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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 12

Key

Limit Versus Function Value: Club Practice

Practice · Independent · 30 min

Limit Versus Function Value: Club Practice. Grade 12 printable practice: Distinguish a removable discontinuity, a limit, and a separately assigned value. 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 12

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Limit Versus Function Value: Garden Practice

Practice · Independent · 30 min

Limit Versus Function Value: Garden Practice. Grade 12 printable practice: Distinguish a removable discontinuity, a limit, and a separately assigned value. 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 12

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Limit Versus Function Value: Library Practice

Practice · Independent · 30 min

Limit Versus Function Value: Library Practice. Grade 12 printable practice: Distinguish a removable discontinuity, a limit, and a separately assigned value. 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 12

Key

Limit Versus Function Value: Workshop Practice

Practice · Independent · 30 min

Limit Versus Function Value: Workshop Practice. Grade 12 printable practice: Distinguish a removable discontinuity, a limit, and a separately assigned value. 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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Conditional Probability Reference Groups and Independence

Inspection flags and confirmed defects

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

This invented table contains 100 parts. A uniformly selected part is the probability model. A flag and a confirmed defect are different events. Use the relevant row, column or whole table as the reference group; do not claim the inspection caused a defect.

Worked example: Of 20 flagged objects, 5 have defects: P(defect | flag) = 5/20. If there are 10 defects overall, P(flag | defect) = 5/10. Use the material to work through each task. Show the requested response.

1.How many parts are flagged?

Practice preview

Grade 12

Key

Conditional Probability Reference Groups and Independence

Practice · Independent · 45 min

Identify table totals and the relevant probability population. Calculate conditional, union and updated probabilities. Test table independence and explain a reversed condition. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Derivatives Rates and Local Models

Position and instantaneous rate

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

An idealized position is s(t) = 1t² + 2t + 0 metres, for 0 ≤ t ≤ 4 seconds. Treat position on a number line, not distance travelled. Study the difference quotient at t = 2 for nonzero increments h with 2 + h in the domain.

Worked example: For p(t)=t² at t=1, [p(1+h)−p(1)]/h = 2+h for h≠0, so p′(1)=2. The value p(1)=1 is different. Use the material to work through each task. Show the requested response.

1.Find s(2), with units.

Practice preview

Grade 12

Key

Derivatives Rates and Local Models

Practice · Independent · 45 min

Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Limits Point Values and Continuity

A hole and a separately assigned value

For x ≠ 1, f(x) = (x² − 1)/(x − 1); separately define f(1) = 7. Compare the approach from both sides with the assigned value. A separate function g(x) = x² is used for rate questions.

Worked example: If p(x) = (x² − 16)/(x − 4) for x ≠ 4 and p(4) = 1, its limit at 4 is 8, while its point value is 1. Use the material to work through each task. Show the requested response.

1.Simplify the quotient for x ≠ 1.

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Grade 12

Key

Limits Point Values and Continuity

Practice · Independent · 45 min

Compare nearby values and a separately defined point value. Calculate selected limits and an average rate. Explain continuity, unequal one-sided limits and a graph with a hole. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Periodic Functions and Model Conditions

A periodic height model

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

A toy mechanism has idealized height h(t) = 7 + 3 cos(2πt/4) metres, with t in seconds, 0 ≤ t ≤ 4. Angles in the formula are radians. This is one full cycle; assume the specified ideal mechanism repeats only when explicitly extending the model.

Worked example: h(t)=6+2cos(2πt/10) has midline 6, amplitude 2, period 10, and height range [4,8]. Use the material to work through each task. Show the requested response.

1.State the midline and its unit.

Practice preview

Grade 12

Key

Periodic Functions and Model Conditions

Practice · Independent · 45 min

Interpret amplitude, midline and period. Evaluate a trigonometric rule and solve selected level equations. Sketch a cycle and explain changes and model extensions. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Calculus: Limits, Continuity & Derivative Rules

Part A: Calculus Computation. Evaluate each limit and derivative problem. Choose the correct mathematical result.

