Testbank for Precalculus, 12th Edition — Michael Sullivan
,PREMIUM TABLE OF CONTENTS
Precalculus, 12th Edition — Michael Sullivan
Complete Premium Test Bank | Updated 2026–2027
PART I — FOUNDATIONS, FUNCTIONS & ALGEBRAIC MODELS
Chapter Core Mathematical Coverage
Coordinate plane • Distance & midpoint • Equations in two variables •
1. Graphs
Intercepts • Symmetry • Lines • Circles
2. Functions and Their Functions • Domain & range • Graph interpretation • Function properties •
Graphs Piecewise functions • Transformations • Mathematical models
3. Linear and Quadratic Linear functions • Linear models • Quadratic functions • Vertices & extrema •
Functions Quadratic models • Quadratic inequalities
4. Polynomial and Rational Polynomial graphs • Zeros & multiplicities • Rational functions • Asymptotes •
Functions Polynomial/rational inequalities • Real zeros
5. Exponential and Composite & inverse functions • Exponential functions • Logarithms • Equations
Logarithmic Functions • Growth & decay • Exponential/logistic models
PART II — TRIGONOMETRY, APPLICATIONS & VECTORS
Chapter Core Mathematical Coverage
Angles & radians • Unit circle • Trigonometric functions • Sine/cosine graphs •
6. Trigonometric Functions
Tangent, cotangent, secant & cosecant • Sinusoidal models
Inverse trigonometric functions • Trigonometric equations • Identities • Sum &
7. Analytic Trigonometry
difference formulas • Double/half-angle formulas • Product-sum formulas
8. Applications of Right-triangle trigonometry • Law of Sines • Law of Cosines • Triangle area •
Trigonometric Functions Simple harmonic motion • Damped motion • Combined waves
9. Polar Coordinates; Polar coordinates & equations • Polar graphs • Complex plane • De Moivre’s
Vectors Theorem • Vectors • Dot product • 3D vectors • Cross product
PART III — ANALYTIC GEOMETRY & ALGEBRAIC SYSTEMS
,Chapter Core Mathematical Coverage
Conic sections • Parabolas • Ellipses • Hyperbolas • Rotation of axes • Polar
10. Analytic Geometry
conics • Parametric equations
11. Systems of Equations Linear systems • Matrices • Determinants • Matrix algebra • Partial fractions •
and Inequalities Nonlinear systems • Systems of inequalities • Linear programming
PART IV — SEQUENCES, PROBABILITY & CALCULUS PREVIEW
Chapter Core Mathematical Coverage
12. Sequences; Induction; Sequences • Arithmetic sequences • Geometric sequences & series • Infinite
the Binomial Theorem series • Mathematical induction • Binomial expansions
Fundamental counting principle • Permutations • Combinations • Probability
13. Counting and Probability
• Conditional probability • Independent events • Multi-step probability
Limits from tables & graphs • Algebraic limits • One-sided limits • Continuity
14. A Preview of Calculus
• Tangent problem • Derivatives • Area problem • Definite integrals
PREMIUM QUESTION ARCHITECTURE
Each chapter integrates:
Mathematical Scenario & Application • Best Method Selection • Advanced Best-Answer MCQs •
Graph/Data/Calculation Interpretation • Integrated Multi-Step Problems
COMPLETE COURSE FLOW
Graphs & Coordinate Geometry
→ Functions & Transformations
→ Linear & Quadratic Models
→ Polynomial & Rational Functions
→ Exponential & Logarithmic Functions
→ Trigonometric Functions
→ Analytic Trigonometry
→ Trigonometric Applications
→ Polar Coordinates & Vectors
→ Analytic Geometry
→ Systems, Matrices & Inequalities
→ Sequences, Series & Induction
→ Counting & Probability
→ Limits, Derivatives & Integrals
PRECALCULUS, 12TH EDITION
Complete Chapters 1–14 • Premium Mathematical Test Bank • Updated 2026–2027
,Ch. F — Foundations: A Prelude to Functions
Premium 12th-Edition Mathematical Exam Bank
Question 1
Let
[
P=(-3,4),\qquad Q=(k,-2).
]
If
[
PQ=6\sqrt2,
]
determine all possible values of (k).
