Algebra Final
Allison Levin
Directions:
Circle the correct answer choice
1)
Evaluate the expression: 3x·2y+7 when x=2 and y=1
a.
19
b. 13
c. -13 d. -19
a.
12
b. -12
c.
9
d. 3
a.
3
b. 4
c.
-3
d. 0
4)
Solve for y: 12x–4y= 24
a.
-y=3+6x
b. y=6–x
c.
y=6+x
d. y=3x+-6
5)
Using the scatter plot below, which of these is true:
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a.
x increases as y increases
b. y decreases as x increases
c.
x decreases as y decreases d.
there is no correlation
3 2 1 |
3 2 1 |
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-1 -2 -3 |
a.
y=1
b. y=3
c.
y=-2
d. y=2
7)Find the equations for the horizontal and vertical lines that
pass through this point: (9,78)
a.
x=78 y=9
b. y=-78 x=9
c. x=9 y=78 d. x= -9 y=78
a.
m= 7
b. m=1/7
c.
m= -7
d. m= -1/7
9) Find the slope and y intercept of these points: (8,4) (7,3)
a.
y=x+4 b.
y=2x+2
c.
y=x-4
d. y= -2x-2
10) If the year 1980 (x) corresponds to zero, put these points in
slope-intercept form: (1985,30) & (1990,40)
a.
y= 2x+ 30 b. y=2x+40
c
y= 2x+ 10 d. y=2x+20
11) If the year 1000 (x) corresponds to zero, turn convert the
numbers into ordered pairs: 1998, 76 & 1000,89 & 1023,42
a.
(98,76), (0,89), (23,42)
b. (998,76), (0,89), (23,42)
c.
(998,76), (100,89), (123,42)
d. (8,76), (1,89), (3,42)
12) Solve the inequality: x-9< 8-9
a.
x<0
b. x<8
c.
x<1
d. x<9
13) Solve the inequality: 6x>36
a.
x>6
b x>-39
c.
x>36
d. x>-6
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14) Which of these is the correct inequality for this number line:
a.
1£x<8
b. 1³x>8
c.
1<x<8
d. 1>x>8
15) Which of these ordered pairs are solutions of the inequality:
2x-3y£4
a.
(2,1) & (3,1)
b. (3,0) & (2,1)
c.
(0,2) & (2,1)
d. (0,1) & (4,0)
16) Use substitution to solve this system: y=x+4 & 3x+y=16
a. (4,4)
b. (8,2)
c. (13,1)
d. (3,7)
17) Which ordered pair is a solution to all of the systems of
linear equalities:
x+y< 2, x-y> 0 and y > -2
a.
(4,3)
b. (1,1)
c.
(1,0)
d. (3,4)
18) Simplify: (5²)²
a.
625
b.620
c.
20
d. 60
19) Rewrite the scientific notation in decimal form: 4.56 x 10^6
a.
4,000,056
b. 456,000,000
c.
4,560,000
d. 4,500,000
20) If the hypotenuse of a right triangle is 10 inches, and one of
the sides is 6 inches, the length of the other side is:
a.
8meters
b. 8 inches
b.
64 meters
d. 64 inches
21)
When using a parabola, which of these statements is false:
a. If a is positive, the parabolas open up
b.
On a parabola that opens up, the lowest
point is the vertex
c. If a is negative, the parabola opens down
d.
On a parabola that opens down, the lowest point is the vertex
22) Subtract the polynomials: (5x^4-2x+7)-(-3x^4+6x^2-5)
a.
8x^4-6x^2-2x+12
b. -8x^4-6x^2+12
c.
2x^4+6x-2x+2
d. 8x^4+6x^2-14x
23) Multiply the polynomials using the distributive property:
(x-3)(3x+1)
a. 3x+8x+3
b. 8x-3
c. -3x- 8x-3
d. 3x ²-8x-3
24) Multiply the polynomials using FOIL: (3x+5)(2x+1)
a.
5x²+10x+5
b. 6x²+13x+5
c.
-6x²+ 13x-5
d 6x+ 13-5
25) Multiply the polynomials using Special-Product Patterns:
(x-7)(x+7)
a.
x=49
b x²+49
c.
x-49
d. x²-49
26) Factor the expression: y²-144
a.
y-12
b.2y-144
c.
y-144
d.2y-12
27) Find the greatest common factor (GCF): 6, 30, 12
a.
3
b. 8
c. 6
d. 30
28) Find the mean of these numbers: 8, 14, 6,12, 6, and 32.
a.12
b. 13
c.
