Free Printable Worksheets - Page 3

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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.

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High School Physics: 1D Kinematics & Motion Graph Analysis

Part A: Kinematics Calculations. Solve each mechanical physics problem below using constant acceleration equations.

1.A high-speed train accelerates uniformly from rest (v₀ = 0 m/s) at a rate of 2.5 m/s² for 10 seconds. What is the train's final velocity vf and total displacement Δx over this interval?

Avf = 25 m/s; Δx = 125 meters

Bvf = 25 m/s; Δx = 250 meters

Cvf = 50 m/s; Δx = 125 meters

Dvf = 12.5 m/s; Δx = 62.5 meters

2.On a Velocity vs. Time (v-t) graph, what physical quantity is represented by the SLOPE of the line, and what is represented by the AREA under the line?

ASlope = Jerk; Area = Kinetic energy

BSlope = Acceleration; Area = Displacement (change in position)

CSlope = Momentum; Area = Force

DSlope = Position; Area = Acceleration

Practice preview

Grade 11

NGSS.HS-PS2-1 Key

High School Physics: 1D Kinematics & Motion Graph Analysis

Practice · Independent · 20 min

High School Physics — 1D Kinematics & Motion Graph Analysis. Calculate average acceleration and state the prediction condition. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

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Practice preview

Grade 11

Key

Read Velocity Data: Apply and Create

Apply · Independent · 20 min

Read Velocity Data — Apply and Create. Calculate average acceleration and state the prediction condition. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Practice preview

Grade 11

Key

Read Velocity Data: Explore and Explain

Explore · Independent · 15 min

Read Velocity Data — Explore and Explain. Calculate average acceleration and state the prediction condition. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Practice preview

Grade 11

Key

Read Velocity Data: Practice Independently

Practice · Independent · 15 min

Read Velocity Data — Practice Independently. Calculate average acceleration and state the prediction condition. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Practice preview

Grade 11

Key

Recognize a Decision Tradeoff: Apply and Create

Apply · Independent · 20 min

Recognize a Decision Tradeoff — Apply and Create. Explain a tradeoff using commitments and priorities. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Practice preview

Grade 11

Key

Recognize a Decision Tradeoff: Explore and Explain

Explore · Independent · 15 min

Recognize a Decision Tradeoff — Explore and Explain. Explain a tradeoff using commitments and priorities. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Practice preview

Grade 11

Key

Recognize a Decision Tradeoff: Practice Independently

Practice · Independent · 15 min

Recognize a Decision Tradeoff — Practice Independently. Explain a tradeoff using commitments and priorities. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Grade 11

C3.D2.His.3.9-12 Key

US History: The Great Depression & FDR's New Deal

Practice · Independent · 20 min

US History — The Great Depression & FDR's New Deal. Distinguish a historical policy’s aim from proof of its effects. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

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Grade 11

Key

Compare Historical Perspectives: Apply and Create

Apply · Independent · 20 min

Compare Historical Perspectives — Apply and Create. Evaluate a source through its purpose and corroborating evidence. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

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Grade 11

Key

Compare Historical Perspectives: Check Your Understanding

Check · Independent · 15 min

Compare Historical Perspectives — Check Your Understanding. Evaluate a source through its purpose and corroborating evidence. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Grade 11

Key

Compare Historical Perspectives: Explore and Explain

Explore · Independent · 15 min

Compare Historical Perspectives — Explore and Explain. Evaluate a source through its purpose and corroborating evidence. Includes a contextual transfer task and answer criteria. Print on US Letter or A4, or save as PDF from the print window.

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Free Printable Worksheet Library

Algebra 2: Exponential & Logarithmic Functions

Exponential Growth Decay and Model Domains: Apply and Create

Exponential Growth Decay and Model Domains: Explore and Explain

Exponential Growth Decay and Model Domains: Practice Independently

Inverse Functions Domains and Branches: Apply and Create

Inverse Functions Domains and Branches: Explore and Explain

Inverse Functions Domains and Branches: Practice Independently

Logarithms Laws Domains and Valid Equations: Apply and Create

Logarithms Laws Domains and Valid Equations: Explore and Explain

Logarithms Laws Domains and Valid Equations: Practice Independently

Rational Radical Equations and Valid Solutions: Apply and Create

Rational Radical Equations and Valid Solutions: Explore and Explain

Rational Radical Equations and Valid Solutions: Practice Independently

High School Physics: 1D Kinematics & Motion Graph Analysis

Read Velocity Data: Apply and Create

Read Velocity Data: Explore and Explain

Read Velocity Data: Practice Independently

Recognize a Decision Tradeoff: Apply and Create

Recognize a Decision Tradeoff: Explore and Explain

Recognize a Decision Tradeoff: Practice Independently

US History: The Great Depression & FDR's New Deal

Compare Historical Perspectives: Apply and Create

Compare Historical Perspectives: Check Your Understanding

Compare Historical Perspectives: Explore and Explain