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Grade 12 practice chapters
101–120 of 600 matching chapters · Page 6 of 30
Clear filtersGrade 12 · Chapter 101
Differential growth models · Initial amount a=3; 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=3; Rate k=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 102
Binomial probability · Trial count n=13; Success probability p=0.6
Use success count k=8. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=13; Success probability p=0.6.
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Open practice chapterGrade 12 · Chapter 103
Vector components and angles · Vector length r=0.5; Final angle (degrees)=30
Evaluate at the signed angle θ=18° (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)=30.
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Open practice chapterGrade 12 · Chapter 104
Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=-1.
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Open practice chapterGrade 12 · Chapter 105
The product rule · Linear shift a=-0.5; Exponential rate b=0
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.
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Open practice chapterGrade 12 · Chapter 106
Implicit circle tangents · Circle radius r=2; Final angle (degrees)=150
Use angle θ=90°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=2; Final angle (degrees)=150.
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Open practice chapterGrade 12 · Chapter 107
Signed accumulation · Slope a=0.5; Subtracted intercept b=1
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=0.5; Subtracted intercept b=1.
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Open practice chapterGrade 12 · Chapter 108
Substitution and bounds · Exponent factor k=0.7; 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=0.7; Final upper bound B=1.75.
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Open practice chapterGrade 12 · Chapter 109
Washer volumes · Outer radius factor a=2; 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=2; Inner radius factor b=0.4.
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Open practice chapterGrade 12 · Chapter 110
Differential growth models · Initial amount a=0.5; Rate k=-0.3
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=-0.3.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 111
Binomial probability · Trial count n=14; Success probability p=0.65
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=14; Success probability p=0.65.
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Open practice chapterGrade 12 · Chapter 112
Vector components and angles · Vector length r=1; Final angle (degrees)=45
Evaluate at the signed angle θ=27° (three fifths of that final angle). Find its dot product with (1,0), its vertical component, and its length. Givens: Vector length r=1; Final angle (degrees)=45.
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Open practice chapterGrade 12 · Chapter 113
Cubic derivatives · Cubic coefficient a=0; 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; Linear coefficient b=-0.5.
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Open practice chapterGrade 12 · Chapter 114
The product rule · Linear shift a=0; 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; Exponential rate b=0.25.
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Open practice chapterGrade 12 · Chapter 115
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=180.
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Open practice chapterGrade 12 · Chapter 116
Signed accumulation · Slope a=1; Subtracted intercept b=1.5
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=1; Subtracted intercept b=1.5.
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Open practice chapterGrade 12 · Chapter 117
Substitution and bounds · Exponent factor k=0.75; 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=0.75; Final upper bound B=2.
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Open practice chapterGrade 12 · Chapter 118
Washer volumes · Outer radius factor a=2.5; Inner radius factor b=0.5
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=2.5; Inner radius factor b=0.5.
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Open practice chapterGrade 12 · Chapter 119
Binomial probability · Trial count n=15; Success probability p=0.7
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=15; Success probability p=0.7.
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Open practice chapterGrade 12 · Chapter 120
Vector components and angles · Vector length r=1.5; Final angle (degrees)=60
Evaluate at the signed angle θ=36° (three fifths of that final angle). Find its dot product with (1,0), its vertical component, and its length. Givens: Vector length r=1.5; Final angle (degrees)=60.
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