A. (k=-9,,3)
B. (k=-6,,6)
C. (k=-3,,9)
D. (k=-9,,9)
Correct Answer: A. (k=-9,,3)
Rationale:
[
PQ^2=(k+3)^2+(-6)^2.
]
Since
[
PQ=6\sqrt2,
]
[
(k+3)^2+36=72.
]
Therefore,
[
(k+3)^2=36,
]
so
[
k+3=\pm6.
]
Hence
[
,\boxed{k=-9\text{ or }k=3}.
]
Why the other options are less appropriate: They result from omitting the vertical distance (6), mishandling the
square root, or failing to translate (k+3=\pm6) correctly.
Question 2
Point (M=(2,-3)) is the midpoint of (P=(-5,7)) and (Q=(a,b)). Determine (a+b).
A. (4)
B. (-2)
C. (-6)
D. (-4)
Correct Answer: D. (-4)
Rationale:
[
\frac{-5+a}{2}=2
\Rightarrow a=9,
]
and
[
\frac{7+b}{2}=-3
\Rightarrow b=-13.
]
Thus
[
a+b=9-13=\boxed{-4}.
]
Why the other options are less appropriate: Both midpoint equations must be satisfied simultaneously; a sign
error in either coordinate changes the sum.
Question 3
The points
[
A=(-2,1),\qquad B=(4,5),\qquad C=(6,-1)
]
form a triangle. Which classification is correct?
,A. Right scalene
B. Acute scalene
C. Obtuse isosceles
D. Right isosceles
Correct Answer: B. Acute scalene
Rationale: Compare squared lengths:
[
AB^2=6^2+4^2=52,
]
[
BC^2=2^2+(-6)^2=40,
]
[
AC^2=8^2+(-2)^2=68.
]
All three are different, so the triangle is scalene.
For the largest side,
[
68<52+40=92.
]
Therefore the triangle is acute.
Why the other options are less appropriate: No two sides are equal, and no squared side length equals the sum
of the other two.
Question 4
Determine the equation of the locus of all points (P=(x,y)) that are equidistant from
[
A=(-4,3)\qquad\text{and}\qquad B=(2,-1).
]
A. (2x-3y+5=0)
B. (3x+2y-5=0)
C. (3x-2y+5=0)
D. (2x+3y+5=0)
Correct Answer: C.
[
\boxed{3x-2y+5=0}
]
,Rationale: Equidistance requires
[
PA^2=PB^2.
]
Thus
[
(x+4)^2+(y-3)^2=(x-2)^2+(y+1)^2.
]
Expand:
[
x^2+8x+16+y^2-6y+9
x^2-4x+4+y^2+2y+1.
]
After cancellation,
[
12x-8y+20=0.
]
Divide by (4):
[
\boxed{3x-2y+5=0}.
]
Why the other options are less appropriate: They result from reversing coordinate differences or incorrectly
combining linear terms after expansion.
Question 5
Four points (A,B,C,D) have squared distances from a fixed point (P) given by
[
PA^2=73,\qquad PB^2=41,\qquad PC^2=65,\qquad PD^2=50.
]
Which method gives the mathematically most efficient conclusion about the nearest point?
A. Evaluate all four square roots to four decimal places.
B. Compare (73,41,65,50) directly; therefore (B) is nearest.
C. Compare the midpoints of (PA,PB,PC,PD).
D. Compare only the coordinate differences.
Correct Answer: B.
Rationale: Since the square-root function is strictly increasing for nonnegative inputs,
[
PA<PB
,\iff
PA^2<PB^2.
]
Thus the smallest squared distance identifies the smallest distance:
[
41<50<65<73.
]
Therefore (B) is nearest.
Why the other options are less appropriate: Taking square roots is unnecessary; midpoints do not compare
lengths; and coordinate differences must be combined through squared sums.
Question 6
Consider
[
x^2+y^4=16.
]
Which statement completely describes its coordinate-axis intercepts and standard symmetries?
A. Intercepts ((\pm2,0),(0,\pm4)); (y)-axis symmetry only
B. Intercepts ((\pm4,0),(0,\pm2)); origin symmetry only
C. Intercepts ((\pm4,0),(0,\pm2)); (x)-axis symmetry only
D. Intercepts ((\pm4,0),(0,\pm2)); symmetry about both axes and the origin
Correct Answer: D.
Rationale: Set (y=0):
[
x^2=16
\Rightarrow
x=\pm4.
