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Browse original practice for Pre-K through Grade 12. Each resource explains its learning goal and opens a workspace to preview, customize where supported, and print or save as PDF.

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21 resources · Page 1 of 1

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Grade 11

Key

Exponential Model Audit: Club Practice

Practice · Independent · 30 min

Exponential Model Audit: Club Practice. Grade 11 printable practice: Interpret initial value and growth factor without overextending an exponential model. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

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Grade 11

Key

Exponential Model Audit: Garden Practice

Practice · Independent · 30 min

Exponential Model Audit: Garden Practice. Grade 11 printable practice: Interpret initial value and growth factor without overextending an exponential model. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

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Grade 11

Key

Exponential Model Audit: Library Practice

Practice · Independent · 30 min

Exponential Model Audit: Library Practice. Grade 11 printable practice: Interpret initial value and growth factor without overextending an exponential model. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

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Grade 11

Key

Exponential Model Audit: Workshop Practice

Practice · Independent · 30 min

Exponential Model Audit: Workshop Practice. Grade 11 printable practice: Interpret initial value and growth factor without overextending an exponential model. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Exponential Growth Decay and Model Domains

A discrete exponential model

Invented practice data or scenario; not a report of a real study.

An idealized sequence follows y = 4 × (2)^n for whole-number steps n ≥ 0. Values are units, not a verified prediction. Compare ratios between consecutive steps and specify the meaning of step zero.

Worked example: For y = 10(0.8)^n, the initial value is 10 and each step retains 80%, a 20% decrease. At n = 2, y = 6.4. Use the material to work through each task. Show the requested response.

1.What is y at step zero, and what does it represent?

Practice preview

Grade 11

Key

Exponential Growth Decay and Model Domains

Practice · Independent · 45 min

Read an exponential rule and its initial value. Calculate values, exponents and per-step percent change. Compare models and preserve units and domain assumptions. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Inverse Functions Domains and Branches

Reverse a restricted mapping

Use f(x) = 2x + 3 on the real numbers. Separately use q(x) = x² restricted to x ≥ 0. Reversing a mapping exchanges its domain and range; do not remove the restriction.

Worked example: If p(x) = 5x + 2, p⁻¹(x) = (x − 2)/5. If r(x) = x² for x ≥ 0, r⁻¹(x) = √x for x ≥ 0. Use the material to work through each task. Show the requested response.

1.Find f(3) and identify which inverse input returns 3.

Practice preview

Grade 11

Key

Inverse Functions Domains and Branches

Practice · Independent · 45 min

Reverse a one-to-one mapping. Calculate inverse values with domain restrictions. Justify a root branch and interpret inverse notation and graphs. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Logarithms Laws Domains and Valid Equations

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Worked example: log₄(16)=2 because 4²=16. For positive u and v, log₄(u)+log₄(v)=log₄(uv); adding the arguments is a different operation. Use the material to work through each task. Show the requested response.

1.Evaluate log_2(8).

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations

Practice · Independent · 45 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Rational Radical Equations and Valid Solutions

Equations before and after squaring

Work over real numbers. Consider √(x + 4) = x − 2. Squaring produces candidates, not automatically valid solutions. Also compare R(x) = (x² − 4)/(x − 2) with its simplified rule; its original denominator restriction remains.

Worked example: √(x + 1) = x − 1 gives x = 0 or 3 after squaring. Only 3 satisfies the original equation; 0 has a negative right side. Use the material to work through each task. Show the requested response.

1.What restriction follows because the square root must equal a nonnegative right side?

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions

Practice · Independent · 45 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Grade 11

HSF.LE.A.4 Key

Algebra 2: Exponential & Logarithmic Functions

Practice · Independent · 35 min

Selected high-school practice with evidence, conditions and a written explanation.

Shuffle this practice

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Exponential Growth Decay and Model Domains: Apply and Create

A discrete exponential model

Invented practice data or scenario; not a report of a real study.

An idealized sequence follows y = 4 × (2)^n for whole-number steps n ≥ 0. Values are units, not a verified prediction. Compare ratios between consecutive steps and specify the meaning of step zero.

Use what you learned to explain, construct or apply an idea.

1.Explain why adding the first-step change repeatedly gives a different model. Check the value at step two.

Practice preview

Grade 11

Key

Exponential Growth Decay and Model Domains: Apply and Create

Apply · Independent · 25 min

Read an exponential rule and its initial value. Calculate values, exponents and per-step percent change. Compare models and preserve units and domain assumptions. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

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Exponential Growth Decay and Model Domains: Explore and Explain

A discrete exponential model

Invented practice data or scenario; not a report of a real study.

An idealized sequence follows y = 4 × (2)^n for whole-number steps n ≥ 0. Values are units, not a verified prediction. Compare ratios between consecutive steps and specify the meaning of step zero.

