1.Which of the following ordered pairs is a solution to the system of equations y =
x − 6 and 2y = –x + 14?
Options are missing
2. Solve the system of equations y = 0.6x + 0.2 and 3x − 5y = 4.
A. There is one solution, and it is . This option is missing
B. There are infinitely many solutions.
C. There is no solution.
D. There is one solution, and it is (0, 0.2).
3. Solve the system of equations 2x − y + z = –7, x − 3y + 4z = –19, and –x + 4y − 3z =
18.
A. There is one solution, (–1, 2, –3).
B. There is one solution, (1, 2, 3).
C. There is one solution, (1, –2, 3).
D. There is one solution, (–1, –2, –3).
4. Graph the following solution set:
x ≤ y2
y≥x
Can you check these equations ?
5. Choose the correct ways to fill in the blanks in the following sentence.
To solve a system of equations using the matrix method, use __________ to transform
the augmented
matrix into one with __________, then proceed to back-substitute.
A. the coefficient matrix, an inverse
B. the coefficient matrix, Gaussian elimination
C. multiplication and addition, zeros in its final column
D. elementary row operations, zeros below the diagonal
6. Graph the inequality y < 3x + 1.
7. Use matrices to help find a general solution for this system of equations.
2x − y + 3z = 5
–x + 4y + 4z = –1
8. Solve the inequality |5x + 10| ≥ 15.
Write the solution in interval notation and graph it.
Answer:
Solution set: (-,-5]U[1,)
Graph:
///////////]_____[//////////////
-5
1
9. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x − y − z = 5.
A. There is one solution, x = 4, y = 2, and z = 3.
B. There is not enough information to solve the problem.
C. There is no solution.
D. There are infinitely many solutions.
10. Solve the equation |x| = 7.
A. x = 7 or x = –7
B. x = 7
C. Undefined
D. x = –7
11. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.
Answer:
Solution set: (-3,7)
Graph: ____(//////////)_____
-3
7
12. Solve the inequality –2 (3 + x) < 4x + 4 < 8x.
Give the result in set notation and graph it.
Answer: Solution set = {x/x>1}
Graph: ________(////////////
1
13. Aunt Jane's Pies had a tent at the county fair. Unfortunately their cash register broke,
so they have no
receipts. They know from counting their left over paper plates that they made 413 sales.
They know from
the cash box that they made $2,243. If they only sell two kinds of items at the fair tent, a
piece of pie for
$4 and pie á là mode for $7, help them figure out how many of each kind they sold.
A. The system of equations is inconsistent, and therefore their plate counting or money counting
must have an error.
B. They sold 610 pieces of pie and 4683 pies á là mode.
C. They sold 355 pieces of pie and 58 pies á là mode.
D. They sold 216 pieces of pie and 197 pies á là mode.
14. The matrix below is the augmented matrix of a system of three equations in the
variables x and y. Solve
for x and y.
Matrix is missing
A. No solution
B. Infinitely many solutions
C. One solution (0, 9)
D. One solution,
15. Graph the following solution set:
x+y≤4
x≥0
y≥0
Answer:
Graph:
16. Graph the inequality y ≥ –3.
Answer:
Graph:
17. If an interval is bounded and has one endpoint, it's called a/an _______ interval.
A. closed
B. half-open
C. unbounded
D. open
18. Solve the system of equations x − 4y = –8 and –3x + 12y = 24.
A. There is one solution, and it is (0, 2).
B. There is no solution.
C. There are infinitely many solutions.
D. There is one solution, and it is (–4, 1).
19. Solve the inequality 4 < –z − 4 < 11. Give the result in set notation and graph it.
Answer:
Solution set: {z/-15<z<-8}
Graph:
(/////////)________
-15
-8
20. When solving a system of equations using Cramer's Rule, if Dx = 0, Dy = –1, Dz = 1,
and D = 0, then
what can you conclude?
A. The system is dependent.
B. The system has one solution, (0, 0, 0).
C. The system has one solution, (0, –1, 1).
D. The system is inconsistent.
21. Are the two equations –6 + y = 2x and 2y − 4x = 12 dependent?
A. Yes, because both are the equations of straight lines.
B. No, because the equations are not written the same.
C. No, because they are not parallel.
D. Yes, because they have the same graph.
23. The first two rows of the following matrix are already in triangular form.
Finish the job by performing Gaussian elimination on row 3.
What are the contents of row 3 after you have done so?
Matrix is missing
A. 0 0 1 9
B. 0 0 3 –11
C. 0 0 –5 –11
D. 0 0 3 29
24. Graph the following solution set:
y≤x−1
y ≥ 2x
Answer:
Graph:
25.Which of these phrases best describes the standard deviation?
A. It is equal to the mean squared.
B. It is a radical expression using n variables.
C. It is a measure of variability.
D. It increases as more measurements are taken.
26. Which of these radical expressions simplifies to x?
A.
B.
C.
D.
27.Expand
and simplify. Assume y ≥ 0.
A.
B.
C.
D.
28.To solve
for x, begin with which of these steps?
A. Eliminate the negative in the second radical expression.
B. Combine the two like radicals, then square both sides.
C. Isolate one radical expression.
D. Square both sides of the equation.
29.
.
A.
B.
C.
D.
30.Combine like radicals in
A.
B.
C.
D.
.
31.Expand
and simplify. Assume c ≥ 0 and d ≥ 0.
A.
B.
C.
D.
32.What are the mean and standard deviation of the data – 6, 12, 2,
– 4, 1, 6, 0, 3?
A. The mean is
and the standard deviation is approximately 5.6252.
B. The mean is
and the standard deviation is approximately 5.6252.
C. The mean is 4.86 and the standard deviation is 5.63.
D. The mean is
and the standard deviation is 5
33.Rationalize the denominator of
.
A.
B.
C.
D.
34.Compute the value of
A.
B.
.
C.
D.
35.Which of these expressions is in simplified form?
A.
B.
C.
D.
36.Which of the following best describes imaginary numbers?
A. They are the complex numbers.
B. They are the values of expressions of the form
numbers a, as long as a ≠ 0.
for various real
C. They are not numbers, but are useful in solving equations.
D. They consist of two values, the principal imaginary number i and its
negative –i.
37. Simplify
A.
B.
C.
.
D.
38. Simplify i23.
A. –1
B. 1
C. –i
D. i
39.Simplify
assuming the
variables represent non-negative numbers.
A.
B.
C.
D.
40.Simplify
.