]
Set (x=0):
[
y^4=16
\Rightarrow
y=\pm2.
]
Because both (x) and (y) occur only with even powers, replacing (x) by (-x), (y) by (-y), or both leaves the
equation unchanged.
Why the other options are less appropriate: The intercepts in A are reversed, while B and C omit valid
symmetries.
,Question 7
For the equation
[
y^2=4-x,
]
which statement is correct?
A. The graph has (x)-intercept ((4,0)), (y)-intercepts ((0,\pm2)), and symmetry about the (x)-axis.
B. The graph has (x)-intercepts ((\pm4,0)) and symmetry about the (y)-axis.
C. The graph has no (y)-intercepts.
D. The graph is symmetric about the origin.
Correct Answer: A.
Rationale: Setting (y=0),
[
0=4-x\Rightarrow x=4.
]
Setting (x=0),
[
y^2=4\Rightarrow y=\pm2.
]
Replacing (y) by (-y) leaves
[
(-y)^2=4-x
]
unchanged, proving (x)-axis symmetry.
Why the other options are less appropriate: There is only one (x)-intercept, two real (y)-intercepts, and no
origin symmetry.
Question 8
The equation
[
x^2+ky^2=36
]
passes through ((3,3)). Determine (k) and the resulting (y)-intercepts.
A. (k=1,;(0,\pm6))
B. (k=4,;(0,\pm3))
, C. (k=3,;(0,\pm2\sqrt3))
D. (k=2,;(0,\pm3\sqrt2))
Correct Answer: C.
Rationale: Substitute ((3,3)):
[
9+9k=36,
]
so
[
9k=27,
\qquad
k=3.
]
For (y)-intercepts set (x=0):
[
3y^2=36,
]
[
y^2=12,
]
[
y=\pm2\sqrt3.
]
Thus
[
\boxed{k=3,\qquad (0,\pm2\sqrt3)}.
]
Question 9
Determine the standard symmetry of
[
y=x^5-4x^3+x.
]
A. (x)-axis symmetry
B. Origin symmetry
C. (y)-axis symmetry
D. No standard coordinate symmetry
Correct Answer: B. Origin symmetry
,PREMIUM TABLE OF CONTENTS
Precalculus, 12th Edition — Michael Sullivan
Complete Premium Test Bank | Updated 2026–2027
PART I — FOUNDATIONS, FUNCTIONS & ALGEBRAIC MODELS
Chapter Core Mathematical Coverage
Coordinate plane • Distance & midpoint • Equations in two variables •
1. Graphs
Intercepts • Symmetry • Lines • Circles
2. Functions and Their Functions • Domain & range • Graph interpretation • Function properties •
Graphs Piecewise functions • Transformations • Mathematical models
3. Linear and Quadratic Linear functions • Linear models • Quadratic functions • Vertices & extrema •
Functions Quadratic models • Quadratic inequalities
4. Polynomial and Rational Polynomial graphs • Zeros & multiplicities • Rational functions • Asymptotes •
Functions Polynomial/rational inequalities • Real zeros
5. Exponential and Composite & inverse functions • Exponential functions • Logarithms • Equations
Logarithmic Functions • Growth & decay • Exponential/logistic models
PART II — TRIGONOMETRY, APPLICATIONS & VECTORS
Chapter Core Mathematical Coverage
Angles & radians • Unit circle • Trigonometric functions • Sine/cosine graphs •
6. Trigonometric Functions
Tangent, cotangent, secant & cosecant • Sinusoidal models
Inverse trigonometric functions • Trigonometric equations • Identities • Sum &
7. Analytic Trigonometry
difference formulas • Double/half-angle formulas • Product-sum formulas
8. Applications of Right-triangle trigonometry • Law of Sines • Law of Cosines • Triangle area •
Trigonometric Functions Simple harmonic motion • Damped motion • Combined waves
9. Polar Coordinates; Polar coordinates & equations • Polar graphs • Complex plane • De Moivre’s
Vectors Theorem • Vectors • Dot product • 3D vectors • Cross product
PART III — ANALYTIC GEOMETRY & ALGEBRAIC SYSTEMS
,Chapter Core Mathematical Coverage
Conic sections • Parabolas • Ellipses • Hyperbolas • Rotation of axes • Polar
