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Grade 12 practice chapters
301–320 of 600 matching chapters · Page 16 of 30
Clear filtersGrade 12 · Chapter 301
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=90.
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Open practice chapterGrade 12 · Chapter 302
Cubic derivatives · Cubic coefficient a=-1.5; Linear coefficient b=-0.5
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=-0.5.
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Open practice chapterGrade 12 · Chapter 303
The product rule · Linear shift a=-2; Exponential rate b=0
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.
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Open practice chapterGrade 12 · Chapter 304
Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=270
Use angle θ=162°. 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)=270.
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Open practice chapterGrade 12 · Chapter 305
Substitution and bounds · Exponent factor k=0.95; 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=0.95; Final upper bound B=1.5.
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Open practice chapterGrade 12 · Chapter 306
Washer volumes · Outer radius factor a=1.5; Inner radius factor b=0.8
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=0.8.
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Open practice chapterGrade 12 · Chapter 307
Differential growth models · Initial amount a=0.5; 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=0.5; Rate k=0.1.
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Open practice chapterGrade 12 · Chapter 308
Binomial probability · Trial count n=8; Success probability p=0.45
Use success count k=5. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=8; Success probability p=0.45.
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Open practice chapterGrade 12 · Chapter 309
Vector components and angles · Vector length r=1; 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=1; Final angle (degrees)=105.
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Open practice chapterGrade 12 · Chapter 310
The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=0.25.
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Open practice chapterGrade 12 · Chapter 311
Implicit circle tangents · Circle radius r=2; 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; Final angle (degrees)=300.
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Open practice chapterGrade 12 · Chapter 312
Signed accumulation · Slope a=1; 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=1; Subtracted intercept b=3.5.
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Open practice chapterGrade 12 · Chapter 313
Substitution and bounds · Exponent factor k=1; 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=1; Final upper bound B=1.75.
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Open practice chapterGrade 12 · Chapter 314
Binomial probability · Trial count n=9; Success probability p=0.5
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=9; Success probability p=0.5.
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Open practice chapterGrade 12 · Chapter 315
Cubic derivatives · Cubic coefficient a=-0.5; Linear coefficient b=0.5
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=0.5.
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Open practice chapterGrade 12 · Chapter 316
The product rule · Linear shift a=-1; 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=-1; Exponential rate b=0.5.
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Open practice chapterGrade 12 · Chapter 317
Implicit circle tangents · Circle radius r=2.5; Final angle (degrees)=330
Use angle θ=198°. 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)=330.
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Open practice chapterGrade 12 · Chapter 318
Signed accumulation · Slope a=1.5; Subtracted intercept b=4
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=4.
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Open practice chapterGrade 12 · Chapter 319
Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.1.
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Open practice chapterGrade 12 · Chapter 320
Differential growth models · Initial amount a=1.5; 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=1.5; Rate k=0.3.
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