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Grade 12 practice chapters
41–60 of 600 matching chapters · Page 3 of 30
Clear filtersGrade 12 · Chapter 41
Average function values · Multiplier a=2.5; Power p=1
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2.5; Power p=1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 42
Washer volumes · Outer radius factor a=3; Inner radius factor b=0.4
Use 0≤x≤1.2 and inspect the cross-section at x=1.2. Calculate the outer radius, washer area, and accumulated volume. Givens: Outer radius factor a=3; Inner radius factor b=0.4.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 43
Differential growth models · Initial amount a=2.5; Rate k=-0.1
Evaluate at t=2.4 time units. Find the amount, instantaneous rate, and multiplier relative to the initial amount; check the rate against the given differential equation. Givens: Initial amount a=2.5; Rate k=-0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 44
Binomial probability · Trial count n=6; Success probability p=0.25
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=6; Success probability p=0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 45
Vector components and angles · Vector length r=3; Final angle (degrees)=75
Evaluate at the signed angle θ=45° (three fifths of that final angle). Find its dot product with (1,0), its vertical component, and its length. Givens: Vector length r=3; Final angle (degrees)=75.
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Open practice chapterGrade 12 · Chapter 46
Cubic derivatives · Cubic coefficient a=0.5; Linear coefficient b=-0.5
Evaluate at x=0.4. Find the function value and first and second derivatives at that input. Givens: Cubic coefficient a=0.5; Linear coefficient b=-0.5.
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Open practice chapterGrade 12 · Chapter 47
The product rule · Linear shift a=0.5; Exponential rate b=0.25
Evaluate at x=0.2. Find the product value, its derivative, and the contribution from differentiating the exponential factor. Givens: Linear shift a=0.5; Exponential rate b=0.25.
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Open practice chapterGrade 12 · Chapter 48
Implicit circle tangents · Circle radius r=1; Final angle (degrees)=60
Use angle θ=36°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=1; Final angle (degrees)=60.
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Open practice chapterGrade 12 · Chapter 49
Signed accumulation · Slope a=3; Subtracted intercept b=2.5
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=3; Subtracted intercept b=2.5.
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Open practice chapterGrade 12 · Chapter 50
Substitution and bounds · Exponent factor k=0.35; Final upper bound B=1.75
Integrate from x=0 to x=1.05. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.35; Final upper bound B=1.75.
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Open practice chapterGrade 12 · Chapter 51
Average function values · Multiplier a=3; Power p=2
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=3; Power p=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 52
Washer volumes · Outer radius factor a=1; Inner radius factor b=0.1
Use 0≤x≤1.2 and inspect the cross-section at x=1.2. Calculate the outer radius, washer area, and accumulated volume. Givens: Outer radius factor a=1; Inner radius factor b=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 53
Differential growth models · Initial amount a=3; Rate k=0
Evaluate at t=2.4 time units. Find the amount, instantaneous rate, and multiplier relative to the initial amount; check the rate against the given differential equation. Givens: Initial amount a=3; Rate k=0.
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Open practice chapterGrade 12 · Chapter 54
Binomial probability · Trial count n=7; Success probability p=0.3
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=7; Success probability p=0.3.
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Open practice chapterGrade 12 · Chapter 55
Vector components and angles · Vector length r=0.5; Final angle (degrees)=15
Evaluate at the signed angle θ=9° (three fifths of that final angle). Find its dot product with (1,0), its vertical component, and its length. Givens: Vector length r=0.5; Final angle (degrees)=15.
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Open practice chapterGrade 12 · Chapter 56
The product rule · Linear shift a=1; Exponential rate b=0.5
Evaluate at x=0.2. Find the product value, its derivative, and the contribution from differentiating the exponential factor. Givens: Linear shift a=1; Exponential rate b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 57
Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=90
Use angle θ=54°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=1.5; Final angle (degrees)=90.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 58
Substitution and bounds · Exponent factor k=0.4; Final upper bound B=2
Integrate from x=0 to x=1.2. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.4; Final upper bound B=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 59
Washer volumes · Outer radius factor a=1.5; Inner radius factor b=0.2
Use 0≤x≤1.2 and inspect the cross-section at x=1.2. Calculate the outer radius, washer area, and accumulated volume. Givens: Outer radius factor a=1.5; Inner radius factor b=0.2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 60
Differential growth models · Initial amount a=0.5; Rate k=-0.4
Evaluate at t=2.4 time units. Find the amount, instantaneous rate, and multiplier relative to the initial amount; check the rate against the given differential equation. Givens: Initial amount a=0.5; Rate k=-0.4.
Question · Worked solution · Animated example
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