10. Analytic Geometry
conics • Parametric equations
11. Systems of Equations Linear systems • Matrices • Determinants • Matrix algebra • Partial fractions •
and Inequalities Nonlinear systems • Systems of inequalities • Linear programming
PART IV — SEQUENCES, PROBABILITY & CALCULUS PREVIEW
Chapter Core Mathematical Coverage
12. Sequences; Induction; Sequences • Arithmetic sequences • Geometric sequences & series • Infinite
the Binomial Theorem series • Mathematical induction • Binomial expansions
Fundamental counting principle • Permutations • Combinations • Probability
13. Counting and Probability
• Conditional probability • Independent events • Multi-step probability
Limits from tables & graphs • Algebraic limits • One-sided limits • Continuity
14. A Preview of Calculus
• Tangent problem • Derivatives • Area problem • Definite integrals
PREMIUM QUESTION ARCHITECTURE
Each chapter integrates:
Mathematical Scenario & Application • Best Method Selection • Advanced Best-Answer MCQs •
Graph/Data/Calculation Interpretation • Integrated Multi-Step Problems
COMPLETE COURSE FLOW
Graphs & Coordinate Geometry
→ Functions & Transformations
→ Linear & Quadratic Models
→ Polynomial & Rational Functions
→ Exponential & Logarithmic Functions
→ Trigonometric Functions
→ Analytic Trigonometry
→ Trigonometric Applications
→ Polar Coordinates & Vectors
→ Analytic Geometry
→ Systems, Matrices & Inequalities
→ Sequences, Series & Induction
→ Counting & Probability
→ Limits, Derivatives & Integrals
PRECALCULUS, 12TH EDITION
Complete Chapters 1–14 • Premium Mathematical Test Bank • Updated 2026–2027
,Ch. F — Foundations: A Prelude to Functions
Premium 12th-Edition Mathematical Exam Bank
Question 1
Let
[
P=(-3,4),\qquad Q=(k,-2).
]
If
[
PQ=6\sqrt2,
]
determine all possible values of (k).
A. (k=-9,,3)
B. (k=-6,,6)
C. (k=-3,,9)
D. (k=-9,,9)
Correct Answer: A. (k=-9,,3)
Rationale:
[
PQ^2=(k+3)^2+(-6)^2.
]
Since
[
PQ=6\sqrt2,
]
[
(k+3)^2+36=72.
]
Therefore,
[
(k+3)^2=36,
]
so
[
k+3=\pm6.
]
Hence
[
,\boxed{k=-9\text{ or }k=3}.
]
Why the other options are less appropriate: They result from omitting the vertical distance (6), mishandling the
square root, or failing to translate (k+3=\pm6) correctly.
Question 2
Point (M=(2,-3)) is the midpoint of (P=(-5,7)) and (Q=(a,b)). Determine (a+b).
A. (4)
B. (-2)
C. (-6)
D. (-4)
Correct Answer: D. (-4)
Rationale:
[
\frac{-5+a}{2}=2
\Rightarrow a=9,
]
and
[
\frac{7+b}{2}=-3
\Rightarrow b=-13.
]
Thus
[
a+b=9-13=\boxed{-4}.
]
Why the other options are less appropriate: Both midpoint equations must be satisfied simultaneously; a sign
error in either coordinate changes the sum.
Question 3
The points
[
A=(-2,1),\qquad B=(4,5),\qquad C=(6,-1)
]
form a triangle. Which classification is correct?
,A. Right scalene
B. Acute scalene
C. Obtuse isosceles
D. Right isosceles
Correct Answer: B. Acute scalene
Rationale: Compare squared lengths:
[
AB^2=6^2+4^2=52,
]
[
BC^2=2^2+(-6)^2=40,
]
[
AC^2=8^2+(-2)^2=68.
]
All three are different, so the triangle is scalene.
For the largest side,
[
68<52+40=92.
]
Therefore the triangle is acute.
Why the other options are less appropriate: No two sides are equal, and no squared side length equals the sum
of the other two.
Question 4
Determine the equation of the locus of all points (P=(x,y)) that are equidistant from
[
A=(-4,3)\qquad\text{and}\qquad B=(2,-1).
]
A. (2x-3y+5=0)
B. (3x+2y-5=0)
C. (3x-2y+5=0)
D. (2x+3y+5=0)
Correct Answer: C.
