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Grade 12 practice chapters
81–100 of 600 matching chapters · Page 5 of 30
Clear filtersGrade 12 · Chapter 81
The product rule · Linear shift a=-2; 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=-2; Exponential rate b=-0.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 82
Implicit circle tangents · Circle radius r=3; Final angle (degrees)=180
Use angle θ=108°. 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)=180.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 83
Signed accumulation · Slope a=2; Subtracted intercept b=2
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.
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Open practice chapterGrade 12 · Chapter 84
Substitution and bounds · Exponent factor k=0.55; Final upper bound B=1
Integrate from x=0 to x=0.6. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.55; Final upper bound B=1.
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Open practice chapterGrade 12 · Chapter 85
Differential growth models · Initial amount a=2; 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; Rate k=-0.1.
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Open practice chapterGrade 12 · Chapter 86
Binomial probability · Trial count n=11; Success probability p=0.5
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=11; Success probability p=0.5.
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Open practice chapterGrade 12 · Chapter 87
Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=75.
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Open practice chapterGrade 12 · Chapter 88
Cubic derivatives · Cubic coefficient a=-1.5; Linear coefficient b=-2
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=-2.
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Open practice chapterGrade 12 · Chapter 89
The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 90
Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 91
Substitution and bounds · Exponent factor k=0.6; Final upper bound B=1.25
Integrate from x=0 to x=0.75. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.6; Final upper bound B=1.25.
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Open practice chapterGrade 12 · Chapter 92
Average function values · Multiplier a=2.5; Power p=2
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2.5; Power p=2.
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Open practice chapterGrade 12 · Chapter 93
Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=0.
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Open practice chapterGrade 12 · Chapter 94
Binomial probability · Trial count n=12; Success probability p=0.55
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=12; Success probability p=0.55.
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Open practice chapterGrade 12 · Chapter 95
Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=90.
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Open practice chapterGrade 12 · Chapter 96
Cubic derivatives · Cubic coefficient a=-1; Linear coefficient b=-1.5
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=-1.5.
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Open practice chapterGrade 12 · Chapter 97
The product rule · Linear shift a=-1; 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=-1; Exponential rate b=-0.25.
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Open practice chapterGrade 12 · Chapter 98
Implicit circle tangents · Circle radius r=1.5; 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=1.5; Final angle (degrees)=120.
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Open practice chapterGrade 12 · Chapter 99
Substitution and bounds · Exponent factor k=0.65; Final upper bound B=1.5
Integrate from x=0 to x=0.9. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.65; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 100
Washer volumes · Outer radius factor a=1.5; 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=1.5; Inner radius factor b=0.3.
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