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Grade 12 practice chapters
501–520 of 600 matching chapters · Page 26 of 30
Clear filtersGrade 12 · Chapter 501
The product rule · Linear shift a=0; 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; Exponential rate b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 502
Substitution and bounds · Exponent factor k=0.6; 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=0.6; Final upper bound B=2.
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Open practice chapterGrade 12 · Chapter 503
Binomial probability · Trial count n=9; 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=9; Success probability p=0.6.
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Open practice chapterGrade 12 · Chapter 504
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=180.
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Open practice chapterGrade 12 · Chapter 505
The product rule · Linear shift a=0.5; 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=0.5; Exponential rate b=-0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 506
Substitution and bounds · Exponent factor k=0.65; 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=0.65; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 507
Binomial probability · Trial count n=10; Success probability p=0.65
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=10; Success probability p=0.65.
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Open practice chapterGrade 12 · Chapter 508
Vector components and angles · Vector length r=1.5; 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=1.5; Final angle (degrees)=15.
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Open practice chapterGrade 12 · Chapter 509
Cubic derivatives · Cubic coefficient a=1.5; 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=1.5; Linear coefficient b=-2.5.
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Open practice chapterGrade 12 · Chapter 510
Substitution and bounds · Exponent factor k=0.7; 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=0.7; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 511
Binomial probability · Trial count n=11; 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=11; Success probability p=0.7.
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Open practice chapterGrade 12 · Chapter 512
Vector components and angles · Vector length r=2; 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=2; Final angle (degrees)=30.
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Open practice chapterGrade 12 · Chapter 513
Cubic derivatives · Cubic coefficient a=2; 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=2; Linear coefficient b=-2.
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Open practice chapterGrade 12 · Chapter 514
Substitution and bounds · Exponent factor k=0.75; Final upper bound B=1
Integrate from x=0 to x=0.6. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.75; Final upper bound B=1.
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Open practice chapterGrade 12 · Chapter 515
Binomial probability · Trial count n=12; Success probability p=0.75
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=12; Success probability p=0.75.
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Open practice chapterGrade 12 · Chapter 516
Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=45.
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Open practice chapterGrade 12 · Chapter 517
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 518
Binomial probability · Trial count n=13; Success probability p=0.8
Use success count k=8. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=13; Success probability p=0.8.
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Open practice chapterGrade 12 · Chapter 519
Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=60.
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Open practice chapterGrade 12 · Chapter 520
Cubic derivatives · Cubic coefficient a=-1.5; 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=-1.5; Linear coefficient b=1.5.
Question · Worked solution · Animated example
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