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Grade 12 practice chapters
441–460 of 600 matching chapters · Page 23 of 30
Clear filtersGrade 12 · Chapter 441
Binomial probability · Trial count n=12; Success probability p=0.7
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=12; Success probability p=0.7.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 442
Vector components and angles · Vector length r=2; 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=2; Final angle (degrees)=180.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 443
Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 444
The product rule · Linear shift a=-1; 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=-1; Exponential rate b=1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 445
Differential growth models · Initial amount a=1.5; 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=1.5; Rate k=-0.5.
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Open practice chapterGrade 12 · Chapter 446
Binomial probability · Trial count n=13; Success probability p=0.75
Use success count k=8. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=13; Success probability p=0.75.
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Open practice chapterGrade 12 · Chapter 447
Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=15.
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Open practice chapterGrade 12 · Chapter 448
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 449
Substitution and bounds · Exponent factor k=0.1; 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=0.1; Final upper bound B=1.25.
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Open practice chapterGrade 12 · Chapter 450
Differential growth models · Initial amount a=2; 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=2; Rate k=-0.4.
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Open practice chapterGrade 12 · Chapter 451
Binomial probability · Trial count n=14; Success probability p=0.8
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=14; Success probability p=0.8.
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Open practice chapterGrade 12 · Chapter 452
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=150.
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Open practice chapterGrade 12 · Chapter 453
Cubic derivatives · Cubic coefficient a=0.5; 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=0.5; Linear coefficient b=2.5.
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Open practice chapterGrade 12 · Chapter 454
The product rule · Linear shift a=0; 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=0; Exponential rate b=-0.75.
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Open practice chapterGrade 12 · Chapter 455
Substitution and bounds · Exponent factor k=0.15; 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=0.15; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 456
Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=-0.3.
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Open practice chapterGrade 12 · Chapter 457
Binomial probability · Trial count n=15; Success probability p=0.85
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=15; Success probability p=0.85.
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Open practice chapterGrade 12 · Chapter 458
Vector components and angles · Vector length r=1; 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; Final angle (degrees)=165.
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Open practice chapterGrade 12 · Chapter 459
Cubic derivatives · Cubic coefficient a=1; 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; Linear coefficient b=3.
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Open practice chapterGrade 12 · Chapter 460
The product rule · Linear shift a=0.5; Exponential rate b=-0.5
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=-0.5.
Question · Worked solution · Animated example
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