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Grade 12 practice chapters
341–360 of 600 matching chapters · Page 18 of 30
Clear filtersGrade 12 · Chapter 341
Binomial probability · Trial count n=13; Success probability p=0.7
Use success count k=8. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=13; Success probability p=0.7.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 342
Vector components and angles · Vector length r=0.5; 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=0.5; Final angle (degrees)=105.
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Open practice chapterGrade 12 · Chapter 343
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 344
The product rule · Linear shift a=1; 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; Exponential rate b=-0.75.
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Open practice chapterGrade 12 · Chapter 345
Implicit circle tangents · Circle radius r=2; 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; Final angle (degrees)=330.
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Open practice chapterGrade 12 · Chapter 346
Signed accumulation · Slope a=0.5; 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=0.5; Subtracted intercept b=3.5.
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Open practice chapterGrade 12 · Chapter 347
Substitution and bounds · Exponent factor k=0.3; 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=0.3; Final upper bound B=2.
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Open practice chapterGrade 12 · Chapter 348
Washer volumes · Outer radius factor a=2; 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; Inner radius factor b=0.1.
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Open practice chapterGrade 12 · Chapter 349
Differential growth models · Initial amount a=0.5; 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=0.5; Rate k=0.2.
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Open practice chapterGrade 12 · Chapter 350
Binomial probability · Trial count n=14; Success probability p=0.75
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=14; Success probability p=0.75.
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Open practice chapterGrade 12 · Chapter 351
Vector components and angles · Vector length r=1; 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=1; Final angle (degrees)=120.
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Open practice chapterGrade 12 · Chapter 352
Cubic derivatives · Cubic coefficient a=2; Linear coefficient b=3
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=3.
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Open practice chapterGrade 12 · Chapter 353
The product rule · Linear shift a=1.5; 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=1.5; Exponential rate b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 354
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=30.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 355
Substitution and bounds · Exponent factor k=0.35; 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=0.35; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 356
Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.2.
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Open practice chapterGrade 12 · Chapter 357
Differential growth models · Initial amount a=1; 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; Rate k=0.3.
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Open practice chapterGrade 12 · Chapter 358
Binomial probability · Trial count n=15; Success probability p=0.8
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=15; Success probability p=0.8.
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Open practice chapterGrade 12 · Chapter 359
Vector components and angles · Vector length r=1.5; 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=1.5; Final angle (degrees)=135.
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Open practice chapterGrade 12 · Chapter 360
Cubic derivatives · Cubic coefficient a=-2; 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=-2; Linear coefficient b=-0.5.
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