Standard 19.0

1
Standard 19.0

• Toni is solving this equation by completing the
  square. ax2 bx c 0 (where a 0)
• Step 1 ax2 bx - c
• Step 2 x2 b/ax - c/a
• Step 3 ?
• Which should be Step 3 in the solution?
• a) b)
• c)
• d)

2

• The key to answering this question is knowing the
  formula for completing the square
• The next step in completing the square is to add
  to both sides of the equation.
• By doing this, you will form a perfect square on
  the left side of the equation.
• At this point, solve the problem for the question
  is asking for step 3. ? d is the answer since
  it is the only one adding (b/2)2 to each side.
• The next two steps are to find the square root of
  each side and solve the equation.

3
Standard 19.0

• Four steps derive the quadratic formula are shown
  below.
• What is the correct order for these steps?
• I, IV, II, III
• I, III, IV, II
• II, IV, I, III
• II, III, I, IV

4

• You must first look over what they give you and
  what they ask you. The question is telling you
  that the quadratic formula is where you end up
  at.
• The question is also helping you on the test.
  Notice steps I and IV were in the previous
  question for completing the square. Use this
  to your advantage. Knowing those two steps and
  knowing the actual formula of
• is very close to step
  III (or
• where you want to end up at) you can assume step
  II is 3rd. ? a is the answer

5
Standard 20.0

• Which is one of the solutions to the equation
  2x2 x 4 0?
• a) b)
• c) d)

6

• Using the quadratic formula, solve.
• ? c is the answer

7
Standard 20.0

• 45. Which state best explains why there is no
  real solution to the quadratic equation
  2x2 x 7 0
• The value of 12- 4 2 7 is positive.
• The value of 12- 4 2 7 is equal to 0.
• The value of 12- 4 2 7 is negative.
• The value of 12- 4 2 7 is not a perfect
  square.

8

• 1st, this is a tricky question so you want to
  take it slow. You are dealing with a quadratic
  equation which means they are asking for what is
  inside the radical sign v in the quadratic
  formula.
• Taking what is inside b²- 4ac, you plug in the
  numbers given to solve. This step has already
  been done for you in the choices given.
• Begin eliminating what you know. If you find the
  value of the numbers given, a and b are false
  statements ruling them out.
• c and d are true statements (answer is -55).
  Now, if the discriminant is a negative number
  your answer is always no real solution.
• ? c is the answer

9
Standard 20.0

• What is the solution set of the quadratic
  equation 8x2 2x 1 0?
• a) b)
• c)
• d) No real solution

10

• Using the quadratic formula, you would plug in
  the values of a, b, and c.
• When you begin to solve you will notice the
  discriminant (b² - 4ac) is negative, this
  equation has no solution in the real number
  system.

? d is the answer
11
Standard 21.0

• The graph of the equation y x2 3x 4 is
  shown below.
• For what value of
• x is y 0?
• x -1 only
• x -4 only
• x -1 and x 4
• x 1 and x - 4

12

• The question is simply asking for the x value
  if y 0. In this case, the parabola intersects
  x in two places. Both places will be the value
  of x.
• Since the line intersects x in two places look
  at c and d first. At points (-1, 0) and (4,
  0), notice y equals 0 and the line intersects
  x.
• Therefore (?) x -1 and x 4 and your answer is
  c.

13
Standard 21.0

• 48. Which best represents the graph of y
  - x2 3?

14

• If the coefficient of x² is positive, the
  parabola (the u shaped line) opens upward, if
  it is negative it opens downward. In this case,
  its negative so c and d are eliminated.
• Finding the vertex (curve of the parabola).
• In this type of problem, if you are missing the
  bx, then c (3) will be your y-intercept.
• ? b is the answer

15
Standard 22.0

• 49. How many times does the graph of y 2x2 2x
  3 intersect the x-axis?
• none
• one
• two
• three

16

• With no negative sign in front of the
  coefficient 2 (2x2 2x 3) the parabola opens
  upward. With y being a positive number, the
  parabola will not intersect the x-axis.
• ? a is the answer

17
Standard 23.0

• 50. An object that is projected straight downward
  with initial velocity v feet per second travels a
  distances s vt 16t2, where t time in
  seconds. If Ramon is standing on a balcony 84
  feet above the ground and throws a penny straight
  down with an initial velocity of 10 feet per
  second, in how many seconds will it reach the
  ground?
• 2 seconds b) 3 seconds
• c) 6 seconds d) 8 seconds

18

• They give you the formula s vt 16t².
• You need to read and dissect the problem and
  place it into the formula.
• s 84 feet. Remember it tells you t
  represents seconds.
• vt 10 ft per second 10/1 (t is unknown)
• 16t² unknown seconds that the vt increased
  by time it hits the ground.
• ? , since you dont go back in time (negative
  number), your answer is 2 seconds or a.

19
Standard 23.0

• 51. The height of a triangle is 4 inches greater
  than twice its base. The area of the triangle is
  168 square inches. What is the base of the
  triangle?
• 7 in.
• 8 in.
• 12 in.
• 14 in.

