SPRING FINAL Review Algebra I 2016

SPRING FINAL Review Algebra I 2016
1. (2A) Henry has $85.50 to spend on
candy at the store each month. What is
a reasonable range for this data?
2. (2I) Meg is making three placemats
for her table, all of them will be equal
in size and shape. If she lines the edge
of each of them with ribbon she will
need 80 inches of ribbon for the
perimeter of each placemat. She will
use 240 inches of ribbon for this
project. Write a system of equations to
represent this situation.
3. (2I) Write the equation of the line in
the graph below.
4. (3B) What is the rate of change?
5. (3C) The cost, 𝐶, of getting your car
repaired is given by where ℎ is the
number of hours in labor the mechanic
works on your car, 55 is the cost per
hour the mechanic charges, and 190 is
the cost for the parts needed to repair
your car. This situation is represented
by 𝐶 = 55ℎ + 190. What would the
𝒙-intercept represent in this situation?
6. (5A) Solve the equation for 𝑥.
8. (3C) Write the equation of this line
in standard form.
9. (6A) What is the range of
𝑓(𝑥) = 2𝑥 2 + 9?
𝒙
5
4.5
2
1.5
0.5
y
60
180
240
540
600
7.(5C) A system of equations is used to
produce the set of points in the table
below. What is the x value of the
solution?
𝑥 −6
−3
𝑦 −18 −12
𝑦 18
12
3
0
0
6
-6
6
9
−12
12
8(𝑥 − 6) = −2𝑥 − 6.9
SPRING FINAL Review Algebra I 2016
10. (7A) The table below represents a
quadratic equation. Complete a new table
and fill in the gaps as
𝑔(𝑥)
𝑥
best you can.
𝑥
−1
2
5
6
9
10
12
14
11. (6C) Write the quadratic equation of the graph below in vertex form.
𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘
𝑔(𝑥)
−55
−16
5
8
5
0
−16
−40
12. (6A) The table below shows
ordered pairs that satisfy the quadratic
function 𝑓. Between
𝑥 𝑓(𝑥)
what interval would I
−2 31
find:
−1 20
1. f(x) = 3
0
11
1
4
2. f(x) = 0
2
−1
3. f(x) = -2.5
3
−4
4
−5
-4
5
14. (7A) Between what two numbers would
I find the positive zero of this parabola?
Between what two numbers would I find the
negative solution?
15. (8A) What are the zeroes of the
function 𝑦 = 𝑥 2 − 16
13. (7B) A quadratic function 𝑓 has
𝑥-intercepts at −6 and 2. Write a
quadratic function in standard form to
represent this situation.
16.(3D) A teacher wants to spend less than $300 on supplies for paper and
pencils. Supplies for 1 ream of paper cost $4 and supplies for 1 box of pencils
cost $9. This relationship is shown in the graph below.
1. Could she buy 20 reams of paper
and 25 boxes of pencils?
2. Could she buy 10 reams of paper
and 25 boxes of pencils?
SPRING FINAL Review Algebra I 2016
17. (9C) The half-life of an element is the length of time it takes for the number of
atoms in a sample to be decreased by half. One element, which has a half-life of 35
years has a function in the form:
𝒕
𝒚 = 𝒂(𝟎. 𝟐𝟓)𝒙
18. (9C) The value of a boat is
depreciating at a rate of 7% per
year. In 2004, the boat was worth
$192,000. Find the worth of the
boat in 2013.
This represents the amount 𝑦 of a substance remaining after 𝑡 years, where 𝑎 is the
initial amount and 𝑥 is the length of the half-life in years. Write an equation that
could be used to find the decay of a 6-gram sample of this element after 8 years?
19. (7C) Given the following quadratic
equations: 𝑓(𝑥) = −𝑥 2 + 64
𝑔(𝑥) = −2𝑥 2 − 51
ℎ(𝑥) = 𝑥 2 + 14
20. (7C) Write an equation for the
function g(x) in vertex form. It is
𝑓(𝑥) = (𝑥 − 8)2 + 10 translated 2
units up and 5 units left.
1. Do they have the same y-intercept?
2. Do they have the same axis of
symmetry?
3. Do they have the same vertex?
4. Do the have a max or a min vertex?
21. (8B) An object is launched into the air.
The table below shows the object’s height
above the ground at various times. Use a
quadratic regression on your calculator to
find the height at 11 seconds.
23. (7C) Identify the transformations of the graph of the
parent function 𝑓(𝑥) = 𝑥 2 needed to obtain the graph of
𝑔(𝑥) = −3(𝑥 + 2)2 + 4.
22. (8A) What is the solution to:
5𝑥 2 − 14𝑥 = 3
24. (8A) What are the solutions to the quadratic equation:
𝑦 = 3𝑥 2 − 7𝑥 + 6?
SPRING FINAL Review Algebra I 2016
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25. (9D) The function 𝑓(𝑡) = 300( )𝑡
4
represents the number of Moose in
Yellowstone park after t years. If this
function is graphed on a coordinate
grid, what would be the meaning of
the 𝑦-intercept?
28. (10E) The area of a rectangular
piece of wood is represented by:
26. (10D) Simplify the following
expression:
(3𝑥 − 2)(5𝑥 + 7)
29. (10F) Factor completely:
4𝑥 2 − 81𝑦 2
Find the dimensions of the piece of
wood.
6𝑥 7 𝑦 2 z−1
30𝑥 4 𝑦 2 𝑧 −4
inches.
30. (11B) Simplify the following
expression:
1
(81𝑎7 )2
2𝑟 2 − 13𝑟 + 21.
31. (11B) Find the area of a square
with a side length of
27. (10E) The base of a triangle is 4
inches less than twice its height. If the
area of the triangle is 132 square inches,
write an equation in standard form to
find the height of the triangle in inches?
Notes: