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Grade 12 practice chapters
321–340 of 600 matching chapters · Page 17 of 30
Clear filtersGrade 12 · Chapter 321
Binomial probability · Trial count n=10; 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=10; Success probability p=0.55.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 322
Cubic derivatives · Cubic coefficient a=0; 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=0; Linear coefficient b=1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 323
The product rule · Linear shift a=-0.5; 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=-0.5; Exponential rate b=0.75.
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Open practice chapterGrade 12 · Chapter 324
Implicit circle tangents · Circle radius r=3; Final angle (degrees)=30
Use angle θ=18°. 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)=30.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 325
Signed accumulation · Slope a=2; Subtracted intercept b=0
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=2; Subtracted intercept b=0.
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Open practice chapterGrade 12 · Chapter 326
Substitution and bounds · Exponent factor k=0.15; 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=0.15; Final upper bound B=1.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 327
Washer volumes · Outer radius factor a=3; Inner radius factor b=0.2
Use 0≤x≤1.2 and inspect the cross-section at x=1.2. Calculate the outer radius, washer area, and accumulated volume. Givens: Outer radius factor a=3; Inner radius factor b=0.2.
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Open practice chapterGrade 12 · Chapter 328
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 329
Binomial probability · Trial count n=11; Success probability p=0.6
Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=11; Success probability p=0.6.
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Open practice chapterGrade 12 · Chapter 330
Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=150.
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Open practice chapterGrade 12 · Chapter 331
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 332
Signed accumulation · Slope a=2.5; Subtracted intercept b=0.5
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=2.5; Subtracted intercept b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 333
Substitution and bounds · Exponent factor k=0.2; 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=0.2; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 334
Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 335
Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=165.
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Open practice chapterGrade 12 · Chapter 336
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 337
Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=300
Use angle θ=180°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=1.5; Final angle (degrees)=300.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 338
Signed accumulation · Slope a=3; Subtracted intercept b=1
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 339
Substitution and bounds · Exponent factor k=0.25; 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=0.25; Final upper bound B=1.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 340
Washer volumes · Outer radius factor a=1.5; Inner radius factor b=0
Use 0≤x≤1.2 and inspect the cross-section at x=1.2. Calculate the outer radius, washer area, and accumulated volume. Givens: Outer radius factor a=1.5; Inner radius factor b=0.
Question · Worked solution · Animated example
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