10
d. 11
29) Billy-Bob-Joe forgot to study for his algebra final. He has to
guess on all the multiple choice questions. There are four choices for each
question What chance is there he
will get the first questions right?
a.
1/4
b.1/16
c.
1/8
d.½
30) Find the median of these numbers: 54, 23, 83, 76, 43
a.
54
b. 83
c.
43
d. 23
Explanations
1)EXPLANATION: 3·2=6;
2·1=2; 6·1=6+7=13
2)EXPLANATION: 4x–3x=1x; 1x=9; x=9
3)EXPLANATION: I used the distributive properties to distribute the
-2 and the 12.
Then I added -2n to both sides.
4)EXPLANATION: add 4y to both sides, divide by 4, subtract 6.
5)EXPLANATION: as the y side becomes lower, the x side becomes
higher
6)EXPLANATION: the horizontal line runs across the point (x,2)
therefore, it the line runs across point y 2
7) EXPLANATION: (9,78) The x-place is 9 and the y-place is 78,
therefore, x=9 and y=78
8)EXPLANATION: (9,9)(8,2) 9-2= 7, 9-8=1; 7/1=7
9)EXPLANATION: 4-3=1, 8-7=1; 1/1=1...... 4+4=8 or 3+4=7
10)EXPLANATION: 1990=10 and 1985=5; (5,30) and (10,40). Therefore,
40-30= 10 and 10-5=5: 10/5=2.........2(5)+20=30 or 2(10)+20= 40
11)EXPLANATION: 1000=0, therefore, 1998=998, 1000=0 and 1023=23.
Nothing happens to the y-intercept so, (998,76)(0,89)(23,42)
12)EXPLANATION: x-9<8-9; 8-9= -1; x-9<-1; add the nine
(because it’s a negative, and you need to cancel out) and you get x<8
(9+-1=8)
13)EXPLANATION: 6x>36; simplify by dividing by 6; x>6
14)EXPLANATION: since there is a closed circle on 1 and an open
circle on 8, there is a £ and a < sign. 1 is less than 8, so the answer is 1£x<8
15)EXPLANATION: when you plug the numbers into the equation, you
get 2(0)-3(2) and 2(2)-3(1) which equal -6 and 1 which are both less than or
equal to four
16)EXPLANATION: Put x+4 in the place of y, and solve. Then put your
answer for y into y=x+4. Solve, and you have (3,7)
17)EXPLANATION: Replace x and y with the ordered pairs, and find
the one that fits the equation (1,0) that is your answer
18)EXPLANATION: Because (5²) is in parenthesis, you multiply the
exponents and have 5^4. Solve, and you have 625
19)EXPLANATION: Simply multiply 4.56 by 10^6. Put .56 over the
decimal point, and then multiply by 10000. (Or just multiply by 1,000,000)
20)EXPLANATION: Use the three, four, five theory. Ten is 5·2, and
Six is 3·2. Therefore, the missing side must be 4·2, or Eight.
21)EXPLANATION: Pg. 465 of Algebra 1 gives the basic rules
of parabolas. It states that on a parabola that opens down the highest
point is the vertex.
22)EXPLANATION: 5x^4–3x^4 is really 5x^4 + 3x^4. 0-6x² is -6x²,
-2x-0 is -2x and 7–5 is 7+5 or 12.
23)EXPLANATION: The problem is now x(3x+1) -3(3x+1), or 3x²+1x-9x-3,
or 3x²-8x-3
24)EXPLANATION: Using FOIL ( multiplying the First , the Outer
numbers, the Inner numbers and the Last numbers) My problem is now 6x²+3x+10x+5,
or 6x²+13x+5
25)EXPLANATION: In this problem, because of the positive and
negative 7, the middle drops out. Therefore, my answer is x²-49
26)EXPLANATION: To factor the expression, you just find the square
root of the numbers, you get y-12
27)EXPLANATION: The greatest common factor is 6 because it goes
into itself, 12 and 30. Because it goes into itself, and it is in the problem,
six is the highest answer possible.
28)EXPLANATION: To find the mean of the numbers you add them up,
and divide them by the number of numbers there. You needed to add up all the
numbers and divide by six, because there were six numbers there.
29)EXPLANATION: Because you can only have one right answer, and
there were four choices, the probability Billy-Bob-Joe will guess correctly is
1/4
30)EXPLANATION: To find the median you put the numbers in order and
find the one in the middle. That would be 54