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Grade 12 practice chapters
61–80 of 600 matching chapters · Page 4 of 30
Clear filtersGrade 12 · Chapter 61
Binomial probability · Trial count n=8; Success probability p=0.35
Use success count k=5. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=8; Success probability p=0.35.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 62
Vector components and angles · Vector length r=1; 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=1; Final angle (degrees)=30.
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Open practice chapterGrade 12 · Chapter 63
Cubic derivatives · Cubic coefficient a=1.5; 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=1.5; Linear coefficient b=0.5.
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Open practice chapterGrade 12 · Chapter 64
The product rule · Linear shift a=1.5; 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=1.5; Exponential rate b=0.75.
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Open practice chapterGrade 12 · Chapter 65
Signed accumulation · Slope a=1; 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=1; Subtracted intercept b=1.
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Open practice chapterGrade 12 · Chapter 66
Substitution and bounds · Exponent factor k=0.45; 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=0.45; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 67
Washer volumes · Outer radius factor a=2; 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=2; Inner radius factor b=0.3.
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Open practice chapterGrade 12 · Chapter 68
Differential growth models · Initial amount a=1; 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=1; Rate k=-0.3.
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Open practice chapterGrade 12 · Chapter 69
Binomial probability · Trial count n=9; Success probability p=0.4
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=9; Success probability p=0.4.
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Open practice chapterGrade 12 · Chapter 70
Vector components and angles · Vector length r=1.5; 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=1.5; Final angle (degrees)=45.
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Open practice chapterGrade 12 · Chapter 71
Cubic derivatives · Cubic coefficient a=2; 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=2; Linear coefficient b=1.
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Open practice chapterGrade 12 · Chapter 72
The product rule · Linear shift a=2; 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=2; Exponential rate b=1.
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Open practice chapterGrade 12 · Chapter 73
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=150.
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Open practice chapterGrade 12 · Chapter 74
Signed accumulation · Slope a=1.5; 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=1.5; Subtracted intercept b=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 75
Substitution and bounds · Exponent factor k=0.5; 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=0.5; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 76
Average function values · Multiplier a=1.5; Power p=4
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=1.5; Power p=4.
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Open practice chapterGrade 12 · Chapter 77
Differential growth models · Initial amount a=1.5; Rate k=-0.2
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=1.5; Rate k=-0.2.
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Open practice chapterGrade 12 · Chapter 78
Binomial probability · Trial count n=10; Success probability p=0.45
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=10; Success probability p=0.45.
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Open practice chapterGrade 12 · Chapter 79
Vector components and angles · Vector length r=2; 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=2; Final angle (degrees)=60.
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Open practice chapterGrade 12 · Chapter 80
Cubic derivatives · Cubic coefficient a=-2; Linear coefficient b=-2.5
Evaluate at x=0.4. Find the function value and first and second derivatives at that input. Givens: Cubic coefficient a=-2; Linear coefficient b=-2.5.
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