Algebra 1 Final Exam

Directions:  For Questions 1-30, write the letter for the correct answer in the corresponding blank at the bottom of the page.

1.       Laura is traveling from Maryland to Virginia by car at a constant speed of 50 MPH for one and one half hours.  How far has Laura traveled?

a.      75 miles                                                  c.  51.5 miles  

b.     100 miles                                                d.  85 miles

2.     A jar contains 4 navy beans, 6 lima beans, and 1 lentil.  What the probability of pulling out a navy bean?

a.      1/11                                                        c.  6/11

b.     4/11                                                        d.  7/11

3.     An unidentified marine organism weighs about 0.000256 ounces.  How much does it weigh in scientific notation?

              a.  2.56 x 10⁵                                                  c.  25.6 x 10⁴

              b.  2.56 x 10^-4                                                d.  25.6 x 10^-5

4.     Subtract (–5x⁴ + 3x² – 8) from (2x⁴ + x² – 10).

              a.  –3x⁴ + 4x² - 18                                          c.  7x⁴ + 4x² – 18

              b.  –2  – 2x² + 7x⁴                                          d.  7x⁴ – 2x² – 2

5.     How long is the hypotenuse of a right triangle with legs of 10 cm and 15 cm?

a.  18.03cm²                                                        c.      cm        

b.  25 cm                                                d.  cm

6.  Multiply (x + 3)(x - 2) using FOIL.

                  a.  x² – x – 6                                               c.  2x + x – 5

                  b.  x² – x – 5                                              d.  x² + x – 6

      7.  Distribute (x² + 4 – 2x)x.

                 a.  x³ – 2x² + 4x                                          c.  x³ –2x² + 4

                 b.  x³ – 2x² + 4x                                         d.  x² – 2x + 4x

      8.   Which of the answers below is a solution to 5x – 5y ≥ 25?

                  a.  (2, 5)                                                     c.  (10, 5)

                  b.  (1, 5)                                                     d.  (-2, 3)

      9.  Solve ⅛x + 2 = 20.

                  a.       x= 2.5                                                  c.  x = 144

                  b.      x = 10                                                  d.  x = 12

   10.   Solve the linear system   3x + 9y = 27 and x + 7y = 17.

                  a.  (3, 2)                                                     c.  (2, 2.3)

                  b.  (-1, 9)                                                   d.  (10, 0)

   11.   Write the slope-intercept form of the equation of the line that passes through the points (1, 2) and (2, 4).

                  a.  y = 2x + 1                                          c.  y= 2x

                  b.  y = ½x                                               d.  y = ½x + 1

   12.   Write (x + 5)² as a perfect square trinomial.

                  a.  x² + 25                                               c.  x + 5x + 25

                  b.  x² + 25x + 25                                     d.  x² + 10x + 25

    13.  Solve for k.  (-2k = 16k – 9)

  a.  k = ½                                                 c.  k = -½k

  b.  k = 12                                                d.  k = 3.5  

    14.  Simplify (5³ x 5²).

  a.  5⁵                                                       c.  3125

  b.  15625                                                d.  (25³)²

                    a.  x is between -1 and 4 (both open circles)

                    b.  x is between -1 (open circle) and does include 4 (closed circle)

                    c.  x is between -1 and 4 (both closed circles)

                   d.  x is less than -1 (open circle) and greater than 4 (closed circle)

     16.  Which of the following equations matches the graph of a vertical line on x = 5?

                    a.  x = 5                                                    c.       x = y

                    b.      y = x                                                   d.      y = 5

     17.   As the years go by, more homes are built in the city of Flügaken, Iceland.  Using the chart below, construct a scatterplot and write an equation to represent your findings.

                     a.  y = 1.85x – 3600.6                             c.  y = x + 25

                     b.  y = 2x – 85.6                                     d.  y = 1.85x – 85.6

     18.  Using linear combination, solve the system x + 3y = 2 and -x + 2y = 3.

                     a.  (3, 3)                                                  c.  (1, -1)

                     b.  (2, 1)                                                  d.  (-3, 2)

     19.  What is the slope of a linear equation if to locate the next point you must run to the right 4 units and rise 4 units?

