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Grade 12 practice chapters

1. Grade 12 · Chapter 201

   Implicit circle tangents · Circle radius r=2.5; 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=2.5; Final angle (degrees)=240.

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2. Grade 12 · Chapter 202

   Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=4.

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3. Grade 12 · Chapter 203

   Substitution and bounds · Exponent factor k=0.3; 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=0.3; Final upper bound B=1.75.

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4. Grade 12 · Chapter 204

   Average function values · Multiplier a=3; Power p=1

   Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=3; Power p=1.

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5. Grade 12 · Chapter 205

   Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.7.

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6. Grade 12 · Chapter 206

   Differential growth models · Initial amount a=3; 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=3; Rate k=0.3.

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7. Grade 12 · Chapter 207

   Binomial probability · Trial count n=10; 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=10; Success probability p=0.5.

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8. Grade 12 · Chapter 208

   Vector components and angles · Vector length r=0.5; Final angle (degrees)=60

   Evaluate at the signed angle θ=36° (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)=60.

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9. Grade 12 · Chapter 209

   Cubic derivatives · Cubic coefficient a=1.5; 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=1.5; Linear coefficient b=1.5.

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10. Grade 12 · Chapter 210

    The product rule · Linear shift a=1; Exponential rate b=1

    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=1.

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11. Grade 12 · Chapter 211

    Implicit circle tangents · Circle radius r=3; 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=3; Final angle (degrees)=270.

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12. Grade 12 · Chapter 212

    Signed accumulation · Slope a=0.5; Subtracted intercept b=2

    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.

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13. Grade 12 · Chapter 213

    Substitution and bounds · Exponent factor k=0.35; 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=0.35; Final upper bound B=2.

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14. Grade 12 · Chapter 214

    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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15. Grade 12 · Chapter 215

    Binomial probability · Trial count n=11; Success probability p=0.55

    Use success count k=7. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=11; Success probability p=0.55.

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16. Grade 12 · Chapter 216

    Vector components and angles · Vector length r=1; Final angle (degrees)=75

    Evaluate at the signed angle θ=45° (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)=75.

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17. Grade 12 · Chapter 217

    Cubic derivatives · Cubic coefficient a=2; Linear coefficient b=2

    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.

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18. Grade 12 · Chapter 218

    The product rule · Linear shift a=1.5; Exponential rate b=-1

    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=-1.

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19. Grade 12 · Chapter 219

    Signed accumulation · Slope a=1; 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=1; Subtracted intercept b=2.5.

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20. Grade 12 · Chapter 220

    Substitution and bounds · Exponent factor k=0.4; 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=0.4; Final upper bound B=0.5.

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