- Calculus 1
- Apply Rolle's Theorem
- Find the derivatives of inverse trigonometric functions
- Use logarithmic differentiation
- Solve optimization problems
- Apply first and second derivative tests
- Find extreme values and critical points
- Apply implicit differentiation and solve for related rates
- Find the definition of the derivative
- Calculate limits
- Find tangent line equations
- Evaluate logarithmic functions
- Evaluate exponential functions
- Evaluate trigonometric functions
- Combine functions
- Transform functions
- Set up and solve function word problems
- Sketch functions
- Determine properties of functions
- General Chemistry 1
- Solve problems relating to the Born-Haber Cycle
- Solve problems relating to Coulomb's Law and properties of ionic compounds
- Solve problems relating to vapor pressure and phase diagrams
- Assess problems relating to intermolecular forces
- Apply the Molecular Orbital Theory
- Apply Lewis, VSEPR, and Valence Bond Theory simultaneously
- Assess dipole moment, polarity, bond order, bond length, and bond energies
- Apply the VSEPR Theory
- Assess electronegativity differences and polarity of bonds
- Draw Lewis structures with exceptions to the octet rule
- Draw Lewis structures
- Solve problems relating to the periodic table and its trends
- Solve problems relating to electron configuration
- Solve problems relating to quantum numbers
- Solve problems relating to quantum mechanics
- Solve problems relating to atomic spectra of hydrogen
- Solve problems relating to electromagnetic radiation
- Solve problems relating to Hess's Law and standard enthalpies of formation
- Solve problems relating to enthalpy and internal energy
- Solve problems relating to pressure-volume work
- Solve problems relating to calorimetry
- Solve problems relating to quantity of heat
- Solve problems relating to real gases
- Solve problems relating to Graham's Law
- Solve problems relating to kinetic-molecular theory
- Solve problems relating to collecting a gas over water
- Solve problems relating to Dalton's Law of Partial Pressures
- Solve problems relating to the ideal gas law
- Solve problems relating to simple gas laws
- Use a manometer to measure gas pressure
- Write redox equations
- Write net ionic equations
- Solve problems relating to limiting reactant
- Solve problems relating to stoichiometry
- Name compounds
- Assign oxidation states
- Solve problems relating to empirical and molecular formulas
- Solve problems relating to Avogadro's number, moles, and mass
- Solve problems relating to isotopes
- Identify the number of protons, neutrons, and electrons in atoms and ions
- Apply laws to solve problems
- Classify matter
- Report measurement
- Calculus 2
- Solve problems relating to Taylor and Maclaurin series
- Solve problems relating to power series
- Solve problems relating to convergence and divergence
- Solve problems relating to the Alternating Series Estimation Theorem
- Solve problems relating to conditional convergence
- Solve problems relating to absolute convergence
- Solve problems relating to comparison tests
- Solve problems relating to the P-Series Test
- Solve problems relating to the Integral Test
- Solve problems relating to the Nth Term Test
- Find the telescopic sum
- Solve problems relating to geometric series
- Solve problems relating to partial sums
- Solve problems relating to sequences
- Evaluate improper integrals by cases
- Apply integration techniques
- Use integration to find the work done
- Find the volume of a solid of revolution
- Solve problems relating to arc length
- Use numerical integration
- Analyze phase planes
- Solve problems relating to polar coordinates
- Apply Euler's method
- Solve problems relating to first-order differential equations
- Solve problems relating to polar coordinate equations
- Find the area under the curve
- Solve problems relating to parametric curves
- Sketch slope fields
- Solve problems relating to area in polar coordinates
- Solve problems relating to intersection of polar curves
- Solve problems relating to logistic models
- AP Calculus AB
- Solve derivatives of trigonometric and natural logarithmic functions
- Connect differentiability and continuity: determine when derivatives do and do not exist
- Solve volume with disc method: revolving around the x- or y-axis
- Define the derivative of a function and use derivative notations
- Estimate limit values from graphs and tables
- Solve Riemann sums, summation notation, and definite integral notation
