Practice
4𝑘−10
𝑘
1. Find an explicit formula for the arithmetic
sequence -11,-3,5,13,...
2. Solve for k.
3. (𝑝 𝑥 )𝑦
4. Factor 3𝑥 2 − 6𝑥 − 9
5. What is the equation of
the line of reflection
that reflects
quadrilateral ABCD onto
quadrilateral A’B’C’D’
6.
7. In the triangle shown below the measuer of angle C is
(𝑥 + 30). The measure of angle A is
a. (90 − 𝑥)
b. (60 − 𝑥)
c. (120 − 𝑥)
d. (𝑥 − 60)
e. (𝑥 − 120)
8. The perimeter of the semicircular top is what in
terms of 𝜋.
=8
3
3
3
9. When 𝑥 3 + 3𝑥 2 − 2𝑥 + 7 𝑖𝑠 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑥 + 1, what
is the remainder?
10. Reduce to lowers terms
11.
12. What is the area of the triangle shown below?
13. What is the equation of the line tangent to the circle
𝑥 2 + 𝑦 2 = 25 at the point (3,4).
14. Suppose 6 = 𝑦 and that x=2 when y=12. What is x
15.
16.
17.
18.
𝑥
when y is 8?
𝑘
2𝑥 2 −3𝑥−2
10+𝑥−3𝑥 2
19.
20.
21.
22.
23. The triangle based oblique pyramid has a volume of
1
13𝑐𝑚3 . Given 𝑉 = 3 ∗ 𝑏𝑎𝑠𝑒 𝑎𝑟𝑒𝑎 ∗ ℎ𝑒𝑖𝑔ℎ𝑡 what is
the height of the pyramid?
24. Quadrilateral K’ is the image of quadriateral k under
dilation. What coordinate point is the center of
Dilation?
25. Find the coordinates of B if B is the midpoint of ̅̅̅̅
𝐴𝐶
̅̅̅̅.
and C is the midpoint of 𝐴𝐷
26. ̅̅̅̅
𝐴𝐵 = 22
̅̅̅̅
𝐵𝐶 = 9
̅̅̅̅
𝐴𝐶 =
27. Find the coordinates of G if F (1, 3.5) is the midpoint
of ̅̅̅
𝐺𝐽 and J has coordinates (6, -2)
29.
28. Find the perimeter of the polygon: Triangle XYZ with
vertices X (1, 6), Y (-5, 2), and Z (5, -4)
30.
31. Using the following coordinates
𝑎(−5,4), 𝐵(3, −4), 𝑋(4,4), 𝑌(−2, −2)
a. Calculate the slope of AB and XY
b. Are the sides parallel, perpendicular, or neither
33. Use Elimination to solve the system
35. Find the measure of angle SOR
37. George who exactly 6 feet tall notices that his
shadow is 7.5 feet long. And the shadow of a
nearby tree is 22.5 feet long. How tall is the
tree? Draw a diagram and write a proportion to
find the height of the tree.
32. Use substitution to solve the system of equations
33.
34. A bank contains 60 coins. There are only nickels and
quarters in the bank. The total value of the coins is
$6.40. Write a system of equations to determine
how many of each coin there is and then solve the
system.
36. Find the measure of angle ABC
38. True or False: ∆ PQR ≅ ∆ XYZ. Show your
reasoning.
P(1, -5), Q(9, 0) R(-1, 6)
X(3, 1) Y(11, 6) Z(1,12)
39.
40.
41. A ladder is leaning against the side of a house and
froms a 65° angle with the ground. The foot of the
ladder is 8 feet from the house. Find the length of
the ladder.
43. Garden Green paint is made from 4 gallons of
yellow paint to 6 gallons of blue paint. How many
gallons of blue paint do you need to make 40
gallons of Garden Green paint?
42. A light house was built at sea level is 150 feet high.
From its top, the angel of depression of a bouy is 25°.
Find the distance from the bouy to the foot of the
light house.
44. Matthew wants to sell laptops and smartphones. He
wants to seel at least 12 devices and earn at least
$4500. If a laptop costs $425 and a smartphone costs
$125 does mathew meet his goal by selling 9 laptops
and 6 smartphones.
46. 4𝑖 ∗ (−7 + 𝑖) =
45. A polynomial p has zeros when
𝑥 = 5, 𝑥 = −1, 𝑎𝑛𝑑 𝑥 = −1/4
What is the equation for p?
47.
What is
its
equation?
48. Gustavo and Aiden are walking due east through
the forest when an angry grizzly bear appears
behind them. Gustavo runs away to the east
for 300m and Aiden runs away in a more
southward line for 250m. Gustavo and Aiden end
up 262m as shown.
How many degrees away from east did Aiden turn before
running?
49. Let 𝑓(𝑥) = 𝑥 5 + 2𝑥 3 − 𝑥 2
Find 𝑓 ′ (𝑥) =
50. Let 𝑔(𝑥) = 𝑥 5 − 3𝑥 2 + 4𝑥
Find 𝑔′(−2)