[
\boxed{3x-2y+5=0}
]
,Rationale: Equidistance requires
[
PA^2=PB^2.
]
Thus
[
(x+4)^2+(y-3)^2=(x-2)^2+(y+1)^2.
]
Expand:
[
x^2+8x+16+y^2-6y+9
x^2-4x+4+y^2+2y+1.
]
After cancellation,
[
12x-8y+20=0.
]
Divide by (4):
[
\boxed{3x-2y+5=0}.
]
Why the other options are less appropriate: They result from reversing coordinate differences or incorrectly
combining linear terms after expansion.
Question 5
Four points (A,B,C,D) have squared distances from a fixed point (P) given by
[
PA^2=73,\qquad PB^2=41,\qquad PC^2=65,\qquad PD^2=50.
]
Which method gives the mathematically most efficient conclusion about the nearest point?
A. Evaluate all four square roots to four decimal places.
B. Compare (73,41,65,50) directly; therefore (B) is nearest.
C. Compare the midpoints of (PA,PB,PC,PD).
D. Compare only the coordinate differences.
Correct Answer: B.
Rationale: Since the square-root function is strictly increasing for nonnegative inputs,
[
PA<PB
,\iff
PA^2<PB^2.
]
Thus the smallest squared distance identifies the smallest distance:
[
41<50<65<73.
]
Therefore (B) is nearest.
Why the other options are less appropriate: Taking square roots is unnecessary; midpoints do not compare
lengths; and coordinate differences must be combined through squared sums.
Question 6
Consider
[
x^2+y^4=16.
]
Which statement completely describes its coordinate-axis intercepts and standard symmetries?
A. Intercepts ((\pm2,0),(0,\pm4)); (y)-axis symmetry only
B. Intercepts ((\pm4,0),(0,\pm2)); origin symmetry only
C. Intercepts ((\pm4,0),(0,\pm2)); (x)-axis symmetry only
D. Intercepts ((\pm4,0),(0,\pm2)); symmetry about both axes and the origin
Correct Answer: D.
Rationale: Set (y=0):
[
x^2=16
\Rightarrow
x=\pm4.
]
Set (x=0):
[
y^4=16
\Rightarrow
y=\pm2.
]
Because both (x) and (y) occur only with even powers, replacing (x) by (-x), (y) by (-y), or both leaves the
equation unchanged.
Why the other options are less appropriate: The intercepts in A are reversed, while B and C omit valid
symmetries.
,Question 7
For the equation
[
y^2=4-x,
]
which statement is correct?
A. The graph has (x)-intercept ((4,0)), (y)-intercepts ((0,\pm2)), and symmetry about the (x)-axis.
B. The graph has (x)-intercepts ((\pm4,0)) and symmetry about the (y)-axis.
C. The graph has no (y)-intercepts.
D. The graph is symmetric about the origin.
Correct Answer: A.
Rationale: Setting (y=0),
[
0=4-x\Rightarrow x=4.
]
Setting (x=0),
[
y^2=4\Rightarrow y=\pm2.
]
Replacing (y) by (-y) leaves
[
(-y)^2=4-x
]
unchanged, proving (x)-axis symmetry.
Why the other options are less appropriate: There is only one (x)-intercept, two real (y)-intercepts, and no
origin symmetry.
Question 8
The equation
[
x^2+ky^2=36
]
passes through ((3,3)). Determine (k) and the resulting (y)-intercepts.
A. (k=1,;(0,\pm6))
B. (k=4,;(0,\pm3))
, C. (k=3,;(0,\pm2\sqrt3))
D. (k=2,;(0,\pm3\sqrt2))
Correct Answer: C.
Rationale: Substitute ((3,3)):
[
9+9k=36,
]
so
[
9k=27,
\qquad
k=3.
]
For (y)-intercepts set (x=0):
[
3y^2=36,
]
[
y^2=12,
]
[
y=\pm2\sqrt3.
]
Thus
[
\boxed{k=3,\qquad (0,\pm2\sqrt3)}.
]
Question 9
Determine the standard symmetry of
[
y=x^5-4x^3+x.
]
A. (x)-axis symmetry
B. Origin symmetry
C. (y)-axis symmetry
D. No standard coordinate symmetry
Correct Answer: B. Origin symmetry
