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Grade 12 practice chapters
121–140 of 600 matching chapters · Page 7 of 30
Clear filtersGrade 12 · Chapter 121
Cubic derivatives · Cubic coefficient a=0.5; Linear coefficient b=0
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 122
The product rule · Linear shift a=0.5; 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=0.5; Exponential rate b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 123
Implicit circle tangents · Circle radius r=3; Final angle (degrees)=210
Use angle θ=126°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=3; Final angle (degrees)=210.
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Open practice chapterGrade 12 · Chapter 124
Substitution and bounds · Exponent factor k=0.8; Final upper bound B=0.5
Integrate from x=0 to x=0.3. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.8; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 125
Average function values · Multiplier a=1.5; Power p=1
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=1.5; Power p=1.
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Open practice chapterGrade 12 · Chapter 126
Washer volumes · Outer radius factor a=3; Inner radius factor b=0.6
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=0.6.
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Open practice chapterGrade 12 · Chapter 127
Binomial probability · Trial count n=16; Success probability p=0.75
Use success count k=10. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=16; Success probability p=0.75.
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Open practice chapterGrade 12 · Chapter 128
Vector components and angles · Vector length r=2; 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=2; Final angle (degrees)=75.
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Open practice chapterGrade 12 · Chapter 129
Cubic derivatives · Cubic coefficient a=1; 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=1; Linear coefficient b=0.5.
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Open practice chapterGrade 12 · Chapter 130
The product rule · Linear shift a=1; Exponential rate b=0.75
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=0.75.
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Open practice chapterGrade 12 · Chapter 131
Implicit circle tangents · Circle radius r=1; Final angle (degrees)=120
Use angle θ=72°. 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)=120.
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Open practice chapterGrade 12 · Chapter 132
Signed accumulation · Slope a=2; 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=2; Subtracted intercept b=2.5.
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Open practice chapterGrade 12 · Chapter 133
Substitution and bounds · Exponent factor k=0.85; Final upper bound B=0.75
Integrate from x=0 to x=0.45. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.85; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 134
Average function values · Multiplier a=2; Power p=2
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2; Power p=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 135
Washer volumes · Outer radius factor a=1; Inner radius factor b=0.3
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=0.3.
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Open practice chapterGrade 12 · Chapter 136
Differential growth models · Initial amount a=2; 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=2; Rate k=0.
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Open practice chapterGrade 12 · Chapter 137
Binomial probability · Trial count n=2; Success probability p=0.1
Use success count k=1. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=2; Success probability p=0.1.
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Open practice chapterGrade 12 · Chapter 138
Vector components and angles · Vector length r=2.5; Final angle (degrees)=90
Evaluate at the signed angle θ=54° (three fifths of that final angle). Find its dot product with (1,0), its vertical component, and its length. Givens: Vector length r=2.5; Final angle (degrees)=90.
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Open practice chapterGrade 12 · Chapter 139
Cubic derivatives · Cubic coefficient a=1.5; Linear coefficient b=1
Evaluate at x=0.4. Find the function value and first and second derivatives at that input. Givens: Cubic coefficient a=1.5; Linear coefficient b=1.
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Open practice chapterGrade 12 · Chapter 140
The product rule · Linear shift a=1.5; Exponential rate b=1
Evaluate at x=0.2. Find the product value, its derivative, and the contribution from differentiating the exponential factor. Givens: Linear shift a=1.5; Exponential rate b=1.
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