Download ALGEBRA I QUIZ 1.1 - Mrs. Matthews Class

ALGEBRA I Quiz 1.1
For questions 1-6, use the following list to match the numbers to their classification. Each word
can only be used once.
Whole number, Composite number, Rational number, Natural/Counting number, Irrational
number, Imaginary, Prime number
1.
= _____________________
2.
= _______________________
3.
1 = ________________________
4.
9 = _______________________
5.
0 = ________________________
6.
23 = ______________________
(12 points)
7.
Match the property to the equation in which it is illustrated (each can only be used once):
Equations
Properties
(i) 8 × ⅛ = 1
(ii) (7 + 4) + 4 = 7 + (4 + 4)
(iii) -2.1 × 1 = -2.1
(iv) 8 + 3.4 = 3.4 + 8
(v) 2•⅞ • (-⅝ )= -⅝ •2• ⅞
(vi) p = r, and q = s, then p = s
(vii) -8.2 + 8.2 = 0
(viii) -x + 0 = -x
(a) Commutative of Multiplication
(b) Associative of Addition
(c) Closure
(d) Reflexive property
(e) Commutative of Addition
(f) Associative of Multiplication
(g) Identity of Addition
(h) Inverse of Multiplication
(j) Density property
(k) Inverse of Addition
(m) Identity of Multiplication
(n) Transitive Property of Equality
(p) Distributive Property
(q) There is no such property
(12 points)
Simplify: -¼(20 – 12t) – 8t
Name the property used in 8(a)
8.
(a)
(b)
9.
Are the odd numbers closed under multiplication? Justify your answer.
10.
(a)
(b)
(2 points)
(2 points)
2⅓ + 1⅝ =
2⅓ ÷ 1⅝ =
(2 points)
ALGEBRA I QUIZ 1.1 (Part II)
1. (a)
(b)
Completely classify –5.
Is the following statement true or false? Explain your choice.
All real numbers are rational numbers.
(2 points)
2. Showing all your work, use the Distributive Property to find the price of 7 CDs that cost $4.99 each.
(1 point)
3. Give a reason to justify each step.
a. 3x + 7 + 2(x – 3) – 2x
= 3x + 7 + 2x – 6 – 2x
= 3x + 7 + 2x + (–6) + (-2x)
b.
= 7 + (–6) + 3x + 2x + (-2x)
c.
= 7 + (–6) + 3x + 0
d.
= 1 + 3x + 0
e
= 1 + 3x
f.
= 3x + 1
(5 points)
4. Write an algebraic expression for: four less than the quotient of a number, n, and 2
(1 point)
Showing your work, simplify the expressions in questions 5-20.
5. 4 53  2 12
6. -2(-3 + 2a)
1
7.
(-12m + 38)
2
8. -(3k – 12)
9. -⅓(6h + 15)
10. 4(2a + 2) – 17
11. -6 – 3(2k + 4)
12. 13 + 2(5c – 2)
13. -4x + 3(2x – 5)
14. 2x + ¾(4x + 16)
15. 5(b + 4) – 6b

16. 3 15  3  4
2
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)
(1 point)

(2 points)
17. 3  32  12  4
18. 13 6 2  5 2  4 2  9
3


 
420  12   4  2 
84
(2 points)
(2 points)
3
19.
20. (a)
(b)
(2 points)
What is the reciprocal of 3 52 ?
(1 point)
What is the opposite of - 52 ?
(1 point)
ALGEBRA I QUIZ 1.2
1. Write an algebraic equation to model the data in the table
Days (d)
2
3
5
6
2. Evaluate
(1 point)
Cost (c)
44
66
110
132
for m = -4, n = -2, and p = 15.
(2 points)
3. In which quadrant or on which axis would you find the point (-2, -4)?
4. For the point (a, b) to be in Quadrant II, a must be ________.
A. Positive
B. negative
5.
6.
C. cannot be determined
(1 point)
Give a reason to justify each step:
4c + 3(2 + c) = 4c + 6 + 3c
a.
= 4c + 3c + 6
b.
= (4c + 3c) + 6
c.
= (4 + 3)c + 6
d.
= 7c + 6
(2 points)
Which expression has a value of 21?
(I)
(5 + 4) × 5 + 15 ÷ 5
(II)
5 + (4 × 5 + 15) ÷ 5
(III)
5 + 4 × (5 + 15) ÷ 5
A. I
7.
