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Grade 12 practice chapters
461–480 of 600 matching chapters · Page 24 of 30
Clear filtersGrade 12 · Chapter 461
Differential growth models · Initial amount a=3; 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=3; Rate k=-0.2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 462
Binomial probability · Trial count n=16; Success probability p=0.9
Use success count k=10. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=16; Success probability p=0.9.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 463
Vector components and angles · Vector length r=1.5; Final angle (degrees)=180
Evaluate at the signed angle θ=108° (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)=180.
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Open practice chapterGrade 12 · Chapter 464
Cubic derivatives · Cubic coefficient a=1.5; Linear coefficient b=-3
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=-3.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 465
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 466
Binomial probability · Trial count n=2; Success probability p=0.25
Use success count k=1. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=2; Success probability p=0.25.
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Open practice chapterGrade 12 · Chapter 467
Vector components and angles · Vector length r=2.5; Final angle (degrees)=15
Evaluate at the signed angle θ=9° (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)=15.
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Open practice chapterGrade 12 · Chapter 468
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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Open practice chapterGrade 12 · Chapter 469
The product rule · Linear shift a=1.5; 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=1.5; Exponential rate b=0.
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Open practice chapterGrade 12 · Chapter 470
Substitution and bounds · Exponent factor k=0.3; 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=0.3; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 471
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 472
Binomial probability · Trial count n=3; Success probability p=0.3
Use success count k=2. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=3; Success probability p=0.3.
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Open practice chapterGrade 12 · Chapter 473
Cubic derivatives · Cubic coefficient a=-2; 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=-2; Linear coefficient b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 474
The product rule · Linear shift a=2; 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=2; Exponential rate b=0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 475
Substitution and bounds · Exponent factor k=0.35; 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=0.35; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 476
Differential growth models · Initial amount a=1.5; 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=1.5; Rate k=-0.4.
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Open practice chapterGrade 12 · Chapter 477
Binomial probability · Trial count n=4; 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=4; Success probability p=0.35.
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Open practice chapterGrade 12 · Chapter 478
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=165.
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Open practice chapterGrade 12 · Chapter 479
Cubic derivatives · Cubic coefficient a=-1.5; 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=-1.5; Linear coefficient b=1.
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Open practice chapterGrade 12 · Chapter 480
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
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