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Grade 12 practice chapters
221–240 of 600 matching chapters · Page 12 of 30
Clear filtersGrade 12 · Chapter 221
Washer volumes · Outer radius factor a=1; Inner radius factor b=0.5
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; Inner radius factor b=0.5.
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Open practice chapterGrade 12 · Chapter 222
Binomial probability · Trial count n=12; 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=12; Success probability p=0.6.
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Open practice chapterGrade 12 · Chapter 223
Vector components and angles · Vector length r=1.5; Final angle (degrees)=90
Evaluate at the signed angle θ=54° (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)=90.
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Open practice chapterGrade 12 · Chapter 224
Cubic derivatives · Cubic coefficient a=-2; 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=-2; Linear coefficient b=-1.5.
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Open practice chapterGrade 12 · Chapter 225
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.
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Open practice chapterGrade 12 · Chapter 226
Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=210
Use angle θ=126°. 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)=210.
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Open practice chapterGrade 12 · Chapter 227
Signed accumulation · Slope a=1.5; Subtracted intercept b=3
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=1.5; Subtracted intercept b=3.
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Open practice chapterGrade 12 · Chapter 228
Substitution and bounds · Exponent factor k=0.45; 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=0.45; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 229
Washer volumes · Outer radius factor a=1.5; Inner radius factor b=0.6
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=0.6.
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Open practice chapterGrade 12 · Chapter 230
Differential growth models · Initial amount a=1.5; Rate k=0.1
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=0.1.
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Open practice chapterGrade 12 · Chapter 231
Binomial probability · Trial count n=13; Success probability p=0.65
Use success count k=8. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=13; Success probability p=0.65.
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Open practice chapterGrade 12 · Chapter 232
Vector components and angles · Vector length r=2; Final angle (degrees)=105
Evaluate at the signed angle θ=63° (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)=105.
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Open practice chapterGrade 12 · Chapter 233
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 234
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.
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Open practice chapterGrade 12 · Chapter 235
Implicit circle tangents · Circle radius r=2; 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=2; Final angle (degrees)=240.
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Open practice chapterGrade 12 · Chapter 236
Signed accumulation · Slope a=2; Subtracted intercept b=3.5
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=3.5.
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Open practice chapterGrade 12 · Chapter 237
Washer volumes · Outer radius factor a=2; Inner radius factor b=0.7
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; Inner radius factor b=0.7.
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Open practice chapterGrade 12 · Chapter 238
Differential growth models · Initial amount a=2; 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=2; Rate k=0.2.
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Open practice chapterGrade 12 · Chapter 239
Binomial probability · Trial count n=14; Success probability p=0.7
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=14; Success probability p=0.7.
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Open practice chapterGrade 12 · Chapter 240
Vector components and angles · Vector length r=2.5; Final angle (degrees)=120
Evaluate at the signed angle θ=72° (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)=120.
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