Download CA ALG 1 Standard 20

CA ALG 1 Standard 20
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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1. Solve
by using the Quadratic Formula.
a. x = 9 or x = 1
c. x = 54 or x = 46
b. x = 1 or x = 9
d. x = 18 or x = 2
2
2. Solve 3x – 6x + 1 = 0 by using the Quadratic Formula. If necessary, round to the nearest hundredth.
a. x 1.82 or x 0.18
c. There are no solutions.
b. x 6.82 or x 5.18
d. x 10.90 or x 1.10
3. A farmer has 120 yards of fencing to build around a rectangular orchard. Let w be the width of the orchard.
Write an equation giving the area of the orchard. Find the dimensions of the orchard when the area is 900
square yards.
a.
; The width is 50 yd, and the length is 18 yd.
b.
; The width is 30 yd, and the length is 30 yd.
c.
; The width is 58 yd, and the length is 62 yd.
d.
; The width is 72 yd, and the length is 48 yd.
4. Solve
a.
b.
by using the Quadratic Formula.
c.
d.
CA ALG 1 Standard 20
Answer Section
MULTIPLE CHOICE
1. ANS: A
Write the equation in standard form:
Formula,
. Substitute for a, –8 for b, and –9 for c in the Quadratic
. Write as two equations, one adding the square root and one subtracting it.
Simplify each equation to find the values of x.
Feedback
A
B
C
D
Correct!
Use the opposite of b, the coefficient of the x-term in the equation.
For the numerator in the Quadratic Formula, find the square root before adding it to or
subtracting it from –b.
The denominator of the Quadratic Formula is 2 times a.
PTS: 1
NAT: 12.5.4.a
2. ANS: A
3x2 – 6x + 1= 0
DIF: Average
STA: 1A20.0
REF: Page 599
OBJ: 9-8.1 Using the Quadratic Formula
TOP: 9-8 The Quadratic Formula
The equation is in standard form, ax2 +bx + c= 0.
Use the Quadratic Formula.
x =
Substitute 3 for a, –6 for b, and 1 for c.
x =
Simplify.
x =
x =
x=
or x =
x 1.82 or x 0.18
There are two solutions.
Use a calculator to approximate x.
Feedback
A
B
C
D
Correct!
First, identify a, b, and c. Then, substitute a, b, and c in the Quadratic Formula and
solve.
There are solutions to this equation.
Check your calculations.
PTS: 1
DIF: Average
REF: Page 599
OBJ: 9-8.2 Using the Quadratic Formula to Estimate Solutions NAT: 12.5.4.a
STA: 1A20.0
TOP: 9-8 The Quadratic Formula
3. ANS: B
Step 1 Find the length of the orchard in terms of w.
Let w represent the width of the orchard.
Step 2 Write an equation for the area of the orchard.
Step 3 Find the dimensions of the orchard when the area is 900 square yards.
Substitute 900 for the area of the orchard.
The equation is in standard form:
,
.
, and
Substitute 1 for a, –60 for b, and 900 for c.
Simplify.
Substitute 30 for w and simplify.
The width and length of the orchard are each 30 yd.
Feedback
A
B
C
D
Substitute 900 for the area of the orchard and solve the equation.
Correct!
If the width is w, then the length is 60 – w.
Check your equation to verify that it shows the correct area.
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: The Quadratic Formula and the Discriminant
4. ANS: A
STA: 1A20.0
KEY: multi-step
Write the Quadratic Formula.
Substitute 1 for a, 7 for b, and 9 for c.
Simplify.
Write in simplest form.
Feedback
A
B
C
D
Correct!
Use the Quadratic Formula.
Use the Quadratic Formula.
Use the Quadratic Formula.
PTS: 1
NAT: 12.5.4.a
DIF: Average
STA: 1A20.0
OBJ: Quadratic Functions with Real Zeros
TOP: The Quadratic Formula