                    a.  1                                                         c.  (-1)

                    b.  2                                                         d.  3

     20.  Factor x² + 18x + 81.

a.  x(x + 18) + 81                                   c.  x - 4²

b.  3x + 2²                                              d.  (x + 9)²

     21.  Match the description of a parabola with a minimum of (0,3) to its correct equation.

a.       y = 2x + 2                                        c.       y = -x² – 2x + 3

b.      y = x² – 2x + 3                                d.   y =  4 – 2x   

     22.  Solve for h:  A = ½bh.

a.  h = 2a/b                                             c.  h = b2a

     23.  Match the correct linear inequalities with the graph of the first being shaded to the right with a solid line and the second with a dashed line and shaded to the right.

a.  2x + y ≤ 4                                          c.  2x + y < 4

     x + 2y > -4                                            -2x + y ≤ 4

b.  x + 2y > 4                                          d.  2x + y ≥ -4

    -x + 2y < 4                                              x – 2y < 4

     24.  Find two solutions to the equation y = 4x – 8.

a.  (2, 0) (3, 0)                                        c.  (-1, 5) (6, 16)

b.  (4, 8) (6, 16)                                      d.  (6, 16) (0, 0)

     25.  Sketch the graph to the linear inequality y ≤ x + 3.

                     a.  A solid line shaded to the right.

                     b.  A solid line shaded to the left.

                     c.  A dotted line shaded to the right.

                     d.  A dotted line shaded to the left.

     26.  Write an equation for the line passing through the points (0, 4) with a slope of two.

   a.  y = 2x + 4                                       c.  y = 2x

   b.  y = 4x – 8                                       d.  y = 4x + 2

     27.  Solve the inequality 2x – 4 ≥ 8.

   a.  x ≤ -6                                              c.  x ≥ 8

   b.  x > 6                                               d.  x ≥ 6

     28.   Which of the descriptions is logical and has positive correlation?

a.  As the time you spend playing video games increases, your grade on the final decreases.

b.  The greater the height in inches, the greater the grade on the final increases.

c.  As the time you study for the final increases, the grade increases.

d.  As the time you study for the final increases, the grade decreases.

     29.  Rewrite 5.2 x 10³ in decimal form.

a.  5200.0                                               c.  521003.0

b.  0.0052                                               d.  10.520

     30.  Using the data below, construct a box and whisker plot and figure out the median.  Data:  3, 6, 8, 7, 5

a.  8                                                        c.  6.5

b.  5.5                                                    d.  6

Answer Key - Letters

1. A
2. B
3. B
4. D
5. A
6. D
7. B
8. C
9. C
10. A
11. C
12. D
13. A
14. B
15. B
16. A
17. A
18. C
19. A
20. D
21. B
22. A
23. D
24. B
25. B
26. A
27. D
28. C
29. A
30. D

Answer Key - Explanation

1. You can solve this problem and get “a” as your answer by using the distance formula (d = rt).  The rate of travel is 50 mph.  The time is one and one-half hours, written simply as 1.5.  When these two numbers are multiplied, they equal the distance, or 75 miles.
2. You can solve this problem by first finding the total number of beans, which is 11.  Then you find how many beans are the favorable outcomes, 4 in this case.  4 goes over 11 because 11 is the total, and you therefore get 4/11. 
3. I solved this problem by moving the decimal for spaces to the right (getting the exponent 10^-4) and the decimal 2.56.  According to my prior knowledge, scientific notation is written as 2.56 x 10^-4, so that is your answer.
4. I solved this problem by first distributing the negative sign to the second parenthesis and combining like terms.  I then put the answer into standard form.
5. Squaring each leg and then adding them can solve this problem.  After that is done, you find the sum’s square root, which you round to the nearest hundredth, and you get 18.03 cm² as your answer.
6. I solved this problem by using FOIL.  FOIL stands for first, outer, inner, and last.  You would multiply the first two numbers in each parenthesis then the first one in the first parenthesis by the second (or outer) one of the second parenthesis.  Then, the inner numbers are multiplied (the ones from each parenthesis that face each other). After this the second number in the first parenthesis is multiplied by the second number in the second parenthesis, or the last number.  The answer is simplified to the final answer, x² + x – 6.
7. This can be solved by distributing x to the terms in the parenthesis.  When this is done, the answer is x³ – 2x² + 4x because the answer must be written in standard form.
8. Plugging in the x and y coordinates can solve this problem, and then you see which one is greater than or equal to 25.
9. I solved this problem by first taking two from each side, so ⅛x = 18.  Then I divided ⅛ from each side to isolate the variable x.  When this was done, x = 144.
10. To solve this problem, you can simplify the second equation.  This is done by subtracting 7y from each side because x is already isolated.  Next, you plug in the new equation wherever x appears.  You simplify, solve for y, and plug y into the x = equation wherever y appears.  Finally, simplifying and solving for x gives you your answer, (3, 2).
11. I calculated the slope to solve this problem.  I plugged both points into the above equation appropriately than simplified.  That is the slope.  Then, using another equation (y = mx + b), I plugged the slope and one point into that equation.  Afterwards, I solved for b.
12. You can write (x + 5)² as a trinomial by first adding 5 to x and doubling it to get 10x.  Then you distribute ² to everything BUT 10x.

