Chapter 9 Test review
1. Find the degree of the polynomial
2. Classify the expression
.
and state its degree.
Find the sum.
3.
Simplify the expression.
4.
Find the difference.
5.
6.
7. During the years 1992 through 1996, the average number of green grapes, g, sold at a farmer's market can be
modeled by g = –0.14 + 1.4t + 46.62. The average number of red grapes, r, sold by the farmer's market can
be modeled by
. Determine the model representing the total number of grapes, n,
sold from 1992 through 1996.
8. Classify the expression
9. Find the sum
by the number of its terms and state its degree.
+
10. Find the difference
11. In order from least to greatest, the side lengths (in inches) of a triangle are 8,
, and
.
a. How much longer is the longest side of the triangle than the second longest side? Explain how you found
your answer.
b. Find the perimeter of the triangle.
c. A student wants to change the length of the shortest side of the triangle so that the triangle has a perimeter
of
inches. What should the new length of the shortest side be? Explain.
Find the product.
12.
13.
14.
15. Write a variable expression for the area of the rectangle.
16. A rectangle has a length of
rectangle in terms of x.
and a width of
. Write an equation that describes the area, A, of the
17. A rectangular garden, with length four times its width, is to be expanded so that both sides are increased by 3
yards.
Let x represent the original width of the garden. Write an expression that models the area of the expanded
garden.
18. Write a variable expression for the area of the shape shown, which is made with
.
19. Use the FOIL pattern to find the product (x – 3)(3x + 5).
20. Use a vertical format to find the product
.
Find the product.
21.
22.
23. The side length of a square garden is
meters.
a. Write a polynomial to describe the area of the garden.
b. Beans are planted in a rectangular section of the garden. The length of the section is
meters and the
width is
meters. Write a polynomial to describe this section of the garden.
c. Tomatoes are planted in another rectangular section of the garden. The length and width of this section are
meters and
meters. Find the area of this section.
d. Given x = 5 m and y = 4 m, find the total area of the garden. What is the area of the part of the garden not
planted with tomatoes or beans? Explain.
24. Explain how you can use a product of a sum and a difference to find the product of
25. Find the greatest common monomial factor of the terms
26. Factor out the greatest common monomial factor from
Solve the equation.
27.
,
, and
.
.
and
.
28.
29. The equation
models the height h, in feet, of a golf ball t seconds after it was hit. Find the
values of t for which h = 0. Explain the meaning of the solutions.
30. A ball bounces straight up from the ground with an initial vertical velocity of 8 feet per second. Use a vertical
motion model to write and solve an equation to find the number of seconds it takes for the ball to return to the
ground. Explain your reasoning.
Factor the polynomial.
31.
Solve the equation.
32.
33. The area of a rectangle is 24 square centimeters and its side lengths are x centimeters and
a. Find the side lengths of the rectangle. Justify your answer.
b. Find the perimeter of the rectangle.
centimeters.
34. An L-shaped room in a house has the dimensions shown.
a. Write an expression that describes the area of the room. Write the expression in polynomial form.
b. The area of the room is 120 square feet. How long are the sides of the room labeled x feet? Explain.
35. Solve the equation
Factor the trinomial.
36.
37.
38. An object is thrown straight upward from the edge of an 80 foot high cliff. Its initial velocity is 64 feet per
second.
a. Use the vertical motion model to write an equation that gives the height h of the ball t seconds after it is
thrown.
b. After how many seconds will the object hit the ground at the bottom of the cliff? Explain how you can use
factoring to solve this problem.
Solve the equation.
39.
Factor the polynomial.
40.
41. An object is launched upward from the ground with an initial vertical velocity of 40 feet per second. After
how many seconds does the object reach a height of 25 feet? Justify your answer.
Solve the equation.
42.
43.
Factor the polynomial completely.
44.
45.
46. Factor the expression
47. Factor the expression
.
.
Chapter 9 Test review
Answer Section
1. ANS:
4
2. ANS:
binomial, 9
3. ANS:
4. ANS:
5. ANS:
6. ANS:
7. ANS:
n=
8. ANS:
binomial, 3
9. ANS:
10. ANS:
11. ANS:
a.
inches longer; Find the difference of the longest side and the second longest side:
.
b.
inches
c. The student should decrease the length of the shortest side to 7 inches. Sample answer: The original
perimeter is
. In order to have a perimeter of
, you need to subtract 1 from the side length.
12. ANS:
13. ANS:
14. ANS:
15. ANS:
16. ANS:
17. ANS:
18. ANS:
19. ANS:
20. ANS:
21. ANS:
22. ANS:
23. ANS:
a. 4x2 + 8xy + 4y2
b. 4x2 – 4y2
c. 4x2 – y2
d. 204 m2; The area of the garden is 324 m2. The area of the section planted with beans is
. The area of the section planted with tomatoes is
planted with beans and tomatoes is
. The area not
.
24. ANS:
Sample answer: Since
and
the product of
and
can be rewritten as
which is the product of a sum and a difference. This product is the difference of two
squares:
25. ANS:
26. ANS:
or
27. ANS:
0, -3
28. ANS:
0, 5
29. ANS:
; these are the times right as the ball is hit and when it lands.
30. ANS:
0.5 seconds; The height h, in feet, of the ball after t seconds is given by the equation
. When
the ball returns to the ground, the height will be 0, so
Factor the right side of the equation to
get
The solutions of the equation are
, or t = 0, and
, or t = 0.5. The solution
t = 0 represents the time at which the ball first bounces, so the other solution, t = 0.5, represents the number of
seconds it takes for the ball to return to the ground.
31. ANS:
32. ANS:
33. ANS:
a. 4 cm and 6 cm; Write and solve an area equation.
So, x = –6 or x = 4. A side length cannot be negative, so choose x = 4. The side lengths are 4 cm and
cm.
b. The perimeter is
centimeters.
34. ANS:
a.
b. 6 feet; Use the polynomial from part (a) to write and solve an equation.
So, x = 20 or x = 6. However, from the diagram, it can be seen that x is less than 10 feet. So, x = 6 is the
solution that makes sense for the problem.
35. ANS:
36. ANS:
37. ANS:
38. ANS:
a.
b. after 5 seconds; Factor the equation.
So,
or
, and t = 5 or t = –1.
Because time cannot be negative, the ball reaches the ground at the bottom of the cliff in 5 seconds.
39. ANS:
g=
40. ANS:
41. ANS:
1
seconds; Sample answer: The equation
is launched upward. Let h = 25 and solve
So,
42. ANS:
43. ANS:
44. ANS:
45. ANS:
, and
.
gives the height h of the object t seconds after it
.
46. ANS:
47. ANS:
_-