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0. Functions(0)

Introduction to Functions
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Piecewise Functions
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Properties of Functions
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Common Functions
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Transformations
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Combining Functions
(0)

Exponent Rules
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Exponential Functions
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Logarithmic Functions
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Properties of Logarithms
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Exponential & Logarithmic Equations
(0)

1. Limits and Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

2. Intro to Derivatives(0)

Tangent Lines and Derivatives
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Derivatives as Functions
(0)

Basic Graphing of the Derivative
(0)

Differentiability
(0)

3. Techniques of Differentiation(0)

Basic Rules of Differentiation
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Higher Order Derivatives
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Product and Quotient Rules
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The Chain Rule
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4. Derivatives of Exponential & Logarithmic Functions(0)

Derivatives of Exponential & Logarithmic Functions
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5. Applications of Derivatives(0)

Implicit Differentiation
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Logarithmic Differentiation
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Related Rates
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Differentials
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Linearization
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6. Graphical Applications of Derivatives(0)

Intro to Extrema
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The First Derivative Test
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Concavity
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The Second Derivative Test
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Curve Sketching
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Finding Global Extrema
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Applied Optimization
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7. Antiderivatives & Indefinite Integrals(0)

Antiderivatives
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Indefinite Integrals
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8. Definite Integrals(0)

Estimating Area with Finite Sums
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Riemann Sums
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Introduction to Definite Integrals
(0)

Fundamental Theorem of Calculus
(0)

Average Value of a Function
(0)

Substitution for Indefinite Integrals
(0)

Substitution for Definite Integrals
(0)

9. Graphical Applications of Integrals(0)

Area Between Curves
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Introduction to Volume & Disk Method
(0)

10. Integrals of Inverse, Exponential, & Logarithmic Functions(0)

Integrals of Exponential Functions
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Integrals Involving Logarithmic Functions
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11. Techniques of Integration(0)

Integration by Parts
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Improper Integrals
(0)

12. Trigonometric Functions(0)

Angles
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Trigonometric Functions on Right Triangles
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Solving Right Triangles
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Trigonometric Functions on the Unit Circle
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Graphs of Sine & Cosine
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Graphs of Other Trigonometric Functions
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Trigonometric Identities
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Derivatives of Trig Functions
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Integrals of Basic Trig Functions
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Integrals of Other Trig Functions
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13: Intro to Differential Equations(0)

Basics of Differential Equations
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Slope Fields
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Separable Differential Equations
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14. Sequences & Series(0)

Sequences
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Review of Factorials
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Series
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15. Power Series(0)

Power Series & Taylor Series
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16. Probability & Calculus(0)

Continuous Probability Models
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Review of Real Numbers(0)

The Distributive Property
(0)

Review of Real Numbers

The Distributive Property

Review of Real Numbers

The Distributive Property: Video e Problemi di Pratica

Videolezioni Pratica Foglio di lavoro

27 problemi

Problema 1Scelta multipla

Rewrite 6(x - 5) without parentheses using the distributive property and simplify.

Problema 2Scelta multipla

Which of the multiple choice statements listed below correctly expresses the distributive property for addition?

Problema 3Scelta multipla

Which is the correct expansion of (4x + 3y - 4)5, and which property justifies distributing the 5 even though it is written on the right?

Problema 4Scelta multipla

Evaluate $5 (3 + 8)$ two ways: (a) solve the inside of the parentheses first using the correct order of operations, and (b) distribute the 5 into the parentheses and then solve for the final result. What are the numerical final results for parts (a), and (b)?

Problema 5Scelta multipla

Select the correct expansion of -3(a - 4).

Problema 6Scelta multipla

Compute 7 - 2(3 + 5).

Problema 7Scelta multipla

Are the expressions 2(x + 3) + 4 and 2x + 10 algebraically equivalent? Choose the best justification.

Problema 8Scelta multipla

Expand and simplify 4(3x - 5y + 2z).

Problema 9Scelta multipla

Which expression is the correct factorization (reverse of distribution) of 12x + 6y - 21z?

Problema 10Scelta multipla

Which one of the following expressions requires the distributive property to remove parentheses because the parentheses contain a variable term?

Problema 11Scelta multipla

Which of the following statements correctly explains why the equation: $a (b - c) = a b - a c$ is written in terms of treating subtraction as an addition of a negative?

Problema 12Scelta multipla

A baker packs 8 muffins and 5 cookies in each box. A customer orders 12 identical boxes and also buys 7 extra cookies. Write an expression for the total number of items.

Problema 13Scelta multipla

Expand and simplify 2(3a - 4b + 5c - 6).

Problema 14Scelta multipla

Compute (x + 2) · 4 by distributing and simplifying.

Problema 15Scelta multipla

Which of the following choices best illustrates how the commutativity of multiplication is applied with the distributive property?

Problema 16Scelta multipla

Which of the following pairs of expressions are algebraically equivalent for all real x?

Problema 17Scelta multipla

Are the expressions -2(x + 5) + 4 and -2x - 6 equivalent? Use distribution and simplification to justify your answer.

Problema 18Scelta multipla

A garden's length is given by 3(x + 2) meters and its width is 2 meters. Express the area in simplified form by distributing and simplifying coefficients.

Problema 19Scelta multipla

Which expansion of -4(2x - 3y + 5) is correct?

Problema 20Scelta multipla

Expand 5(0.2x + 3).

Problema 21Scelta multipla

Expand 4(2 + x) and then check your result by evaluating both the original and expanded expressions at x = 3.

Problema 22Scelta multipla

Simplify the expression 3(2x + 4y - 5z + 1).

Problema 23Scelta multipla

Write an equivalent expression by distributing for (2x + 6)3, then simplify. Emphasize the commutative property used.

Problema 24Scelta multipla

A student expands -2(4x - 7) and gets -8x + 14. Another student claims the correct expansion is -8x - 14. Evaluate both claims and decide which student, if any, is correct. Provide reasoning.

Problema 25Scelta multipla

Use the distributive property to expand 3(x + 4). Then, calculate the value when x = -2 and verify it by directly substituting x = -2 into the original expression.

Problema 26Scelta multipla

Identify the correctly expanded form of 7(2x - 3).

Problema 27Scelta multipla

Consider the pair of expressions: A = 2(a + b) + 3b and B = 2a + 5b. Are A and B equivalent for all values of a and b? Provide justification.

Continuous Probability Models Problemi di pratica

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