UCS JH Algebra I SEM2 REVIEW GUIDE #1 SUGGESTED QUESTIONS
1 / Suppose you invest $1500 in an account paying 4.75% annual interest.Find the account balance after 25 yr with the interest compounded the
following ways.
a. annually b. semiannually c. quarterly d. monthly
Standard: A.SSE.1b / a) $4785.66
b)$4850.51
c)$4884.02
d)$4906.79
2 / Mrs. Anderson and her students have been creating patterns and finding rules to describe those patterns.One pattern thatthey created using triangles is shown below.
Write an explicit formula that Mrs. Anderson and her studentscan use to find the number of triangles in the pattern at the nth stage?
Standard: F.BF.1a / Answer:
3 / The sign below shows the costs for one pizza with toppings.
Number of
Toppings / Cost
1 / $4.75
2 / $6.00
3 / $7.25
4 / $8.50
5 / $9.75
Standard: F.LE.2 / Answer: a1 = 4.75
at = at-1 + 1.25
4 / A rectangle has sidesand .If is theperimeter of the rectangle, what is the coefficient ofin ?
Standard:A.SSE.1a (Quad) / Answer:2
5 / What is the greatest common factor of the terms of ?
Standard: A.SSE.2 (Quad) / Answer:
6 / A rectangular plot of land has an area ofsquare yards. What are the dimensions of the plot of land?
Standard: A.SSE.3a / Answer:
7 / Write a quadratic function, in both standard and factored form, with x-intercepts at and
Standard: A.SSE.3a / Answer:
Factored Form:
Standard Form:
8 / A quarterback throws a football across a field. The equation models the path of the ball while it is in the air, where is the height of the ball in feet and is the time in seconds. What is the maximum height reached by the ball?
Standard: A.SSE.3b (Quad) / Answer:12.25 ft
9 / A rectangular flower box measures 7 feet by 5 feet. If each side of this flower box is extended by feet, what will be the area of the new box?
Standard: A.APR.1 (Quad) / Answer: square feet
10 / You are building a rectangular wading pool. You want the area of the bottom to be 90 ft2. You want the length of the pool to be 3 ft longer than twice its width. What will the dimensions of the pool be?
Standard: A.CED.1 / Answer: 6 by 15
11 / What is the vertex form of the equation of the function graphed below?
Standard: A.CED.2 / Answer:
12 / The volume of wax used in making a cylindrical candle is given by the formula .What is the height of the candle in terms of the volume and radius?
Standard:A.CED.4 / Answer:
13 / Solve the quadratic by completing the square:
Standard:A.REI.4a / Answer:
14 / Below is the formula for figuring the time it takes for an object to fall when dropped. The time in seconds is represented by , and is the height in feet from which the object is dropped.
If you drop your least favorite music CD from a height of 40 feet, how long will it be before it hits the ground?
Standard: A.REI.4b (Quad) / Answer: 1.58 Seconds
15 / The path of a golf ball can be modeled by the equation , where is the initial velocity, and is the initial height. When will the ball hit the ground if the initial velocity is 20 ft/s and the initial height is 6 ft.
Standard:A.REI.4b / Answer: 1.5 seconds
16 / Solve the following system of equations algebraically and check.
Standard:A.REI.7 / Answer: (1,8) and (-3,4)
17 / x / y
-2 / -26
-1 / -2
0 / 6
1 / -2
2 / -26
Is the following data linear, quadratic, or neither? If linear or quadratic, find the function rule that models the data.
Standard:A.REI.10 / Answer: Quadratic
18 / Given the zeros of –5 and 3, find the following (assume a=1):
- Factored Form of the equation
- Standard Form of the equation
- Coordinates of the Vertex
- Vertex Form of the equation
- Axis of Symmetry
- Is the Vertex a Max or Min
- The y-intercept
Standard: F.IF.4 / Answer: a) y=(x+5)(x–3)
b)
c) (-1, -16)
d)
e)x=-1
f) min
g) -15
19 / A student launches a rocket into the air. The parabola below shows the height of the rocket in feet. Write an expression to describe the domain for this situation.
Standard: F.IF.5 / Answer: all real numbers between 0 and 8 inclusive
20 / What is the minimum point of the graph of the equation ?
Standard:F.IF.7a / Answer: (-2,1)
21 / The graph of is shown below. Use the method of completing the square to re-write in vertex form and identify the vertex and axis of symmetry.
Standard: F.IF.8a / Answer:
Vertex (2,2) Axis of Symmetry x=2
22 / What could be a possible equation for the graph given the graph at the right?
Write the results in factored form and standard form.
Standard: F.IF.8a / Answer:
23 / Karatranslated theparent function, . Write an equation for each situation below.
- up 10 units
- down 16 units
- wider than the parent function and opens up
- more narrow than the parent function and opens down
- up 5 units and left 3 units
- reflected over the x-axis
Standard:F.BF.3 / Answer: a.
b.
c. anything with “a” being
d. anything with “a” being
e.
f.
24 / Write as a complex number in the form a + bi.
Standard: N.CN.1 / Answer: 2 + 8i
25 / What is the value of
Standard: N.CN.1 / Answer: 7i
26 / What is the sum of the coefficients of the following polynomial:
Standard: A.SSE.1a / Answer: 1
27 / Factor
Standard: A.SSE.2 / Answer:
28 / Graph these two functions on the coordinate place and find the solutions.