(1 point)
Simplify:
B.
II
C.
12 – 3(6z – 5)
III
(2 points)
D.
None of the above
(1 point)
Solve the equations in questions 8-15.
8. x – 50 = -49
9. y = -10
4
10. 18 – d = 13
11. 5p – 18 = -43
7
12. 7y + 5 – 3y = -31
13. 3(y + 6) = 30
14. -¼(4 – 8a) + 3a = 19
15. 8a + 10 = 3a – 5
(1 point)
(1 point)
(2 points)
(2 points)
(2 points)
(2 points)
(3 points)
(2 points)
ALGEBRA QUIZ 1.3
1. Is the statement true or false? If the statement is false, justify your answer:
(1 point)
The set of whole numbers is reasonable to use to record the daily temperature of Alaska.
Simplify the expressions in questions 2-3.
2. 12 – 4 × 2 + 8 ÷ 2
3. 5x – 4y – 11x – 2y
(1 point)
(1 point)
4. Sirus wrote a check for $67. He subtracted that amount from his account balance and found that
the balance was $329 after writing the check. Write and solve an equation to find his balance
before writing the check.
(2 points)
5. You are driving to visit a friend in another state who lives 440 miles away. You are driving 55
miles per hour and have already driven 275 miles. Write and solve an equation to find how
much longer in hours you must drive to reach your destination.
(2 points)
____
6. Choose the coordinates of the point that lies in the second quadrant:
A.
(7,2) B.
(-7,-2)
C.
(-7,2)
D.
(7, -2)
(1 point)
7. Which equation is an identity?
A.
B.
(2 points)
C.
D.
Solve the equations in questions 8-17.
8. 14
(2 points)
9. 4a + 2 = 3a – 5
(2 points)
1 3
5
 x x
10.
(2 points)
4 8
16
11. 2h – 6 = 2
(2 points)
6
3
12. 3p – 1 = 5(p – 1) – 2(7 – 2p)
(3 points)
13. |z| = 12
(1 point)
14. |3x – 4| = 5
(2 points)
15. 12|8 – y| = 36
(2 points)
16. |5c – 1| – 3 = 16
(2 points)
17. | y | + 1 = -4
(2 points)
5
18. Suppose a video store charges non-members $4 to rent each video. A store membership costs
$21 and members pay only $2.50 to rent each video. For what number of videos is the cost the
same?
(2 points)
Solve the equations in questions 15&16 for the given variable.
19.
20.
for b1.
for z.
(2 points)
(1 point)
ALGEBRA I QUIZ 1.4
1. Evaluate -3xy2 for x = -3 and y = -4
2. Which number is a solution of the inequality:
x(7 – x) > 8
A. -1
B. 8
C. 2
D. 0
3. Identify the graph of the inequality from the given description: x is negative.
A.
C.
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
B.
(1 point)
(½ point)
(½ point)
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
D.
4. Write an inequality for the graph:
–5
–4
–3
–2
–1
0
1
2
3
4
5
(½ point)
5. Write an inequality that the graph could represent:
–5
Solve the inequalities in questions 6-10, then graph your solution.
6. a + 8 – 2(a – 12) > 0
7. 12x – 3x + 11 ≥ 4x – (17 – 9x)
–4
–3
–2
–1
0
1
2
3
4
5
(½ point)
(2 points)
(2 points)
8.
(2 points)
(2 points)
9.
10.
(3 points)
11. Your class hopes to collect at least 325 cans of food for the annual food drive. There were 132 cans
donated the first week and 146 more the second week. Write and solve an inequality to find how many
cans are needed to meet or surpass your goal? Let c represent the number of cans of food that must be
collected by the end of the third week for your class to meet or surpass your goal.
(1 point)
12. The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an
inequality to find the length of the rectangle.
(2 points)
13. Susie has designed an exercise program for herself. One part of the program requires her to walk between
25 and 30 miles each week. She plans to walk the same distance each day five days a week. Write an
inequality to show the range of miles that she should walk each day?
(2 points)
A
student
scored
83
and
91
on
her
first
two
quizzes.
Write
and
solve
a
compound
inequality
to find the
14.
possible values for a third quiz score that would give her an average between 85 and 90. (2 points)
For questions 15-17 solve the equation.