- Sketch graphs of functions and their derivatives
- Apply the Chain Rule
- Apply derivative rules: power, constant, sum, difference, and constant multiple
- Work with the Intermediate Value Theorem
- Connect limits at infinity and horizontal asymptotes
- Connect infinite limits and vertical asymptotes
- Confirm continuity over an interval
- Define continuity at a point
- Use the first and second derivative test to determine relative (local) extrema
- Find particular solutions using initial conditions and separation of variables
- Find the area between curves expressed as functions of y
- Integrate using substitution
- Solve exponential models with differential equations
- Find general solutions using separation of variables
- Reason using slope fields
- Sketch slope fields
- Verify solutions for differential equations
- Model situations with differential equations
- Solve volume with washer method: revolve around other axes
- Solve volume with washer method: revolve around the x- or y-axis
- Solve volume with disc method: revolving around other axes
- Solve volumes with cross sections: triangles and semicircles
- Solve volumes with cross sections: squares and rectangles
- Find the area between curves that intersect at more than two points
- Find the area between curves expressed as functions of x
- Use accumulation functions and definite integrals in applied contexts
- Connect position, velocity, and acceleration of functions using integrals
- Find the average value of a function on an interval
- Select techniques for antidifferentiation
- Integrate functions using long division and complete the square
- Find antiderivatives and definite integrals: basic rules and notation - Part 2
- Find antiderivatives and definite integrals: basic rules and notation - Part 1
- Find antiderivatives and indefinite integrals: basic rules and notation
- Apply properties of definite integrals
- Interpret the behavior of accumulation functions involving area
- Solve the fundamental theorem of calculus and accumulation functions
- Approximate areas with Riemann sums
- Determine concavity of functions over their domains
- Use the candidates test to determine absolute (global) extrema
- Determine intervals on which a function is increasing or decreasing
- Solve problems relating to Extreme Value Theorem, global vs. local extrema, and critical points
- Approximate values of a function using local linearity and linearization
- Straight-line motion: connect position, velocity, and acceleration
- Interpret the meaning of the derivative in context
- Calculate higher-order derivatives
- Differentiate inverse functions
- Use implicit differentiation
- Apply the Product Rule and Quotient Rule
- Define average and instantaneous rates of change at a point
- Connect multiple representations of limits
- Determine limits by the Squeeze Theorem
- Determine limits by algebraic manipulation
- Determine limits by direct substitution
- Determine limits by limit properties
- AP Calculus BC
- Apply the Comparison Tests for convergence
- Apply derivative rules: power, constant, sum, difference, and constant multiple
- Find the area of the region bounded by two polar curves
- Find the area between curves that intersect at more than two points
- Integrate using substitution
- Find antiderivatives and indefinite integrals: basic rules and notation
- Approximate values of a function using local linearity and linearization
- Interpret the meaning of the derivative in context
- Differentiate inverse functions
- Apply the Chain Rule
- Connect position, velocity, and acceleration of functions using integrals
- Interpret the behavior of accumulation functions involving area
- Use the first and second derivative test to determine relative (local) extrema
- Determine concavity of functions over their domains
- Use the candidates test to determine absolute (global) extrema
- Determine intervals on which a function is increasing or decreasing
- Straight-line motion: connect position, velocity, and acceleration
- Use implicit differentiation
- Find the derivatives of tan, cot, sec, and/or csc functions
- Work with the Intermediate Value Theorem
- Find radius and interval of convergence of power series
- Sketch slope fields
- Model situations with differential equations
- [BC only] Solve the arc length of a smooth, planar curve and distance traveled
- Solve volume with washer method: revolve around other axes
- Solve volume with disc method: revolving around other axes
- Solve volumes with cross sections: squares and rectangles