20

• Using the formula A½bh, plug in the given to
  solve
• Set it up as a quadratic equation equal to 0.
• -14 is not an answer nor does it make sense to be
  an answer. 12, however is given.
• ? c is the answer

21
Standard 12.0

• 52. What is
  reduced to
• lowest terms.
• a)
• b)
• c)
• d)

22

• 1st, factor the numerator.
• Next, reduce the denominator by factoring out
  what is common, 3y.
• Finally, reduce what you have in common in the
  numerator and denominator.
• ? your answer is b

23
Standard 12.0

• 53. Simplify to
  lowest terms.

24

• After factoring you are left with answer b

25
Standard 12.0

• 54. What is reduced to
  lowest terms.
• b)
• c) d)

26

• UNFOIL or factor the numerator and denominator
• Reduce
• ? a is the answer

27
Standard 13.0

• 55.
• b)
• c) d)

28

• Factor, reduce, then multiply the (numerator
  numerator) and the (denominator denominator)
• ? a is the answer

29
Standard 13.0

• 56. Which fraction equals the product?
• b)
• c) d)

30

• To solve this problem you use FOIL for the
  numerators and denominators
• Numerators (x 5)(2x 3)
• Denominator (3x 2)(x 5)
• Numerator Denominator
• (x 5)(2x 3) (3x 2)(x
  5)
• 2x² - 3x 10x 15 3x² - 15x 2x - 10
• 2x² 7x 15 3x² - 13x - 10
• ? d is the answer

31
Standard 13.0

• 57.
• a) b)
• c) d)

32
? c is the answer.
33
Standard 15.0

• 58. A pharmacist mixed some 10 saline solution
  with some 15 saline solution to obtain 100 mL of
  a 12 saline solution. How much of the 10 saline
  solution did the pharmacist use in the mixture?
• 60 mL
• 45 mL
• 40 mL
• 25 mL

34

• Create a chart to keep track of all the
  information then set up equation to solve.
• The answer is 60mL
• ? a is the answer

35
Standard 15.0

• 59. Andys average driving speed for a 4-hour
  trip was 45 miles per hour. During the first 3
  hours he drove 40 miles per hour. What was his
  average speed for the last hour of his trip?
• 50 miles per hour
• 60 miles per hour
• 65 miles per hour
• 70 miles per hour

36

• Setup a chart to keep track of the given.
• Next, use what you know. The total trip is 180
  miles by using Rate Time Distance (rtd). Also
  using the same formula, Andy drove for 120 miles.
  To find the average speed for miles per hour you
  subtract the two distances.
• ? b is the answer

37
Standard 15.0

• 60. One pipe can fill a tank in 20 minutes,
  while another takes 30 minutes to fill the same
  tank. How long would it take the two pipes
  together to fill the tank?
• 50 min
• 25 min
• 15 min
• 12 min

38

• 1st, reduce your choices with what you know. You
  can eliminate a and b since one pipe alone
  can fill up the tank in 20 minutes, thus two
  tanks will not take as long. Then set up as
  fractions.
• 1 tank per 12 minutes. ? d is the answer

39
Standard 15.0

• Two airplanes left the same airport traveling in
  opposite directions. If one airplane averages 400
  miles per hour and the other airplane averages
  250 miles per hour, in how many hours will the
  distance between the two planes be 1625 miles?
• 2.5
• 4
• 5
• 10.8

40

• In finding distance the formula is rtd (rate
  time distance)
• 2.5 hours would be your answer. ? a is the
  answer

41
Standard 16.0

• 62. Which relation is a function?
• (-1, 3), (-2, 6), (0, 0), (-2,-2)
• (-2, -2), (0, 0), (1, 1), ( 2, 2)
• (4, 0), (4, 1), (4, 2), (4, 3)
• (7, 4), (8, 8), (10, 8), (10, 10)

42

• Knowing what a relation and a function are is
  key.
• A relation is grouping of inputs (x) with outputs
  (y) normally shown as ordered pairs (x, y).
• A function is a relation however, each input has
  only one output. No inputs will be used twice.
• Notice in a, -2 is used twice, c 4 is used
  more than once, and d 10 is used twice. Only
  b does not have a repeating input. Perform the
  vertical line test to verify.
• ? b is the answer

43
Standard 17.0
63. For which equation graphed below are all the
y-values negative?
44

• This is the type of problem you want to do
  quickly and not over think it.
• Notice the question asked for the y-values that
  are all negative. To solve, you look at the
  lines in the graphs. In short, if the line goes
  above or on the x-axis it is not the answer.
  Thus, answers b, c, and d all go past the
  x-axis. When they do this y 0 (y is greater
  than or equal to zero) making those three choices
  incorrect.
• ? a is the answer

45
Standard 17.0
64. What is the domain of the function shown on
the graph below?

• -1, -2, -3, -4
• -1, -2, -4, -5
• 1, 2, 3, 4
• 1, 2, 4, 5

46

• This problem is clearly a trick trying to
  determine if you know the difference between
  domain (its x) and range (its y). (x, y)
  or (domain, range)
• Now, knowing that domain is x, and all the
  points are to the right of zero (positive
  numbers), answers a and b are eliminated
  (negative numbers)
• Then use what you see. There is a point at
  (5, -2). Answer c has no 5 while d does.
• ? d is the answer