Download ExamView - Advanced Systems of Equations Problem Set.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Advanced Systems of Equations Problem Set
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Which values of x are in the solution set of the
following system of equations?
y = 3x − 6
3. Which ordered pair is in the solution set of the
system of equations shown below?
y 2 − x 2 + 32 = 0
y = x2 − x − 6
a.
b.
c.
d.
3y − x = 0
0, − 4
0, 4
6, − 2
−6, 2
a.
b.
c.
d.
2. Which ordered pair is a solution of the system of
equations shown below? x + y = 5
(x + 3) 2 + (y − 3) 2 = 53
a.
b.
c.
d.
(2,3)
(5,0)
(−5,10)
(−4,9)
1
(2,6)
(3,1)
(−1,−3)
(−6,−2)
Name: ________________________
ID: A
Short Answer
6. Solve the following system of equations
algebraically: 9x 2 + y 2 = 9
4. Solve the following systems of equations
algebraically: 5 = y − x
4x 2 = −17x + y + 4
3x − y = 3
-
-
5. A pelican flying in the air over water drops a crab
from a height of 30 feet. The distance the crab is
from the water as it falls can be represented by the
function h(t) = −16t 2 + 30 , where t is time, in
seconds. To catch the crab as it falls, a gull flies
along a path represented by the function
g(t) = −8t + 15. Can the gull catch the crab before
the crab hits the water? Justify your answer. [The
use of the accompanying grid is optional.]
7. Solve the following systems of equations
algebraically: x 2 − 2y 2 = 23
x − 2y = 7
2
ID: A
Advanced Systems of Equations Problem Set
Answer Section
MULTIPLE CHOICE
1. ANS: B
x 2 − x − 6 = 3x − 6
x 2 − 4x = 0
x(x − 4) = 0
x = 0,4
PTS: 2
KEY: equations
2. ANS: C
REF: 081015a2
x+y = 5
STA: A2.A.3
TOP: Quadratic-Linear Systems
. −5 + y = 5
y = −x + 5
y = 10
(x + 3) 2 + (−x + 5 − 3) 2 = 53
x 2 + 6x + 9 + x 2 − 4x + 4 = 53
2x 2 + 2x − 40 = 0
x 2 + x − 20 = 0
(x + 5)(x − 4) = 0
x = −5,4
PTS: 2
REF: 011302a2
STA: A2.A.3
KEY: equations
3. ANS: D
x = 2y . y 2 − (3y) 2 + 32 = 0 . x = 3(−2) = −6
TOP: Quadratic-Linear Systems
y 2 − 9y 2 = −32
−8y 2 = −32
y2 = 4
y = ±2
PTS: 2
KEY: equations
REF: 061312a2
STA: A2.A.3
1
TOP: Quadratic-Linear Systems
ID: A
SHORT ANSWER
4. ANS:
ÊÁ 9 1 ˆ˜
Ê
ˆ
ÁÁ − , ˜˜ and ÁÁÁ 1 , 11 ˜˜˜ . y = x + 5
. 4x 2 + 17x − 4 = x + 5
ÁÁ 2 2 ˜˜
ÁÁ 2 2 ˜˜
Ë
¯
Ë
¯
y = 4x 2 + 17x − 4 4x 2 + 16x − 9 = 0
(2x + 9)(2x − 1) = 0
x=−
1
9
and x =
2
2
9
1
1
11
y = − + 5 = and y = + 5 =
2
2
2
2
PTS: 6
KEY: equations
5. ANS:
REF: 061139a2
Yes.
PTS: 4
KEY: graph
STA: A2.A.3
.
REF: 060228b
TOP: Quadratic-Linear Systems
.
STA: A2.A.3
2
TOP: Quadratic-Linear Systems
ID: A
6. ANS:
.
(0,−3) and (1,0).
.
PTS: 4
REF: 060627b
STA: A2.A.3
KEY: equations
7. ANS:
(−19,−13), (5,−1). x = 2y + 7. (2y + 7) 2 − 2y 2 = 23
.
TOP: Quadratic-Linear Systems
. x = 2y + 7 = 2(−13) + 7 = −19 .
4y 2 + y + 14y + 14y + 49 − 2y 2 = 23
2y 2 + 28y + 26 = 0
y 2 + 14y + 13 = 0
(y + 13)(y + 1) = 0
y = −13,− 1
x = 2y + 7 = 2(−1) + 7 = 5
PTS: 4
KEY: equations
REF: 061032b
STA: A2.A.3
3
TOP: Quadratic-Linear Systems
Name: ________________________ Class: ___________________ Date: __________
ID: A
Advanced Systems of Equations Problem Set
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Which values of x are in the solution set of the
following system of equations?
y = 3x − 6
3. Which ordered pair is in the solution set of the
system of equations shown below?
y 2 − x 2 + 32 = 0
y = x2 − x − 6
a.
b.
c.
d.
