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Grade 12 practice chapters

1. Grade 12 · Chapter 361

   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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2. Grade 12 · Chapter 362

   Signed accumulation · Slope a=1.5; 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=1.5; Subtracted intercept b=0.

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3. Grade 12 · Chapter 363

   Washer volumes · Outer radius factor a=3; Inner radius factor b=0.3

   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=0.3.

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4. Grade 12 · Chapter 364

   Binomial probability · Trial count n=16; Success probability p=0.85

   Use success count k=10. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=16; Success probability p=0.85.

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5. Grade 12 · Chapter 365

   Vector components and angles · Vector length r=2; Final angle (degrees)=150

   Evaluate at the signed angle θ=90° (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)=150.

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6. Grade 12 · Chapter 366

   Cubic derivatives · Cubic coefficient a=-1.5; 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=-1.5; Linear coefficient b=0.

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7. Grade 12 · Chapter 367

   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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8. Grade 12 · Chapter 368

   Implicit circle tangents · Circle radius r=1; 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=1; Final angle (degrees)=300.

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9. Grade 12 · Chapter 369

   Substitution and bounds · Exponent factor k=0.45; Final upper bound B=1

   Integrate from x=0 to x=0.6. 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=1.

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10. Grade 12 · Chapter 370

    Differential growth models · Initial amount a=2; Rate k=0.5

    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=0.5.

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11. Grade 12 · Chapter 371

    Binomial probability · Trial count n=2; Success probability p=0.2

    Use success count k=1. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=2; Success probability p=0.2.

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12. Grade 12 · Chapter 372

    Vector components and angles · Vector length r=2.5; Final angle (degrees)=165

    Evaluate at the signed angle θ=99° (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)=165.

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13. Grade 12 · Chapter 373

    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.

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14. Grade 12 · Chapter 374

    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.

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15. Grade 12 · Chapter 375

    Implicit circle tangents · Circle radius r=1.5; 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=1.5; Final angle (degrees)=330.

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16. Grade 12 · Chapter 376

    Substitution and bounds · Exponent factor k=0.5; 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=0.5; Final upper bound B=1.25.

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17. Grade 12 · Chapter 377

    Differential growth models · Initial amount a=2.5; Rate k=-0.5

    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=2.5; Rate k=-0.5.

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18. Grade 12 · Chapter 378

    Binomial probability · Trial count n=3; Success probability p=0.25

    Use success count k=2. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=3; Success probability p=0.25.

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19. Grade 12 · Chapter 379

    Vector components and angles · Vector length r=3; Final angle (degrees)=180

    Evaluate at the signed angle θ=108° (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)=180.

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20. Grade 12 · Chapter 380

    Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=1.

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