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Grade 12 practice chapters
241–260 of 600 matching chapters · Page 13 of 30
Clear filtersGrade 12 · Chapter 241
Cubic derivatives · Cubic coefficient a=-1; 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; Linear coefficient b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 242
The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=0.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 243
Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=270.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 244
Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=4.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 245
Substitution and bounds · Exponent factor k=0.55; 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=0.55; Final upper bound B=1.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 246
Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.8.
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Open practice chapterGrade 12 · Chapter 247
Binomial probability · Trial count n=15; 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=15; Success probability p=0.75.
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Open practice chapterGrade 12 · Chapter 248
Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=135.
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Open practice chapterGrade 12 · Chapter 249
Cubic derivatives · Cubic coefficient a=-0.5; Linear coefficient b=0
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.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 250
The product rule · Linear shift a=-1; 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; Exponential rate b=0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 251
Implicit circle tangents · Circle radius r=3; 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=3; Final angle (degrees)=300.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 252
Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=0.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 253
Washer volumes · Outer radius factor a=3; 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=3; Inner radius factor b=0.
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Open practice chapterGrade 12 · Chapter 254
Differential growth models · Initial amount a=3; 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=3; Rate k=0.4.
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Open practice chapterGrade 12 · Chapter 255
Binomial probability · Trial count n=16; Success probability p=0.8
Use success count k=10. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=16; Success probability p=0.8.
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Open practice chapterGrade 12 · Chapter 256
Cubic derivatives · Cubic coefficient a=0; 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; Linear coefficient b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 257
The product rule · Linear shift a=-0.5; 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=-0.5; Exponential rate b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 258
Implicit circle tangents · Circle radius r=1; 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; Final angle (degrees)=210.
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Open practice chapterGrade 12 · Chapter 259
Signed accumulation · Slope a=0.5; Subtracted intercept b=2.5
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=2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 260
Substitution and bounds · Exponent factor k=0.65; 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=0.65; Final upper bound B=1.75.
Question · Worked solution · Animated example
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