Worked example: For y = 10(0.8)^n, the initial value is 10 and each step retains 80%, a 20% decrease. At n = 2, y = 6.4. Explore the material. Talk through your reasoning with suitable support.

1.What is y at step zero, and what does it represent?

Practice preview

Grade 11

Key

Exponential Growth Decay and Model Domains: Explore and Explain

Explore · Independent · 12 min

Read an exponential rule and its initial value. Calculate values, exponents and per-step percent change. Compare models and preserve units and domain assumptions. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Exponential Growth Decay and Model Domains: Practice Independently

A discrete exponential model

Invented practice data or scenario; not a report of a real study.

An idealized sequence follows y = 4 × (2)^n for whole-number steps n ≥ 0. Values are units, not a verified prediction. Compare ratios between consecutive steps and specify the meaning of step zero.

Use the material to work through each task. Show the requested response.

1.Use the rule to find y at n = 4.

Practice preview

Grade 11

Key

Exponential Growth Decay and Model Domains: Practice Independently

Practice · Independent · 20 min

Read an exponential rule and its initial value. Calculate values, exponents and per-step percent change. Compare models and preserve units and domain assumptions. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Practice preview

Grade 11

Key

Inverse Functions Domains and Branches: Apply and Create

Apply · Independent · 25 min

Reverse a one-to-one mapping. Calculate inverse values with domain restrictions. Justify a root branch and interpret inverse notation and graphs. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Inverse Functions Domains and Branches: Explore and Explain

Reverse a restricted mapping

Use f(x) = 2x + 3 on the real numbers. Separately use q(x) = x² restricted to x ≥ 0. Reversing a mapping exchanges its domain and range; do not remove the restriction.

Worked example: If p(x) = 5x + 2, p⁻¹(x) = (x − 2)/5. If r(x) = x² for x ≥ 0, r⁻¹(x) = √x for x ≥ 0. Explore the material. Talk through your reasoning with suitable support.

1.Find f(3) and identify which inverse input returns 3.

Practice preview

Grade 11

Key

Inverse Functions Domains and Branches: Explore and Explain

Explore · Independent · 12 min

Reverse a one-to-one mapping. Calculate inverse values with domain restrictions. Justify a root branch and interpret inverse notation and graphs. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Practice preview

Grade 11

Key

Inverse Functions Domains and Branches: Practice Independently

Practice · Independent · 20 min

Reverse a one-to-one mapping. Calculate inverse values with domain restrictions. Justify a root branch and interpret inverse notation and graphs. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Logarithms Laws Domains and Valid Equations: Apply and Create

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Use what you learned to explain, construct or apply an idea.

1.A learner writes log_2(u) + log_2(v) = log_2(u + v). Correct this for positive u and v. Check using u = v = 2.

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations: Apply and Create

Apply · Independent · 25 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Logarithms Laws Domains and Valid Equations: Explore and Explain

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Worked example: log₄(16)=2 because 4²=16. For positive u and v, log₄(u)+log₄(v)=log₄(uv); adding the arguments is a different operation. Explore the material. Talk through your reasoning with suitable support.

1.Evaluate log_2(8).

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations: Explore and Explain

Explore · Independent · 12 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Logarithms Laws Domains and Valid Equations: Practice Independently

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Use the material to work through each task. Show the requested response.

1.State the real domain for the two logarithms in the material.

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations: Practice Independently

Practice · Independent · 20 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Rational Radical Equations and Valid Solutions: Apply and Create

Equations before and after squaring

Work over real numbers. Consider √(x + 4) = x − 2. Squaring produces candidates, not automatically valid solutions. Also compare R(x) = (x² − 4)/(x − 2) with its simplified rule; its original denominator restriction remains.

Use what you learned to explain, construct or apply an idea.

1.Explain why squaring made x = 0 appear as a candidate although it fails the original equation.

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions: Apply and Create

Apply · Independent · 25 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Rational Radical Equations and Valid Solutions: Explore and Explain

Equations before and after squaring

Work over real numbers. Consider √(x + 4) = x − 2. Squaring produces candidates, not automatically valid solutions. Also compare R(x) = (x² − 4)/(x − 2) with its simplified rule; its original denominator restriction remains.

Worked example: √(x + 1) = x − 1 gives x = 0 or 3 after squaring. Only 3 satisfies the original equation; 0 has a negative right side. Explore the material. Talk through your reasoning with suitable support.

1.What restriction follows because the square root must equal a nonnegative right side?

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions: Explore and Explain

Explore · Independent · 12 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Rational Radical Equations and Valid Solutions: Practice Independently

Equations before and after squaring

Work over real numbers. Consider √(x + 4) = x − 2. Squaring produces candidates, not automatically valid solutions. Also compare R(x) = (x² − 4)/(x − 2) with its simplified rule; its original denominator restriction remains.

Use the material to work through each task. Show the requested response.

1.List all roots of that quadratic.

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions: Practice Independently

Practice · Independent · 20 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

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