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Grade 12 practice chapters
281–300 of 600 matching chapters · Page 15 of 30
Clear filtersGrade 12 · Chapter 281
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=300.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 282
Substitution and bounds · Exponent factor k=0.8; 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=0.8; Final upper bound B=0.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 283
Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 284
Differential growth models · Initial amount a=2; 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; Rate k=0.3.
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Open practice chapterGrade 12 · Chapter 285
Binomial probability · Trial count n=5; Success probability p=0.3
Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.3.
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Open practice chapterGrade 12 · Chapter 286
Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=135.
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Open practice chapterGrade 12 · Chapter 287
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 288
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 289
Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=0.
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Open practice chapterGrade 12 · Chapter 290
Substitution and bounds · Exponent factor k=0.85; 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=0.85; Final upper bound B=1.
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Open practice chapterGrade 12 · Chapter 291
Washer volumes · Outer radius factor a=3; Inner radius factor b=0.1
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=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 292
Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=0.4.
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Open practice chapterGrade 12 · Chapter 293
Binomial probability · Trial count n=6; Success probability p=0.35
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=6; Success probability p=0.35.
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Open practice chapterGrade 12 · Chapter 294
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 295
The product rule · Linear shift a=2; 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=2; Exponential rate b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 296
Implicit circle tangents · Circle radius r=1; Final angle (degrees)=240
Use angle θ=144°. Find both coordinates and the tangent slope; identify a vertical tangent instead of dividing by zero when necessary. Givens: Circle radius r=1; Final angle (degrees)=240.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 297
Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=0.5.
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Open practice chapterGrade 12 · Chapter 298
Substitution and bounds · Exponent factor k=0.9; 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=0.9; Final upper bound B=1.25.
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Open practice chapterGrade 12 · Chapter 299
Differential growth models · Initial amount a=3; 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=3; Rate k=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 300
Binomial probability · Trial count n=7; Success probability p=0.4
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=7; Success probability p=0.4.
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