Download North Seattle Community College Math 084 Chapter 1 Review

North Seattle Community College
Math 084
Chapter 1 Review
For the test, be sure to show all work! Turn off cell phones.
Perform the operation.
Perform the operation.
Write the product using exponents.
Perform the operation and simplify the result if possible.
Perform the operation and simplify the result, if possible.
Perform the operation and simplify the result if possible.
Write the fraction as a decimal. If the result is a repeating decimal,
use an overbar.
Add.
Add, then simplify your answer.
Perform the operation.
PAGE 1
Perform the operation.
Translate the verbal model into an equation.
The number of waiters w needed is the quotient of the number of
customers c and 8.
Perform the operation and simplify the result when possible.
Subtract.
Subtract, then simplify your answer.
Perform the operation.
Evaluate the expression.
Evaluate the expression.
Translate the phrase to an algebraic expression.
Twice the sum of 210 and t.
PAGE 2
Translate the phrase to an algebraic expression.
Tickets to a circus cost $3 each. Express how much tickets will
cost for a family of x people if they also pay for two of their
neighbors.
Use the formula to complete the table.
t = 2000 - d
-
Deductions
d
Take-home
pay
t
Perform the operation and simplify the result when possible.
Perform the operation.
Perform the operation.
Please enter your answer as a decimal fraction or integer.
Evaluate the expression, given that x = 3, y = - 2, and z = - 10.
Perform the operation and simplify the result, if possible.
Perform the operation.
PAGE 3
ANSWER KEY
Chapter 1 Review
2.
4.
6.
1.
3.
5.
8.
7.
9.
10.
11.
12.
13.
14.
15.
16.
18.
17.
20.
19.
21.
Deductions
d
Take-home
pay
t
22.
23.
24.
25.
27.
ANSWER KEY - Page 4
26.
North Seattle Community College
Math 097
Chapter 2 Review
Things to Remember:
•
•
•
•
•
•
1.
All test questions will be short answer. There will be no multiple-choice or true/false questions.
Show all of your work. I give partial credit, so even if your final answer is not correct, you might receive
some points if your works shows that you were on the right track.
No books or notes are allowed.
Calculators are allowed.
The test problems will be similar to the problems in your homework, those worked in class, or on this
review.
There will be application problems on the test such as problems demonstrated in class.
Simplify the expression:
Solve each equation:
2.
3.
2x + 5 = 11
12.
Solve the formula for the given variable.
for
13.
h = vt + 16t 2
14.
- 3(3y - 3) - 2y = 8
6.
7.
for
Solve each inequality. Write the solution
set in interval notation,
and graph the solution set.
4.
5.
for v
15.
16.
9y - 1 = 5y + 5
17.
8.
18.
9.
19. Use the distributive property to remove
the parentheses:
10.
b g b g
8 x + 2 2 − x = 6 x + 2 − 10
11. 3(s + 2) + 2 = 2(s + 4) + s
PAGE 1
20. Simplify the expression by combining like
terms:
answers
1.
11. All Real Numbers
2.
12.
3.
13.
4.
14.
5.
15.
6.
16.
7.
17.
8.
18.
9.
19.
10.
20.
PAGE 2
h − 16t 2
v=
t
or
v=
h
− 16t
t
North Seattle Community College
Math 084/097
For the test, be sure to show all work!
Chapter 4/5 Review
Simplify. Assume there are no divisions by
.
Simplify. Assume there are no divisions by
.
Simplify the expression. Write the answer without using
parentheses or negative exponents.
Simplify the expression. Write the answer without using
parentheses or negative exponents.
Write the number in scientific notation.
0.00073
On July 4, 1997, the Pathfinder, carrying the rover vehicle called
Sojourner, landed on Mars to perform a scientific investigation of
the planet. The distance from Mars to Earth is approximately
miles. Use scientific notation to express this distance in
feet. (Hint: 5,280 feet = 1 mile .)
Find the degree of the polynomial.
Perform the operations.
Find the product.
PAGE 1
Find the product.
Find the product.
Find the product.
Find the product.
Find the product.
Perform the division.
Perform the division.
The area of the furnace filter is
Find its length.
PAGE 2
square inches.
Factor by grouping. Remember to factor out the GCF first.
Factor the polynomial.
Factor completely.
Factor the polynomial completely. If a polynomial is not factorable,
write prime.
Solve the equation.
Solve the equation.
Solve the equation.
Simplify the polynomial.
PAGE 3
Math 097
Chapters 4 & 5 Review
1.
14.
2.
15.
3.
16.
4.
17.
5.
5.0261 X 10− 4
Answer key
18.
6.
19.
7.
20.
8.
21.
9.
22.
10.
23.
11.
24.
12.
25.
13.
note: There will be application problems on the test such as problems demonstrated in class
or assigned from the text.
Beginning Algebra
Chapter 3-7 Review
For the in class test: Show all work. Use only pencil. Turn off cell phones.
For problems 1-3, graph the equation. Carefully label the graph.
1.
3x + y = 2
2. y = −
3.
Find 3 ordered points by using a “t” chart then graph the line.
3
x − 2 Find the y intercept then count the slope. Graph the line.
4
y = −3
Graph the line.
Problems:
Answers:
4.
Write the equation of the line with a
3
slope of
and a y intercept of -4.
5
4.
5.
Find the slope of the line through
(4, -2) and (-7, 8)
5.
6.
7.
Write the equation of the line passing through (3, -7) and
(-3, 1)
Solve the system by graphing.
4 x − 2 y = 8