Standard: A.REI.11 / Answer:
29 / State the domain and range for the following function.
Standard: F.IF.1 / Answer: D: All Real Numbers
R: y
30 / Suppose a football player kicks a ball and gives it an initial upward velocity of 47 ft/s. The starting height of the football is 3 ft. Where is the football after 1 second? Where is the football after 2 seconds? When will the football hit the ground?
.
Standard: FIF.2 / Answers:
1sec: 34ft
2sec: 33 ft.
Ground: 3 sec
31 / Solve using the Quadratic Formula:
Standard: A.REI.4b / Answer: (2.13, 0) and (0.12, 0)
32 / Match each equation with the correct answers.
1. / Crossing zeros: -2 / Touching zeros: 6, -4 / y-intercept: -16
2. / Crossing zeros: 6, -4 / Touching zeros: -2 / y-intercept: -16
3. / Crossing zeros: -6, 4 / Touching zeros: 2 / y-intercept: -8
4. / Crossing zeros: 2 / Touching zeros: -6, 4 / y-intercept: -32
A / / C /
B / / D /
Standard:F.IF.7c & A.APR.3 / Answer: 1--B ; 2--D ; 3--C ; 4--A
33 / Given the equation
a) State the crossing zeros
b)State the touching zeros
c)State the end behavior
d)State the y-intercept
e)Sketch the graph
Answer a) -1
b) -4,-4,3, 3
c)
d)12
e) use your graphing calculator to show graph.
Standard: FIF.7
34 / Based on her data,Janice expects20 out of135 high school centers at abasketball tournamentto be at least 80 inches tall.
Is this a valid inference? Explain your reasoning.
Use words, numbers, and/or pictures to show your work.
Standard: S.I.D. 1 / SCORING RUBRIC
Correct Answers:
•Her inference is incorrect. According to the data, about 27 centerswould be expected to beat least 80 inches tall.
•Note that the graph provides the following information:
•There are 2 players who measure between 60and 64 inches.
•There are10 players who measure between 65 and 69 inches.
•There are21 players who measure between 70and 74 inches.
•There are 23 players who measure between 75and79 inches.
•There are 12 players who measure between 80and 84 inches.
•There are 2 players who measure between 85and89 inches.
•That means that there are14 centers (12 + 2 = 14) out of 70 centers in all(2 + 10 + 21 + 23+ 12 +2 = 70) who measure 80 inches or greater. As a percentage, this can be expressed as:
•
•So, based on Janice’s results, sheshould expect 20% of the 135 high school centers at a basketball tournament to be at least 80 inches tall. Since 20% of 135 = (0.20)(135) = 27,that means that 27 centers out of the groupcan be expected to be at least 80 inches tall.
35 / This table shows the maximum speed, in miles per hour,ofsix different animals.
Which animal’s speed is closest to the mean speed.
Standard: SID.2 / Answer: coyote at 43 mph
36 / Alicia is training to run in a marathon. The table shows how far she ran each day last week.
Alicia found the mean, median, and mode of the distances she ran. On Sunday, she did not run at all. If she includes Sunday’s distance (0 kilometers), what will be the effect on the mean, median, and mode?
Standard: S.ID.3 / Answer:The median and mode will stay the same, while the mean will decrease.
37 / A mathematics teacher recorded the gender and hair color of all the students in two of his classes as shown below.
What percentage of the male students have red hair?
Standard: S-ID.5 / Answer: 14.7%
38 / The box and whisker plot shows the weight distribution among 200 professional football players.
Give the BEST estimate for the number of players that weigh less than 210 pounds.
Standard: S.ID.1 / Answer: 50
39 / Atable and a scatter plot ofthe same datashowing the length of timeseveral people studied for a test and the corresponding gradeeach of them received are shown below.
What is the approximate correlation coefficientof the linear model for this relationship?
Standard: S.ID.8 / Answer: 0.91
40 / Both Adam and Bethany have cell phones, but they have different cell phone carriers. On Saturday, they each used their cell phones to call home. This graph shows Adam’s phone (phone A) and Bethany’s (phone B) cell phone charges for these calls.
What is the difference between the charges per minute of the two cell phone carriers?
Standard: S.ID.7 / Answer: $0.25
41 / The table below show both Average Daily Ice Cream Sales and Average Daily Pool Attendance for a swimming center by month. The graph below shows Average Daily Ice Cream Sales versus Average Daily Pool Attendance. The correlation coefficient for this graph is 0.99. Is there a causation or correlation or both or neither.
Jan / Feb / Mar / Apr / May / Jun / Jul / Aug / Sep / Oct / Nov / Dec
Average Daily Pool Attendance / 212 / 231 / 328 / 503 / 704 / 821 / 834 / 798 / 646 / 522 / 231 / 198
Average Daily Ice Cream Sales / 70 / 82 / 101 / 165 / 232 / 270 / 278 / 297 / 211 / 179 / 70 / 64
ANSWER: There is a correlation because the warmer the weather more people may want to swim and have ice cream. No Causation, just because you go to the pool, does not mean you will buy ice cream.
Standard: SID 9
42 / A vending machine owner tested different prices for a 20-ounce bottle of water to see how much profit could be made. This scatter plot shows the different prices and the quantity sold at each price.
Use the ordered pairs (0.50, 500) and (1.50, 200) to find the line of best fit. Use your equation to predict the quantity if the price is $0.25.
Standard: S.ID.6 / Answer: y = -300x + 650; 575