15.
16.
17.
(2 points)
For questions 18-20 solve the equation for the given variable.
18. dx + fy = g; y
19.
20.
(2 points)
(2 points)
;x
(1 point)
(1 point)
; F.
(1 point)
Algebra I Quiz 2.1
1. The graph below represents the speed of a skater as he skates through the mountains. Explain what each
section of the graph indicates.
(2 points)
2. State the domain and range of the relation below. Determine whether the relation is a function.
(2 points)
3. Graph the function
.
(5 points)
4. A taxi company charges passengers a $2.00 base fee for a ride and an additional $0.20 for each mile
traveled. a. Write a function rule that describes the relationship between the number of miles m and the
total cost of the ride c(m).
b. What is the charge for a 2.7-mile ride?
(2 points)
5. Using a complete sentence, explain the difference between inductive and deductive reasoning.
(1 point)
6. (a)
Write a suitable conclusion for the following argument:
All dogs have their day.
Lassie is a dog.
Conclusion: ____________________________
(1 point)
(b)
What kind of reasoning allowed you to make the above conclusion?
7. Make up an original example of an argument that uses inductive reasoning.
(1 point)
(3 points)
For questions 8-11, (a) write a function rule to represent the sequence, and (b) find the specified term.
8.
9.
10.
11.
Find the 12th term of the following sequence:
Find the 10th term of the following sequence:
Find the 15th term of the following sequence:
Find the 50th term of the following sequence:
2, –10, 50, –250, . . .
2, -2, -6, -10, …
–164, –82, –41, –20.5, . . .
9, 13, 17, 21, . . .
(2 points)
(2 points)
(2 points)
(2 points)
12. Find the rate of change for the following graph and explain what the rate of change means for the
situation.
(2 points)
Resale Value of a Refrigerator
600
Amounts ($)
500
400
300
200
100
3
6
9
12
15
18
Years after original purchase
13. Using the graph below a. which plant was the tallest at the beginning?
b. Which plant has the fastest growth rate over the 6 weeks? Explain.
(1 point)
(2 points)
Plant Growth
6
Height (in.)
5
4
3
2
1
Plant 1 ___ Plant 2 - - 1
2
3
Plant 3 __ __
4
5
6
Time (Weeks)
14. Is the rate of change constant in the following table? If so, state the rate of change and explain what the
rate of change means for the situation.
(2 points)
Time (days)
Cost ($)
3
75
4
100
5
125
6
150
15.
Find the slope of the following lines:
(a)
(4 points)
(b)
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
(c)
–4
–3
–2
3
4
x
5
y
5
5
4
4
3
3
2
2
1
1
–1
–1
2
(d)
y
–5
1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
16.
Find the slope of the line through each pair of points:
(3 points)
(a)
(9,3) & (19,-17)
(b)
(-4,7) & (-6,-4)
(c)
(17,-13) & (17,8)
Do the equations in questions 17-18 represent a direct variation? If so, state the constant of variation.
17. 5x + 12.5y = 0
(1 point)
18. y – 12x = 12
(1 point)
19. The table shows the height of a plant as it grows. Is the data a direct variation? If so, model the data
with an equation.
(2 points)
Time (months) Plant Height (cm)
3
9
5
15
7
21
9
27
20. The amount you fill a tub, a, varies directly with the amount of time t you fill it. Suppose you fill 25
gallons in 5 minutes. What is an equation that relates a and t? What is the graph of the equation? (2 pts)
ALGEBRA I Quiz 2.2
1.
2.
3.
You drop a ball from a height of 0.5 meter. Each curved path has 52% of the height of the
previous path.
a. Write a rule for the sequence using centimeters.
b. What height will the ball be at the top of the third path?
(2 points)
You budget $100 for parking each month. Each day you use the downtown parking lot, it costs
you $5. Write a rule to represent the amount of money left in your monthly budget. How much
money is left in your budget after you have used the downtown parking lot 11 times this month?
(2 points)
You start an investment account with $3000 and save $100 each month. Write a rule to
represent the total amount of money you invest into your account. How much money
will you have invested after 12 months?
(2 points)
4.
Suppose a manufacturer invented a computer chip in 1980 that had a computational speed of 2s.
The company improves its chips so that every 2 years, the chip triples in speed. What would the
chip’s speed have been for the year 2002? Write your solution in terms of s.