13. This problem can be solved by subtracting 16k from both sides, which gives  you –18k = -9.  Then, to isolate k, you divide –18 from both sides and the    quotient is ½.

14. Because the bases are the same, you can first add 5³⁺² to solve this problem.  The simplified exponent is 5⁵, and when further simplified your answer is 3125.

 15.  This problem is solved realizing that one line would be 4 and over with a full         dot and the other would be less than –1 with an empty dot.  I matched this         information with the graph to solve.

 16.   I first realized that the line was vertical, so it’s equation would be  x =.  Then,          I counted what line this line was located on and discovered it to be positive         5.  Therefore, x = 5.

 17.  I solved this problem with my calculator.  In a series of steps, I first entered         the data, made sure the plots were on then graphed.  I then went back to the        “stat” button and found the information to create my equation.

 18.  I used the vertical method of combination to solve this problem.  Both of the         x’s cancel each other out than you are left with 5y = 5.  Next, you would          simply divide both sides by 5 to isolate y and get    y = 1.  After this you plug         y = 1 into the 1^st equation wherever there is a y.  After simplifying, you are left        with x = -1, or (-1, 1).

 19.   I solved this problem by counting the rise and run of the line.  I then put the         rise over the run, simplified, and figured out that the answer is 1.

 20.  I solved this problem by factoring.  In other words, I found the greatest             common factor, which was 9.  Ten, I found the square root of x², which is         x.  I added these together in a parenthesis with ² outside of it.  ((x + 9)²).

21.  To solve this, I took one pint and plugged it into all the equations.  After doing        this, I knew the one that was correct with this point (ex. 1, 2) was correct.  I        graphed it on my calculator and looked at a table of values to check for other        points to make sure my calculations were correct.

22.  I solved for h by isolating it.  To do this, I had to first divide b from both sides,       leaving me with a/b = ½h.  I then multiplied both sides by two to cancel out the       denominator, thus leaving me with 2a/b = h.

23.    The first step I took to solve this was to plug in was to see which ones were        eligible to be answers because of shading.  After this elimination, I examined        the equations to see if the lines were negative, dotted, or solid.  Following this,         I then eliminated more.  With the ones left, I typed the equations into my           calculator and matched the correct one with the first graph. 

24.    I made a table of values to find the solutions (see fig. 1).  I simply chose a few numbers to be x, then plugged them in to find y.  I noticed a pattern and examined the selection of possible solutions and noticed one had the correct pattern.

 25.   I used my calculator to sketch this graph.  I first turned the calculator and pressed the “y =” button.  Next, I plugged in the equation and chose the correct shading (left and down for this problem) then graphed it.  I matched that graph to the one on the answer sheet.

 26.  This problem was actually very easy to solve.  I simply substituted the point and slope for y = mx + b, so it was then 4 = 2(0) + b.  Then I multiplied 2 by 0, subtracted that from 4 and got the answer y = 2x + 4.

27.  To solve the inequality 2x – 4 ≥ 8, I had to add 4 to both sides first.  Afterwards, I divided two from both sides and received x ≥ 6 as my answer. 

28.  I solved this problem by using my prior knowledge about correlation.  I knew that positive correlation forms what looks like a positive line, like a constellation that looks like a dipper.  I searched for the one with this type of correlation and found C to be the correct answer.

29.  5.2 x 10³ can be written in decimal form by moving the decimal three spaces to the right (thus, adding 2 zeros).  After doing this I added one zero after the decimal and transformed it back into scientific notation to make sure it was true.