1.Evaluate the limit analytically: lim (x -> 3) [(x² - 9) / (x - 3)]

BUndefined (Division by zero)

2.Find the derivative f'(x) of the cubic polynomial function: f(x) = 4x³ - 5x² + 7x - 12

Af'(x) = 12x² - 10x + 7

Bf'(x) = 12x³ - 10x² + 7x

Cf'(x) = 4x² - 5x + 7

Df'(x) = x⁴ - x³ + 7

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Grade 12

HSF.IF.B.4 Key

Calculus: Limits, Continuity & Derivative Rules

Practice · Independent · 35 min

Selected optional calculus practice with evidence, conditions and a written explanation.

Shuffle this practice

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Conditional Probability Reference Groups and Independence: Apply and Create

Inspection flags and confirmed defects

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

This invented table contains 100 parts. A uniformly selected part is the probability model. A flag and a confirmed defect are different events. Use the relevant row, column or whole table as the reference group; do not claim the inspection caused a defect.

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

1.Are defect and flag independent in this table? Compare a conditional probability with the unconditional probability.

Practice preview

Grade 12

Key

Conditional Probability Reference Groups and Independence: Apply and Create

Apply · Independent · 25 min

Identify table totals and the relevant probability population. Calculate conditional, union and updated probabilities. Test table independence and explain a reversed condition. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

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Conditional Probability Reference Groups and Independence: Explore and Explain

Inspection flags and confirmed defects

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

This invented table contains 100 parts. A uniformly selected part is the probability model. A flag and a confirmed defect are different events. Use the relevant row, column or whole table as the reference group; do not claim the inspection caused a defect.

Worked example: Of 20 flagged objects, 5 have defects: P(defect | flag) = 5/20. If there are 10 defects overall, P(flag | defect) = 5/10. Explore the material. Talk through your reasoning with suitable support.

1.How many parts are flagged?

Practice preview

Grade 12

Key

Conditional Probability Reference Groups and Independence: Explore and Explain

Explore · Independent · 12 min

Identify table totals and the relevant probability population. Calculate conditional, union and updated probabilities. Test table independence and explain a reversed condition. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Conditional Probability Reference Groups and Independence: Practice Independently

Inspection flags and confirmed defects

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

This invented table contains 100 parts. A uniformly selected part is the probability model. A flag and a confirmed defect are different events. Use the relevant row, column or whole table as the reference group; do not claim the inspection caused a defect.

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

1.Find P(defective | flagged).

Practice preview

Grade 12

Key

Conditional Probability Reference Groups and Independence: Practice Independently

Practice · Independent · 20 min

Identify table totals and the relevant probability population. Calculate conditional, union and updated probabilities. Test table independence and explain a reversed condition. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Derivatives Rates and Local Models: Apply and Create

Position and instantaneous rate

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

An idealized position is s(t) = 1t² + 2t + 0 metres, for 0 ≤ t ≤ 4 seconds. Treat position on a number line, not distance travelled. Study the difference quotient at t = 2 for nonzero increments h with 2 + h in the domain.

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

1.Write a tangent-line equation at t = 2 and interpret the slope.

Practice preview

Grade 12

Key

Derivatives Rates and Local Models: Apply and Create

Apply · Independent · 25 min

Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Derivatives Rates and Local Models: Explore and Explain

Position and instantaneous rate

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

An idealized position is s(t) = 1t² + 2t + 0 metres, for 0 ≤ t ≤ 4 seconds. Treat position on a number line, not distance travelled. Study the difference quotient at t = 2 for nonzero increments h with 2 + h in the domain.

Worked example: For p(t)=t² at t=1, [p(1+h)−p(1)]/h = 2+h for h≠0, so p′(1)=2. The value p(1)=1 is different. Explore the material. Talk through your reasoning with suitable support.

1.Find s(2), with units.

Practice preview

Grade 12

Key

Derivatives Rates and Local Models: Explore and Explain

Explore · Independent · 12 min

Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Derivatives Rates and Local Models: Practice Independently

Position and instantaneous rate

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

An idealized position is s(t) = 1t² + 2t + 0 metres, for 0 ≤ t ≤ 4 seconds. Treat position on a number line, not distance travelled. Study the difference quotient at t = 2 for nonzero increments h with 2 + h in the domain.

