Unit 3 – Investigating Algebra / Name:
Multiple Choice (2 points each) Choose the best answer.
1. / (– 5x2 + x – 8) – (– 3x2 – 8x – 3)
(A) / – 2x2 + 9x – 11 / (B) / – 2x2 – 7x – 11
(C) / – 2x2 + 9x – 5 / (D) / – 2x2 + 9x + 5
2. / 3x2(5x – x2 + 7).
(A) / – 3x4 + 8x3 + 21x2 / (B) / – 3x4 + 8x3 + 10x2
(C) / – 3x4 + 15x3 + 21x2 / (D) / 3x4 + 15x3 + 21x2
3. / Factor 64y2 – 49.
(A) / (8y + 7)(8y + 7) / (B) / (8y + 7)(8y – 7)
(C) / (8y – 7)(8y – 7) / (D) / 8(y + 7)(y – 7)
4. / Solve .
(A) / 15 / (B) / 30 / (C) / 5.5 / (D) / 225
5. / Solve algebraically.
(A) / / (B) / / (C) / / (D) /
6. / Which interval would best describe the solutions of? Use the given table of values for .
(A) / – 1 < x < 0 / x / y
– 2 / 7
– 1 / 1
0 / – 3
1 / – 5
2 / – 5
3 / – 3
(B) / 1 < x < 2
(C) / 3 < x < 4
(D) / both a and c
7. / Find the value of c that makes the trinomial a perfect square: x2 – 60x + c
(A) / 30 / (B) / 900 / (C) / 3600 / (D) / 459
8. / Describe the nature of the roots of the equation:
(A) / 1 real root / (B) / 2 real rational roots
(C) / 2 real irrational roots / (D) / 2 imaginary roots
9. / Which is the value of ?
(A) / 1 / (B) / –1 / (C) / i / (D) / –i
10. / Simplify:
(A) / / (B) / / (C) / / (D) / –13
Free Response (6 points each)
Answer each question showing all work algebraically, graphically, and/or verbally to indicate understanding.
11.Simplify each expression.
a.
b.
c.
12.Jose Canusee followed two diagonal paths to get from his house to a neighborhood store (see diagram below).
What is the total distance traveled from Jose’s house to the store?
13.Use algebraic techniques to answer each geometric connection.
a.Find a polynomial expression for the volume of the prism shown.
Simplify completely.
b.Find the perimeter of the isosceles trapezoid. Simplify completely.
14.Divide (3x2 + 11x + 10) by (x + 2):
15.Determine the requested value:
a.If x 2 + y 2 = 20 and xy = 15, find the value of (x + y) 2.
b.If x 2 – y 2 = 40 and (x + y) = 5, find the value of (x – y).
16.A student solved as shown.
a.In words, explain the student’s mistake.
b.Solve the equation correctly.
17.The length of a garden is (x + 5) yards and the width is (x – 3) yards.
The area of the garden is 9 square yards.
a.Find the value of x algebraically.
b.Find the length and width of the garden.
18.Solve the equation two ways:
a.algebraically (by factoring).
x / f(x) / g(x)– 4
– 3
– 2
– 1
0
1
2
3
4
b.graphically (using a table for graphing accuracy).
19.Graph .
Identify zeros, intervals of increase and decrease, vertex axis of symmetry.
Vertex: ______
Axis of symmetry: ______
Zeros: ______
Interval of increase: ______
Interval of decrease: ______
20.Graph
Higher-level Standardized Test Questions (4 points each)21. / The surface area S of a cube is 150 ft2. Find the value (in feet) of a side length, s.
(A) / 5 /
(B) /
(C) / 5
(D) / 25
22. / If (x+3)(x+5) – (x – 4)(x – 2) = 0, then x =
(A) / 2 / (B) / - 1/2 / (C) / 1/2 / (D) / – 2
23. / You have a rectangular-shaped garden where one side is three feet more than half the other side. If you need to cover the garden with six inches of compost, find an expression that represents the volume needed.
(A) / / (B) /
(C) / / (D) /
24. / What is the ratio of the area of the small rectangle to the large rectangle?
(A) /
/
(B) /
(C) /
(D) /
25. / If and , then
a. /
b. /
c. /
d. /
Solutions:
- c
- c
- b
- d
- b
- a
- b
- b
- b
- b
- a)
b)
c)
- 42m
- a)
b)
14.
15. a) 50
b) 8
16. a) The student factored before subtracting 8.
b) x=-5, 1
17. a) x=4, or x=-6 (extraneous solution)
b) Length = 9 yds, Width = 1 yd
18. a) x = 3, -1
b)
x / f(x) / g(x)-4 / 36 / 15
-3 / 24 / 12
-2 / 14 / 9
-1 / 6 / 6
0 / 0 / 3
1 / -4 / 0
2 / -6 / -4
3 / -6 / -6
4 / -4 / 9
- Vertex (3,1)
Axis of symmetry: x=3
Zeros: No real zeros
Interval of increase: x>3
Interval of decrease: x<3
20.
- x=2
- x=-5, 3
- c
- d
- a
- a
- a