Practice test #3 This in addition to quizzes, homework and prior tests and practice test need to be studied.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine whether the given point is in the solution set to the given system.
1) (7, 2, -5)
3x - 8y + z = 0
2x + 4y - 3z = 37
-x + 2y - z = 2
2) -1,
4
4
,3
3
9x + 6y + 9z = 5
6x + 3y - 3z = 14
x - y + 2z = -3
Solve the system of equations.
3) x + y + z = 4
x - y + 3z = 10
4x + y + z = -5
4) 3x + 4y + z = -11
4x - 4y - z = -17
2x + y + 5z = 16
5) 2x + 8y + 10z = 112
x + 4y + 5z = -28
x + y + z = -4
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
6)
x+ y+z = 9
2x - 3y + 4z = 7
x - 4y + 3z = -2
Solve the system.
7) x2 + y2 = 61
x + y = 11
8) xy = 20
x+y=9
9) xy - x2 = -20
x - 2y = 3
10) 4x2 - 2y2 = 4
2x2 + 3y2 = 66
1
Graph the linear inequality.
11) -2x - 5y ≤ 10
y
10
5
-10
-5
10
x
6 8 10
x
5
-5
-10
Graph the inequality.
12) x2 + (y + 3)2 ≤ 9
y
10
8
6
4
2
-10 -8 -6 -4 -2-2
2
4
-4
-6
-8
-10
Graph the solution set of the system.
13) 2x + y ≥ 4
x- 1 ≥0
4
y
4 x
-4
-4
2
14) y ≤ -x2 - 6x - 4
y ≥ x2 + 6x + 4
y
6
4
2
-6
-4
-2
2
4
6
x
2
4
6
x
-2
-4
-6
15) (x + 2)2 + (y - 4)2 ≤ 9
(x - 2)2 + (y - 4)2 ≤ 9
y
6
4
2
-6
-4
-2
-2
-4
-6
16) y ≥ 4x - 4
x2 + y2 < 9
10
y
5
-10
-5
5
x
-5
-10
Solve the equation.
17) 2 (5 - 3x) =
1
16
3
Solve the equation. If necessary, round to thousandths.
18) 4 (x - 3) = 11
19) 4e3x + 6 = 24
20) 2 (5x - 1) = 13
Solve the equation. Give an exact solution.
21) log(x + 20) = 3
22) ln(2x - 3) = ln(3) - ln(x - 1)
23) log9 (x - 2) + log9 (x - 2) = 1
24) log(x + 13) = 0
Solve the problem.
25) In the formula A = Iekt, A is the amount of radioactive material remaining from an initial amount I at a given
time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope
decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.
26) A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year
would be required for a given amount of this isotope to decay to 20% of that amount?
27) The decay of 978 mg of an isotope is given by A(t) = 978e-0.032t, where t is time in years. Find the amount left
after 14 years.
Write the standard form of the equation of the circle with the given center and radius.
28) (8, -3); 9
29) (0, -6);
3
Graph the equation and state its domain and range. Use interval notation
30) x2 + y2 = 49
10
y
5
-10
-5
5
10 x
-5
-10
4
Graph the equation.
31) x2 + y2 + 12x + 8y + 43 = 0
10
y
5
-10
-5
5
10 x
-5
-10
32) x2 + y2 - 10x - 2y + 17 = 0
10
y
5
-10
-5
5
10 x
-5
-10
5
Answer Key
Testname: PRACTICE TEST 112 3
1)
2)
3)
4)
5)
Yes
No
{(-3, 2, 5)}
{(-4, -1, 5)}
∅
7z 34 2z 11
6) {(,
, z)}
+
+
5
5 5
5
7) {(6, 5), (5, 6)}
8) {(5, 4), (4, 5)}
9)
(5, 1), -8, -
11
2
10) {(3, 4), (-3, 4), (3, -4), (-3, -4)}
11)
y
10
5
-10
-5
5
10
x
6 8 10
x
-5
-10
12)
y
10
8
6
4
2
-10 -8 -6 -4 -2-2
2
4
-4
-6
-8
-10
6
Answer Key
Testname: PRACTICE TEST 112 3
13)
y
4
4 x
-4
-4
14)
y
6
4
2
-6
-4
-2
2
4
6
x
2
4
6
x
-2
-4
-6
15)
y
6
4
2
-6
-4
-2
-2
-4
-6
7
Answer Key
Testname: PRACTICE TEST 112 3
16)
10
y
5
-10
-5
5
x
-5
-10
17) {3}
18) 4.730
19) -1.403
20) 0.940
21) 980
5
22)
2
23) 5
24) -12
25) 252 yr
26) 2902 years
27) 625 mg
28) (x - 8)2 + (y + 3)2 = 81
29) x2 + (y + 6)2 = 3
30)
10
y
5
-10
-5
5
10 x
-5
-10
Domain = (-7, 7); Range = (-7, 7)
8
Answer Key
Testname: PRACTICE TEST 112 3
31)
10
y
5
-10
-5
5
10 x
5
10 x
-5
-10
32)
10
y
5
-10
-5
-5
-10
9