3y − x = 0
0, − 4
0, 4
6, − 2
−6, 2
a.
b.
c.
d.
2. Which ordered pair is a solution of the system of
equations shown below? x + y = 5
(x + 3) 2 + (y − 3) 2 = 53
a.
b.
c.
d.
(2,3)
(5,0)
(−5,10)
(−4,9)
1
(2,6)
(3,1)
(−1,−3)
(−6,−2)
Name: ________________________
ID: A
Short Answer
6. Solve the following system of equations
algebraically: 9x 2 + y 2 = 9
4. Solve the following systems of equations
algebraically: 5 = y − x
4x 2 = −17x + y + 4
3x − y = 3
-
-
5. A pelican flying in the air over water drops a crab
from a height of 30 feet. The distance the crab is
from the water as it falls can be represented by the
function h(t) = −16t 2 + 30 , where t is time, in
seconds. To catch the crab as it falls, a gull flies
along a path represented by the function
g(t) = −8t + 15. Can the gull catch the crab before
the crab hits the water? Justify your answer. [The
use of the accompanying grid is optional.]
7. Solve the following systems of equations
algebraically: x 2 − 2y 2 = 23
x − 2y = 7
2
ID: A
Advanced Systems of Equations Problem Set
Answer Section
MULTIPLE CHOICE
1. ANS: B
x 2 − x − 6 = 3x − 6
x 2 − 4x = 0
x(x − 4) = 0
x = 0,4
PTS: 2
KEY: equations
2. ANS: C
REF: 081015a2
x+y = 5
STA: A2.A.3
TOP: Quadratic-Linear Systems
. −5 + y = 5
y = −x + 5
y = 10
(x + 3) 2 + (−x + 5 − 3) 2 = 53
x 2 + 6x + 9 + x 2 − 4x + 4 = 53
2x 2 + 2x − 40 = 0
x 2 + x − 20 = 0
(x + 5)(x − 4) = 0
x = −5,4
PTS: 2
REF: 011302a2
STA: A2.A.3
KEY: equations
3. ANS: D
x = 2y . y 2 − (3y) 2 + 32 = 0 . x = 3(−2) = −6
TOP: Quadratic-Linear Systems
y 2 − 9y 2 = −32
−8y 2 = −32
y2 = 4
y = ±2
PTS: 2
KEY: equations
REF: 061312a2
STA: A2.A.3
1
TOP: Quadratic-Linear Systems
ID: A
SHORT ANSWER
4. ANS:
ÊÁ 9 1 ˆ˜
Ê
ˆ
ÁÁ − , ˜˜ and ÁÁÁ 1 , 11 ˜˜˜ . y = x + 5
. 4x 2 + 17x − 4 = x + 5
ÁÁ 2 2 ˜˜
ÁÁ 2 2 ˜˜
Ë
¯
Ë
¯
y = 4x 2 + 17x − 4 4x 2 + 16x − 9 = 0
(2x + 9)(2x − 1) = 0
x=−
1
9
and x =
2
2
9
1
1
11
y = − + 5 = and y = + 5 =
2
2
2
2
PTS: 6
KEY: equations
5. ANS:
REF: 061139a2
Yes.
PTS: 4
KEY: graph
STA: A2.A.3
.
REF: 060228b
TOP: Quadratic-Linear Systems
.
STA: A2.A.3
2
TOP: Quadratic-Linear Systems
ID: A
6. ANS:
.
(0,−3) and (1,0).
.
PTS: 4
REF: 060627b
STA: A2.A.3
KEY: equations
7. ANS:
(−19,−13), (5,−1). x = 2y + 7. (2y + 7) 2 − 2y 2 = 23
.
TOP: Quadratic-Linear Systems
. x = 2y + 7 = 2(−13) + 7 = −19 .
4y 2 + y + 14y + 14y + 49 − 2y 2 = 23
2y 2 + 28y + 26 = 0
y 2 + 14y + 13 = 0
(y + 13)(y + 1) = 0
y = −13,− 1
x = 2y + 7 = 2(−1) + 7 = 5
PTS: 4
KEY: equations
REF: 061032b
STA: A2.A.3
3
TOP: Quadratic-Linear Systems