 y = −3 x + 6
__________________
________________
6.
________________
8.
Solve the system by the elimination method.
− 2 x + 5 y = −11

7 x − 3 y = −5
8.
________________
9.
Solve the system by the elimination method.
x − y = 1

 − x − y = −7
9.
_________________
10. Solve the system by the substitution method.
 x − y = −2

 y = −2 x − 10
10
.
________________
11. Solve the system by the substitution method.
 y = 3x − 2

− 6 x + 2 y = −4
11
.
________________
12. a. Write the following equation in standard form of a line.
y=
12
.
a________________
5
x+3
3
b. Is the slope of the line negative or positive? Why?
b_________________
c. Find the x and y intercepts of the equation. Write the
answer as ordered pairs.
c._____________ ___
d. Find the equation of the line parallel to 12-a that passes
through the point (0, -1)
d.________________
Solve the following problems.
Be sure to set up a system with two variables and use either the
substitution method or elimination method to solve the system.
13._______________
13. A total of $14,000 was invested. Part of the $14,000 was
invested at 6% and the rest invested at 8%. If the interest for
one year is $1060, how much was invested at each rate?
14. The sum of two numbers is 18. If twice the smaller number
is 6 more than the larger, find the two numbers.
15.
Graph the inequality.
3x − 2 y > 6
14._______________
North Seattle Community College
Math 085
Chapter 8 Review
For full credit on your test, be sure to show all work.
Problems:
Answers:
For problems 1-10, find the roots. Assume all variables represent positive numbers.
100 x 4 y 16
1.
1.
2.
− 80b 14
2.
3.
15 32m 5 n 7
3.
4.
− x 3 48x 11
4.
5.
−
6.
7
81
144 x 10 y 22
121
5.
6.
2
7.
− 7 100
7.
5
50
6
8.
8.
For problem 9 and 10, add or subtract.
9.
7 242 + 9 32
10.
7.
7 108a 7 − a 3 75a
9.
9.
10.
10.
For problems 11-14, multiply.
11.
(
12.
(7
6 −2
)(
6 + 12
)(
)
w +6 7 w −6
)
11.
11.
12.
12.
3
For problem 13, rationalize the denominator.
17 + 8
13.
17 − 8
13.
For problems 14 –16, solve the equation.
14.
8x − 8 + 2 = 0
14.
15.
6 x + 13 − 2 = 5
15.
16.
y+2 = 4− y
16.
For problems 17-18, simplify the expression.
17.
18.
3
− 54
36
−
3
2
17.
18.
North Seattle Community College
Math 085
Chapter 9 REVIEW F’06
For problems 1-2, use the square root property to solve each quadratic equation.
1.
x 2 = 44
2.
(3 x − 6 )2
= − 81
For problems 3 & 4, complete the square to solve the equation.
3.
x 2 − 8x − 3 = 0
4.
5x 2 + 9 x − 2 = 0
2
For problems 5 & 6, use the quadratic formula to solve the equation.
5.
x 2 + 4x − 7 = 0
6.
5 x 2 + 10 x + 1 = 0
Write as a complex number.
7.
− 98
Combine like terms and simplify.
8.
(2 − 3i ) − (5 − 2i ) + (5 − i )
For problems 9 & 10, multiply and simplify.
9.
7i (5 + 2i )
3
(3 − 4i )(5 + i )
10.
Divide.
