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Grade 12 practice chapters
421–440 of 600 matching chapters · Page 22 of 30
Clear filtersGrade 12 · Chapter 421
Binomial probability · Trial count n=9; Success probability p=0.55
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=9; Success probability p=0.55.
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Open practice chapterGrade 12 · Chapter 422
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=135.
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Open practice chapterGrade 12 · Chapter 423
Cubic derivatives · Cubic coefficient a=-2; 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=-2; Linear coefficient b=0.
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Open practice chapterGrade 12 · Chapter 424
The product rule · Linear shift a=2; 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=2; Exponential rate b=0.
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Open practice chapterGrade 12 · Chapter 425
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=90.
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Open practice chapterGrade 12 · Chapter 426
Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=2.
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Open practice chapterGrade 12 · Chapter 427
Substitution and bounds · Exponent factor k=0.85; 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=0.85; Final upper bound B=1.25.
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Open practice chapterGrade 12 · Chapter 428
Differential growth models · Initial amount a=3; 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=3; Rate k=-0.3.
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Open practice chapterGrade 12 · Chapter 429
Binomial probability · Trial count n=10; Success probability p=0.6
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=10; Success probability p=0.6.
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Open practice chapterGrade 12 · Chapter 430
Vector components and angles · Vector length r=1; 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; Final angle (degrees)=150.
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Open practice chapterGrade 12 · Chapter 431
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 432
Implicit circle tangents · Circle radius r=3; 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=3; Final angle (degrees)=120.
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Open practice chapterGrade 12 · Chapter 433
Substitution and bounds · Exponent factor k=0.9; 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=0.9; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 434
Differential growth models · Initial amount a=0.5; 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=0.5; Rate k=0.4.
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Open practice chapterGrade 12 · Chapter 435
Binomial probability · Trial count n=11; Success probability p=0.65
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=11; Success probability p=0.65.
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Open practice chapterGrade 12 · Chapter 436
Vector components and angles · Vector length r=1.5; Final angle (degrees)=165
Evaluate at the signed angle θ=99° (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)=165.
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Open practice chapterGrade 12 · Chapter 437
Cubic derivatives · Cubic coefficient a=-1; 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; Linear coefficient b=1.
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Open practice chapterGrade 12 · Chapter 438
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 439
Substitution and bounds · Exponent factor k=0.95; 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=0.95; Final upper bound B=1.75.
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Open practice chapterGrade 12 · Chapter 440
Differential growth models · Initial amount a=1; Rate k=0.5
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=0.5.
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