- Find the area between curves expressed as functions of y
- [BC only] Evaluate improper integrals
- Represent functions as power series
- Find Taylor or Maclaurin series for a function
- Apply Lagrange error bound
- Find Taylor polynomial approximations of functions
- Apply alternating series error bound
- Determine absolute or conditional convergence
- Apply the Ratio Test for convergence
- Apply the Alternating Series Test for convergence
- Apply the Harmonic Series and P-Series
- Apply the Integral Test for convergence
- Apply the Nth Term Test for divergence
- Work with geometric series
- Define convergent and divergent infinite series
- Find the area of a polar region or area bounded by a single polar curve
- Define polar coordinates and differentiate in polar form
- Solve motion problems using parametric and vector-valued functions
- Integrate vector-valued functions
- Define and differentiate vector-valued functions
- Find arc lengths of curves given by parametric equations
- Find second derivatives of parametric equations
- Define and differentiate parametric equations
- [BC only] Solve logistic models with differential equations
- Solve exponential models with differential equations
- Find particular solutions using initial conditions and separation of variables
- Find general solutions using separation of variables
- [BC only] Approximate solutions using Euler's method
- Reason using slope fields
- Verify solutions for differential equations
- Solve volume with washer method: revolve around the x- or y-axis
- Solve volume with disc method: revolving around the x- or y-axis
- Solve volumes with cross sections: triangles and semicircles
- Find the area between curves expressed as functions of x
- Use accumulation functions and definite integrals in applied contexts
- Find the average value of a function on an interval
- Select techniques for antidifferentiation
- [BC only] Integrate using integration by parts
- Integrate functions using long division and complete the square
- Find antiderivatives and definite integrals: basic rules and notation - Part 2
- Find antiderivatives and definite integrals: basic rules and notation - Part 1
- Apply properties of definite integrals
- Solve the fundamental theorem of calculus and accumulation functions
- Solve Riemann sums, summation notation, and definite integral notation
- Approximate areas with Riemann sums
- Sketch graphs of functions and their derivatives
- Solve problems relating to Extreme Value Theorem, global vs. local extrema, and critical points
- Calculate higher-order derivatives
- Apply the Product Rule and Quotient Rule
- Solve derivatives of cos x, sin x, e^x, and ln x
- Connect differentiability and continuity: determine when derivatives do and do not exist
- Define the derivative of a function and use derivative notations
- Define average and instantaneous rates of change at a point
- Connect limits at infinity and horizontal asymptotes
- Connect infinite limits and vertical asymptotes
- Confirm continuity over an interval
- Define continuity at a point
- Connect multiple representations of limits
- Determine limits by the Squeeze Theorem
- Determine limits by algebraic manipulation
- Determine limits by direct substitution
- Determine limits by limit properties
- Estimate limit values from graphs and tables
- General Chemistry 2
- Solve problems relating to solubility and Ksp
- Solve problems relating to the equilibrium constant expression
- Relate equilibrium concentrations of reactants and products
- Solve problems relating to the effect of temperature on reaction rates
- Solve problems relating to the rate law
- Solve problems involving equilibrium calculations
- Solve problems involving Ecell as a function of concentrations
- Solve problems involving strong acids, strong bases, weak acids, and weak bases
- Solve problems involving acids, bases, and conjugate acid-base pairs
- Solve problems relating to standard Gibbs energy and K
- Solve problems involving redox reactions
- Use Le Chatelier's Principle, Q, and K
- Use molecular structure to predict acid-base behavior and demonstrate the common-ion effect
- Solve problems involving titrations
- Solve problems relating to entropy
- Measure reaction rates
- Solve problems relating to reaction mechanisms
- Solve problems relating to precipitation
- Solve problems involving electrolysis
- Solve problems relating to standard Gibbs energy
- Solve problems relating to reactions of various orders
- Solve problems involving buffer solutions