11.
4 − 5i
4 + 5i
12. Graph the following quadratic equation. Be sure to answer all questions. Label your
points carefully and be sure to draw the axis of symmetry.
y = x 2 + 7 x + 10
The shape of this graph is a________________________________.
The graph opens________________________________________.
The vertex is______________________.
The axis of symmetry is__________________.
The y intercept is________________________.
The x roots are__________________________.
North Seattle Community College
1.
Solve the equation.
Math 085 Final Review
2.
Solve the system by graphing.
3.
Use the quadratic formula to solve the equation.
4.
Solve the equation.
5.
(1.3 × 10 )(4.8 × 10 )
4
Write the solution in scientific notation.
−3
1.2 × 10 −5
6.
Solve the proportion.
7.
Write an equation of the line that passes through the points (7, - 4) and (- 11, 2).
Write your result in slope-intercept form.
8.
Solve the equation by completing the square.
9.
Use the elimination method to solve the system.
10.
Simplify the expression, if possible.
11.
Simplify the complex fraction.
12.
Use the substitution method to solve the system.
13.
Perform the operation. Simplify, if possible.
14.
Perform the division.
15.
Use the quadratic formula to solve the equation.
16.
17.
Multiply and simplify, if possible.
It takes a grounds keeper 40 minutes to prepare a softball field for a game. It takes
his assistant 65 minutes to prepare the same field. How long will it take if they work
together to prepare the field?
Math 085 Final Review
18.
Solve the equation.
19.
Find the square root. Assume that the variable represents a nonnegative number.
20.
Perform the operation. Simplify, if possible.
21.
Simplify if possible. Assume that
22.
Assume that
.
23.
Perform the operations.
24.
Graph the quadratic equation.
25.
Assume that
.
26.
Simplify the expression. Write the answer without using parentheses or negative
varies directly with
varies inversely with
represents a positive number.
. If
when
. If
, find
when
, find
when
when
exponents.
27.
Graph the inequality.
28.
Use the most convenient method to find all real solutions. If a solution contains a
radical, give the exact solution.
29.
Use the square root property to solve the equation.
30.
Find the product.
31.
Solve the inequality; write the solution in interval notation. −
32.
33.
Divide
1
2 5
≥ x−
9 6
3
4 + 3i
2+i
Solve. Graph the solution. Write the answer in interval notation.
−1 ≤
4x −1
<5
3
Math 085 Final Review
Answer Key
1.
17.
2.
3.
18.
19.
or
1±
22
2
4.
5.
6.
20.
5.2 × 10 6
21.
22.
7.
23.
8.
9.
24.
25.
10.
26.
11.
27.
12. infinitely many solutions
28.
13.
29.
14.
15.
30.
31.
16.
32.
33.
24
no solution
27.
See below
See below
7
±
2
7
− ±
2
−
5
2
5
2
2 
2
 - ∞, 
15, 
15 
11 2
+ i
5 5
 1 
− 2 ,4 
x≤