The meat of this
book is problem after problem organized by topic so you can focus
on your weak areas.

-K. Paye
on Acing the new SAT I Math




    CONTENTS:

  • About the Exams


  • PART A: Math Review


  • Chapter 1: Limits and Continuity
    • 1.1: Rates of Change
    • 1.2: The Limit of a Function and One Sided Limits
    • 1.3: Calculating Limits Using the Limit Laws
    • 1.4: Properties of Continuity and Intermediate Value Theorem
    • 1.5: Limits and Asymptotes
    • Answers and Explanations

  • Chapter 2: Differentiation
    • 2.1: Definition of Derivatives and the Power Rule
    • 2.2: The Product and Quotient Rules and Higher Derivatives
    • 2.3: The Chain Rule and the Composite Functions
    • 2.4: Derivatives of Trigonometric Functions
    • 2.5: Derivatives of Exponential and Logarithmic Functions
    • 2.6: The Tangent Lines and the Normal Lines
    • 2.7: Implicit Differentiation
    • 2.8: Derivatives of an Inverse Function
    • 2.9: Derivatives of Inverse Trigonometric Functions
    • 2.10 Apporximating a Derivative
    • Answers and Explanations

  • Chapter 3: Applications of Differentiation
    • 3.1: Related Rates
    • 3.2: Position, Velocity, and Acceleration
    • 3.3: Roll's Theorem and The Mean Value Theorem
    • 3.4: The First Derivative Test and the Extreme Values of Functions
    • 3.5: The Second Derivative Test
    • 3.6: Curves of ƒ, ƒ', ƒ'' and Curve Sketching
    • 3.7: Optimization Problems
    • 3.8: Tangent Line Approximation and Differentials
    • Answers and Explanations

  • Chapter 4: Integration
    • 4.1: Antiderivatives and Indefinite Integrals
    • 4.2: Riemann Sums and Area Approximation
    • 4.3: Definite Integral, Area Under a Curve, and Application
    • 4.4: Properties of Definite Integral
    • 4.5: Trapezoidal Rule
    • 4.6: The Fundamental Theorem of Calculus Part 1
    • 4.7: The Fundamental Theorem of Calculus Part 2
    • 4.8: Integration by Substitution
    • 4.9: Integration of Exponential and Logarithmic Function
    • Answers and Explanations

  • Chapter 5: Applications of Integration
    • 5.1: Area of a Region between Two Curves
    • 5.2: Volumes by Disk and Washers
    • 5.3: Volumes of Solids with Known Cross-Sections
    • 5.4: The Total Change Theorem (Application of FTC)
    • 5.5: Motion of a Particle, Distance, and Displacement
    • 5.6: Average Value of a Function
    • 5.7: Length of a Curve (Distance Traveled Along a Curve) BC
    • Answers and Explanations

  • Chapter 6: Techniques of Integration
    • 6.1: Basic Integration Rules
    • 6.2: Trigonometric Integrals
    • 6.3: Trigonometric Substitutions
    • 6.4: L'Hospital's Rule
    • 6.5: Integration by Partial Fractions BC
    • 6.6: Integration by Parts BC
    • 6.7: Improper Integrals BC
    • Answers and Explanations

  • Chapter 7: Further Applications of Integration
    • 7.1: Slope Field
    • 7.2: Separable Differential Equations
    • 7.3: Exponential Growth and Decay
    • 7.4: Logistic Equations BC
    • 7.5: Euler's Method BC
    • Answers and Explanations

  • Chapter 8: Parametric Equations, Vectors, and Polar Coordinates BC
    • 8.1: Slopes and Tangents to the Parametric Curves
    • 8.2: Arc Length (Distance Traveled Along a Curve) in Parametric Form
    • 8.3: Vector Valued Functions
    • 8.4: Polar Coordinates and Slopes of the Curves
    • 8.5: Areas in Polar Coordinates
    • Answers and Explanations

  • Chapter 9: Infinite Sequences and Series BC
    • 9.1: Sequences and Series
    • 9.2: The Integral Test and ρ-Series
    • 9.3: The Comparison Tests
    • 9.4: Alternating Series and Error Bound
    • 9.5: The Ratio Test
    • 9.6: Convergence of Power Series
    • 9.7: Representations of Functions as Power Series
    • 9.8: Taylor Polynomial and Lagrange Error Bound
    • 9.9: Taylor Series and Maclaurin Series
    • Answers and Explanations


  • PART B: Practice Tests


  • AP Calculus AB Practice Test 1
    • SECTION I, Part A and Part B
    • SECTION II, Part A and Part B
    • Answers and Explanations

  • AP Calculus AB Practice Test 2
    • SECTION I, Part A and Part B
    • SECTION II, Part A and Part B
    • Answers and Explanations

  • AP Calculus BC Practice Test 1
    • SECTION I, Part A and Part B
    • SECTION II, Part A and Part B
    • Answers and Explanations

  • AP Calculus BC Practice Test 2
    • SECTION I, Part A and Part B
    • SECTION II, Part A and Part B
    • Answers and Explanations



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