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Grade 12 practice chapters
381–400 of 600 matching chapters · Page 20 of 30
Clear filtersGrade 12 · Chapter 381
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 382
Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 383
Substitution and bounds · Exponent factor k=0.55; 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=0.55; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 384
Differential growth models · Initial amount a=3; 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=3; Rate k=-0.4.
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Open practice chapterGrade 12 · Chapter 385
Binomial probability · Trial count n=4; Success probability p=0.3
Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=4; Success probability p=0.3.
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Open practice chapterGrade 12 · Chapter 386
Vector components and angles · Vector length r=0.5; Final angle (degrees)=120
Evaluate at the signed angle θ=72° (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)=120.
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Open practice chapterGrade 12 · Chapter 387
Cubic derivatives · Cubic coefficient a=0; 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=0; Linear coefficient b=1.5.
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Open practice chapterGrade 12 · Chapter 388
The product rule · Linear shift a=-0.5; 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=-0.5; Exponential rate b=1.
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Open practice chapterGrade 12 · Chapter 389
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=60.
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Open practice chapterGrade 12 · Chapter 390
Signed accumulation · Slope a=0.5; Subtracted intercept b=4
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=4.
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Open practice chapterGrade 12 · Chapter 391
Substitution and bounds · Exponent factor k=0.6; 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=0.6; Final upper bound B=1.75.
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Open practice chapterGrade 12 · Chapter 392
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.
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Open practice chapterGrade 12 · Chapter 393
Binomial probability · Trial count n=5; Success probability p=0.35
Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.35.
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Open practice chapterGrade 12 · Chapter 394
Vector components and angles · Vector length r=1; Final angle (degrees)=135
Evaluate at the signed angle θ=81° (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)=135.
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Open practice chapterGrade 12 · Chapter 395
Cubic derivatives · Cubic coefficient a=0.5; 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=0.5; Linear coefficient b=2.
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Open practice chapterGrade 12 · Chapter 396
Implicit circle tangents · Circle radius r=3; 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=3; Final angle (degrees)=90.
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Open practice chapterGrade 12 · Chapter 397
Substitution and bounds · Exponent factor k=0.65; 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=0.65; Final upper bound B=2.
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Open practice chapterGrade 12 · Chapter 398
Differential growth models · Initial amount a=1; 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=1; Rate k=0.4.
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Open practice chapterGrade 12 · Chapter 399
Binomial probability · Trial count n=6; Success probability p=0.4
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=6; Success probability p=0.4.
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Open practice chapterGrade 12 · Chapter 400
Vector components and angles · Vector length r=1.5; Final angle (degrees)=150
Evaluate at the signed angle θ=90° (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)=150.
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