Algebra Final

Allison Levin   May 7, 2001

 

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

  2) Solve: 4x–3x=9

a. 12                           b. -12

c. 9                             d. 3

  3) Solve to find what n equals: -2(3–n)=12(4n–2)

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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y

 

 

 

 

 

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x

 

 

 

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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

  6) Identify the line:

 

 

 

 

 

 

3     2      1

 

3

 

2

 

1

 

                  

 

-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

 

  8) Find the slope of these points: (9,9)(8,2)

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

 

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