This exam was adminstered in January 2025.
January 2025 Algebra, Part II
Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.
25. The graph below models Sally’s drive to the store.
State an interval when Sally is traveling at a constant speed.
Explain your reasoning
Answer:
Sally's spped is the y-coodinate, so a constant speed means a horizontal line, not a line with a constant slope.
From 5 hours to 9 hours, Sally is driving at a constant speed of 35 mph as indicated by the horizontal line. The rate of change is 0.
26. Graph the function f(x) = x2 + 4x + 3.
Sate the equation of the axis of symmetry of f(x).
Answer:
Use your calculator to find the table of values for the parabola. The axis of symmetry is the vertical line that goes through the vertex of the graph and has the equation x = -b/(2a).
The following points are on the graph (-4,3), (-3,0), (-2,-1), (-1,0) and (0,3). Plot these and draw the curve. Remember to put arrows at the end because the graph continues upward.
The access of symmetry is x = -4/(2(1), which is x = -2.
This question is only worth two points, so if you gave the vertex instead of the axis, you didn't get any credit.
27. The function f(x) is shown in the table below.
State an appropriate value for m in the table, so that f(x) remains a function. Explain your reasoning.
Answer:
The relation is a function as long as the x values do not repeat. (Again! I wrote this very same comment in June 2024 and August 2024 for Question 27!)
Therefore, m can have any value except 0, 1, 2, 3, 4, 5, or 6, which are already used. Valid values include 7, 8, 9, or larger; -1, -2, -3, or lower; 1.5, 6 1/2, π.
You are not being asked to define the function or predict what the next value should be.
Reason: the number you selected has not already been used in the table as a value of x. The values of x cannot be repeated in a function.
28. Solve x2 + 8x = 33 for x by completing the square.
Answer:
You must complete the square. Any other method, so long as it yields the correct answer, is only worth 1 point.
The square of a binomial, such as (x + n)2, looks like x2 + 2n + n2. So the middle term of the quadratic expression is 2n and the original n is half as much.
Half of 8 is 4, so the binomial that is being squared is (x + 4).
If you square (x + 4), you get x2 + 8x + 16, so to "COMPLETE THE SQUARE", we need to add 16 to both sides of the equation: x2 + 8x + 16 = 33 + 16.
Factor this into: (x + 4)2 = 49.
Now you can solve this:
(x + 4)2 = 49
x + 4 = + 7
x = 7 - 4 or x = -7 - 4
x = 3 or x = -11
29. If f(x) = (-3x - 5)/2, algebraically determine the value of x when f(x) = -22
Answer:
Note that the problem does NOT say x = -22, what is f(-22)? The question says if f(x) = -22, then what is x?
Replace f(x) with (-3x - 5)/2 in the equation, like this:
-3x - 5 = - 44
-3x = -39
x = 13
If you evaluated f(-22) = 30.5, you received half credit.
30. Rationalize the denominator of the fraction below. Express the solution in simplest form.
Answer:
Multiply the fraction by √(2) / √(2) to rationalize the denominator, and then reduce the fraction.
4 / √(2) * √(2) / √(2) = 4 √(2) / 2 = 2 √(2)
End of Part II
How did you do?
Questions, comments and corrections welcome.
I also write Fiction!The NEW COLLECTION IS AVIALABLE! A Bucket Full of Moonlight, written by Christopher J. Burke, contains 30+ pieces of short stories and flash fiction. It's available from eSpec Books! Order the softcover or ebook at Amazon. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants. |
 |
|
| My older books include my Burke's Lore Briefs series and In A Flash 2020. |  |
 |
|
If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you! |
 |
 |
No comments:
Post a Comment