- Write equilibrium constant expressions for reactions involving pure solids or liquids
- Solve problems relating to polyprotic acids and ions as acids and bases
- Solve problems relating to zero-, first-, and second-order reactions
- AP Chemistry
- Solve problems involving galvanic (voltaic) and electrolytic cells
- Solve problems involving solubility equilibria
- Solve problems involving buffers and titrations
- Solve problems involving second-order reactions
- Solve problems involving nomenclature (molecular compounds)
- Solve problems involving ionic and net ionic equations
- Solve problems involving single- and double-replacement reactions
- Solve problems involving entropy and Gibbs free energy
- Solve problems involving spectroscopy and the electromagnetic spectrum
- Solve problems involving acid-base equilibria
- Solve problems involving atomic structure and electron configuration
- Solve problems involving gases
- Solve problems relating to Lewis structures and molecular geometry
- Solve problems involving compounds and ions
- Solve problems involving types of bonds
- Solve problems involving internal energy, heat, and work
- Solve problems involving nomenclature (ionic compounds)
- Solve problems involving zero- and first-order reactions
- Solve problems involving intermolecular forces
- Solve problems involving cell potentials under nonstandard conditions
- Solve problems involving the factors that affect chemical equilibrium
- Solve problems involving acids, bases, and pH
- Solve problems involving standard cell potentials
- Solve problems involving Arrhenius equation and reaction mechanisms
- Solve problems involving atoms
- Solve problems involving the equilibrium constant
- Solve problems involving reaction rates and the rate law
- Solve problems involving enthalpy
- Solve problems involving precipitation reactions
- Solve problems electrolytic cells and electrolysis
- Solve problems involving periodic table trends
- Solve problems involving solutions and mixtures
- Solve problems involving redox reactions
- Microeconomics
- Elucidate Application of Demand and Supply
- Understanding Ecotourism
- Identify and Explain Factors affecting Demand and Supply
- Explaining the Democratic System of Government
- Understanding International Externalities
- Understanding the concept of Public Goods
- Understanding economic systems and globalization
- Explaining Imperfect Information
- Understanding Immigration
- Elucidate definitions calculation and graphs of Costs and profit in short run
- Explain the functioning of a Monopoly
- Defining Positive externality
- Finding out Market-Oriented Environmental Tools
- Define and Calculate Different Types of Elasticity
- Explain key concepts in the process of Production in Short Run with key definitions
- Identifying Government encouragement to innovation
- Defining Negative Externality
- Understanding How Businesses Raise Financial Capital
- Explaining the concept of Labor union
- Define and Explain Types of Costs and Profit
- Explain and Analyze Efficiency in Perfect Competitive Markets
- Understanding Insurance and Imperfect Information
- Explaining the Theories of International Trade
- Explain the functioning of a Monopoly, Anti-competitive behaviour and regulations
- Understanding the Labor Markets
- Explain and Analyze Price Controls, Surplus and Efficiency
- Analyze the Factors affecting Consumption Choices
- Explain Changes in Elasticity
- Explain the broad aspects of economic systems
- Explain functioning of Monopolistic Competition and Oligopoly
- Understanding Special Interest Politics
- Define and Explain Perfect Competition - Price, Output and profit
- Evaluating the Government Policies to Reduce Income Inequality
- Define and Analyze the Problems of Scarcity and Choices
- Finding out the Tradeoff between Economic Output and Environment
- Explaining Income Inequality
- Discusssing the Arguments in Support of Restricting Imports
- Understanding Protectionism
- Understanding the reason behind Intra-industry Trade between Similar Economies
- Knowing about Public Economy
- Explaining Households Supply of Financial Capital
- Understanding Poverty
- Decoding Employment Discrimination
- Undertaking Marginal Analysis of pollution reduction
- Analyze Costs in the Long run
- Explain Relationship between Consumer Choices and Utility
- Define and Graph Demand, Supply and Equilibrium
- Analyze Problems of Scarcity and Social Choices
- Macroeconomics
- Exchange rates demand and supply shifts
- Automatic stablizers