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

1.Take the limit as h → 0 to find s′(2). State its unit.

Practice preview

Grade 12

Key

Derivatives Rates and Local Models: Practice Independently

Practice · Independent · 20 min

Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Limits Point Values and Continuity: Apply and Create

A hole and a separately assigned value

For x ≠ 1, f(x) = (x² − 1)/(x − 1); separately define f(1) = 7. Compare the approach from both sides with the assigned value. A separate function g(x) = x² is used for rate questions.

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

1.Is f continuous at 1 as currently defined? Use the limit and value to explain.

Practice preview

Grade 12

Key

Limits Point Values and Continuity: Apply and Create

Apply · Independent · 25 min

Compare nearby values and a separately defined point value. Calculate selected limits and an average rate. Explain continuity, unequal one-sided limits and a graph with a hole. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Limits Point Values and Continuity: Explore and Explain

A hole and a separately assigned value

For x ≠ 1, f(x) = (x² − 1)/(x − 1); separately define f(1) = 7. Compare the approach from both sides with the assigned value. A separate function g(x) = x² is used for rate questions.

Worked example: If p(x) = (x² − 16)/(x − 4) for x ≠ 4 and p(4) = 1, its limit at 4 is 8, while its point value is 1. Explore the material. Talk through your reasoning with suitable support.

1.Simplify the quotient for x ≠ 1.

Practice preview

Grade 12

Key

Limits Point Values and Continuity: Explore and Explain

Explore · Independent · 12 min

Compare nearby values and a separately defined point value. Calculate selected limits and an average rate. Explain continuity, unequal one-sided limits and a graph with a hole. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Practice preview

Grade 12

Key

Limits Point Values and Continuity: Practice Independently

Practice · Independent · 20 min

Compare nearby values and a separately defined point value. Calculate selected limits and an average rate. Explain continuity, unequal one-sided limits and a graph with a hole. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Periodic Functions and Model Conditions: Apply and Create

A periodic height model

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

A toy mechanism has idealized height h(t) = 7 + 3 cos(2πt/4) metres, with t in seconds, 0 ≤ t ≤ 4. Angles in the formula are radians. This is one full cycle; assume the specified ideal mechanism repeats only when explicitly extending the model.

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

1.Sketch one cycle using the five table points. Label axes, the midline and the period.

Practice preview

Grade 12

Key

Periodic Functions and Model Conditions: Apply and Create

Apply · Independent · 25 min

Interpret amplitude, midline and period. Evaluate a trigonometric rule and solve selected level equations. Sketch a cycle and explain changes and model extensions. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Periodic Functions and Model Conditions: Explore and Explain

A periodic height model

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

A toy mechanism has idealized height h(t) = 7 + 3 cos(2πt/4) metres, with t in seconds, 0 ≤ t ≤ 4. Angles in the formula are radians. This is one full cycle; assume the specified ideal mechanism repeats only when explicitly extending the model.

Worked example: h(t)=6+2cos(2πt/10) has midline 6, amplitude 2, period 10, and height range [4,8]. Explore the material. Talk through your reasoning with suitable support.

1.State the midline and its unit.

Practice preview

Grade 12

Key

Periodic Functions and Model Conditions: Explore and Explain

Explore · Independent · 12 min

Interpret amplitude, midline and period. Evaluate a trigonometric rule and solve selected level equations. Sketch a cycle and explain changes and model extensions. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Periodic Functions and Model Conditions: Practice Independently

A periodic height model

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

A toy mechanism has idealized height h(t) = 7 + 3 cos(2πt/4) metres, with t in seconds, 0 ≤ t ≤ 4. Angles in the formula are radians. This is one full cycle; assume the specified ideal mechanism repeats only when explicitly extending the model.

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

1.Find the maximum and minimum heights.

Practice preview

Grade 12

Key

Periodic Functions and Model Conditions: Practice Independently

Practice · Independent · 20 min

Interpret amplitude, midline and period. Evaluate a trigonometric rule and solve selected level equations. Sketch a cycle and explain changes and model extensions. 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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