equation.
11) 48x3 - 64x2 - 3x + 4 = 0
12)
2z
3
= -1
z-2 z+5
13) 10
= 14 + (q - 5)1/3
1
Solve the equation by using substitution.
14) 3(t2 - 9)2 + 22(t2 - 9) = -7
15) z2/3
+ 2z1/3 - 3 = 0
Solve and express your solution in simplified form.
16) x4 - 11x2 + 28 =0
Solve the inequality. Write the solution set in interval notation.
17) -2(7y - 7) + y > 2y - (-2 + y)
18) -2
< -2y + 15 < 12
Solve the absolute value equation.
19) 6z - 3 = 8
20) |2r +
1| = |5r - 15|
Solve the absolute value inequality. Write the solution in interval notation.
21) 3|x - 3| + 9 < 18
22) 3|x -
1| - 9 ≥ -6
Find the exact distance between the points.
23) (-3, 7) and (-5, 3)
24) (
7, - 2) and (-6 7, -4 2)
Find the midpoint of the line segment whose endpoints are the given points.
25) ( 5, - 7) and (6 5, 5 7)
2
Estimate the x- and y-intercepts from the graph.
26)
10 y
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10 x
-2
-4
-6
-8
-10
Find the x- and y-intercepts.
27) x2 + y = 16
Solve the inequality. Write the solution set in interval notation.
28) -x2 + 13x - 40 ≥ 0
29) 5y2
30)
+ 7y ≤ -2(5y + 7)
5h
> -2
h -2
3
Answer Key
Testname: EXAM1 REVIEW
{7, 2}
1 3
2) - , 5 2
1)
{6 + i 2, 6 - i 2}
{5 - 3i, 5 + 3i}
26
5) 1 ±
4
3)
4)
6)
23 5
23
5
i, +
i
4
4
4
4
Two imaginary solutions
1
8)
4
7)
8 in. by 14 in.
10) 3.5 seconds
4 1
11)
,±
3 4
9)
12)
-
37
5
±
3
3
13) {-59}
14)
±
78
,± 2
3
15) {1,
-27}
16) {±2, ± 7}
6
17) -∞,
7
18)
3 17
,
2 2
19)
11 5
,6
6
20)
2,
16
3
21) (0,
6)
22) (-∞, 0] ∪ [2, ∞)
23) 2 5
24) 19
4
Answer Key
Testname: EXAM1 REVIEW
25)
7 5
,2 7
2
(-10, 0), (4, 0)
y-int: (0, -6.3), (0, 6.3)
27) x-intercepts: (-4, 0) and (4, 0); y-intercept: (0, 16)
28) [5, 8]
7
29) -2, 5
26) x-int:
30)
-∞,
4
∪ (2, ∞)
7
5