- National debt
- International Trade and Capital flows
- Graphs, variables, and economic models
- Equilibrium and Stabilization
- National Income
- Unemployment and related terms
- Aggregate Demand
- Money Supply
- Fiscal policy
- Phillips Curve
- Unemployment: Short run
- Opportunity Cost
- Measures of Inflation
- Solving for Scarcity
- Monetary and Fiscal Policy: Application
- Cost and Benefit of Inflation
- Discretionary fiscal policy
- Unemployment: Long run
- AD-AS Model Equilibrium
- Globalization and Protectionism
- Policies and events affecting an open economy
- Loanable funds
- Exchange Rate polcies
- Foreign Exchange
- Macro economics of open economies
- Velocity and Quantity equation
- Inflation
- Money
- Federal Reserve System
- Interest rates
- Discretionary fiscal policy
- Types of fiscal policy
- Taxation
- Government spending
- Indexing
- Causes of inflation
- Understanding Inflation
- Computation of unemployment rate
- Types of unemployment
- Aggregate Supply
- IS-LM Model
- Basic Demand-Supply
- GDP
- Consumer Price Index
- Mechanics 1
- Understanding the aspects of acceleration due to gravity
- Understanding the concept of linear momentum
- Understanding the concept of angular motion
- Understanding the concept of center of mass and using them to solve problems
- Understanding the concept of energy
- Understanding the concept of collisions
- Understanding the concept of conservation of momentum
- Understanding phenomena based on gravity occurring in everyday life
- Graphing and using energy diagrams
- Applying the law of energy conservation
- Understanding potential energy
- Understanding work done by a variable force
- Understanding how work and kinetic energy are related
- Understanding the concept of power
- Understanding the concept of work
- Understanding the concepts of energy and kinetic energy
- Solving problems based on gravity
- Understanding the basics of motion and acceleration
- Understanding the basics of gravity
- Understanding frictional forces
- Understanding projectile motion
- Solving problems using Newton's Laws of Motion
- Understanding kinematic graphs
- Solving problems based on the equations of motion
- Understanding the concept of rotational motion
- Electricity and Magnetism
- Understanding the force on a moving charge in a magnetic field
- Understanding the combinations of capacitors and the energy stored in a capacitor
- Applying Gauss’s law
- Understanding magnetic properties of matter
- Understanding Series-Parallel circuit
- Understanding the magnetic effect of an electric current
- Understanding magnetic dipole moment
- Understanding Ohm's Law & Current electricity
- Understanding DC Parallel circuit
- Understanding dynamic or motional electromagnetic induction
- Understanding Krichoff's Law
- Understanding capacitors
- Understanding Gauss’s law
- Electric potential and electric potential energy
- Electric field and force on charges
- Electric charge and application of Coulomb’s law
- Solving problems based on the applications of electromagnetic induction
- Understanding energy stored in an inductor
- Solving problems based on inductance
- Solving problems by applying the concept of induced EMF
- Understanding the production of induced EMF
- Understanding Power and Power Factor in an AC Circuit
- Understanding RLC circuit
- Understanding capacitive reactance
- Understanding inductive reactance
- Understanding AC waveform
- Understanding DC Series circuit
Mathematics skill
Sketch functions
With this skill you will learn
- Graph lines written in the form y = mx + b
- Graph piecewise-defined functions
- Roughly sketch factored polynomials (specifically, cubic)
- Find vertical asymptotes of rational functions
- Find horizontal asymptotes of rational functions when deg(P) = deg(Q)
Sketch functions Questions
Questions that need this skill to solve them
.OC user
in Mathematics·
30 Aug 2020
.OC user
in Mathematics·
20 Feb 2021
, sketch the graph of 
.OC user
in Mathematics·
20 Feb 2021
, sketch the graph of 
.OC user
in Mathematics·
20 Feb 2021
.OC user
in Mathematics·
13 Jul 2020
.OC user
in Mathematics·
13 Jul 2020
, sketch the graph of 
.OC user
in Mathematics·
20 Feb 2021
.
is the Heaviside function:
OC user
in Mathematics·
13 Jul 2020
.OC user
in Mathematics·
6 Jan 2021
OC user
in Mathematics·
6 Jan 2021
OC user
in Mathematics·
14 Jan 2021
OC user
in Mathematics·
14 Jan 2021
OC user
in Mathematics·
14 Jan 2021
OC user
in Mathematics·
6 Jan 2021
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