(2 points)
5.
(a)
The rate of change is constant in the table below. Find the rate of change. Explain what
the rate of change means for the situation.
(2 points)
Time (hours)
Distance (miles)
4
260
6
390
8
520
650
10
(b)
The rate of change is constant in the graph. Find the rate of change. Explain what the rate
of change means for the situation.
(2 points)
Height of a Balloon
4
3.5
Height (1000 ft)
3
2.5
2
1.5
1
0.5
10
20
30
40
50
60
Time (s)
6. (a) Write an equation for the line that passes through the point (10, 1) with slope m = 1
5
(b) Write an equation for the line that passes through the points (–2, 2) and (2, –8).
(3 points)
7.
At 6:00 A.M., there were 800,000 gallons of water remaining in a reservoir. After 8 hours of
irrigation, there were 100,000 gallons of water remaining. Write a linear
equation that describes the number of gallons of water remaining as a
function of the time the field had been irrigated.
(2 points)
8.
Hudson is already 40 miles away from home on his drive back to college.
He is driving 65 mi/h. Write an equation that models the total distance d
travelled after h hours. Graph the equation.
(2 points)
9.
Graph each equation.
(a)
y = 2x + 1
(b)
y = -¾x + 2
(c)
y = -5
10.
Write the slope-intercept form of the equation for each line.
(6 points)
(5 points)
ALGEBRA I QUIZ 2.3
1.
2.
A line passes through (1, –5) and (–3, 7). Write the equation of the line in all three forms.
(4 points)
What happens to the graph of y = 4x – 1 if the constant is changed?
(1 point)
A. The line will pivot
B. The line will move vertically
C. The line will remain the same
D. There is not enough information
3.
What happens to the graph of y = 6x + 2 if the coefficient is changed?
A. The line will pivot
B. The line will move vertically
C. The line will remain the same
D. There is not enough information
4.
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
1
y =  x – 11
2
(1 point)
(1 point)
16x – 8y = –8
5.
Use the map to answer the following. Show your work.
a. City contractors would like to build a library on a road that is parallel to Fir Street at the
indicated spot. They will call that street Peach Street. What is the equation on Peach Street?
b. City contractors would like to build a gym on a road that is perpendicular to Elm Street at the
indicated spot. They will call that street Power Street. What is the equation on Power Street?
(3
points)
6. Bella wants to write two equations to model the streets on this map. She can use y = x – 4 to
describe Platte Way. Write one absolute value equation to describe Marteen Rd and Smith St.
(1 point)
y
5
St
4
Sm
it h
3
2
1
–3
–2
–1
–1
1
2
M
4
5
x
ay
te
ar
–2
3
en
W
–4
Rd
–3
–4
Pl
at
te
–5
–5
Solve the following systems by graphing.
7. y = x + 6
y = –2x – 3
(3 points)
8. y = ⅞x
y – 1 = ⅞(x – 8)
(3 points)
9. -4x + 3y = –12
-2x + 3y = –18
(3 points)
10. A local pizzeria sells a small pizza with one topping for $6 and a small pizza with three toppings
for $8. Write and solve a system by graphing to find the cost for a plain small pizza. What is the
charge for each topping? (Let x represent each topping and y the plain pizza.)
(4 points)
Solve the following systems by substitution.
11. y = 3x + 7
y=x–9
12.
-5x + y = -5
-4x + 2y = 2
13.
3x – 6y = 12
2x – 4y = 8
14.
7y = 7x + 28
3y – 12 = 3x
15. y – 2x + 3 = 0
9y = 18x – 27
(15 points)
16. Without graphing or substitution, decide whether the system has one solution, no solution, or
infinitely many solutions. Explain.
17. (a)
(b)
(c)
(d)
(e)
(f)
Make a scatter plot for the data in the table below.
Draw a trend line on your scatter plot.
Make 2 comments about the data set.
Write the equation of the line of best fit for the data below.
Calculate and interpret the value of the correlation coefficient
What would be the stopping distance at a speed of 40 mph?
Speed (mph)
10
15
20
25
m = nΣxy - Σx Σy
nΣx2 – (Σx)2
b = Σy – mΣx
n
Stopping distance (ft)
27
44
63
85
(1 point)
(3 points)
(1 point)
(1 point)
(3 points)
(1 point)
(1 point)