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Grade 12 practice chapters

1. Grade 12 · Chapter 21

   Signed accumulation · Slope a=1.5; Subtracted intercept b=1

   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=1.

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2. Grade 12 · Chapter 22

   Substitution and bounds · Exponent factor k=0.2; 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=0.2; Final upper bound B=1.

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3. Grade 12 · Chapter 23

   Average function values · Multiplier a=1.5; Power p=3

   Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=1.5; Power p=3.

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4. Grade 12 · Chapter 24

   Washer volumes · Outer radius factor a=2; 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; Inner radius factor b=0.2.

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5. Grade 12 · Chapter 25

   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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6. Grade 12 · Chapter 26

   Binomial probability · Trial count n=4; Success probability p=0.15

   Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=4; Success probability p=0.15.

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7. Grade 12 · Chapter 27

   Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=-1.5.

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8. Grade 12 · Chapter 28

   Implicit circle tangents · Circle radius r=2.5; Final angle (degrees)=120

   Use angle θ=72°. 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)=120.

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9. Grade 12 · Chapter 29

   Signed accumulation · Slope a=2; Subtracted intercept b=1.5

   Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=2; Subtracted intercept b=1.5.

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10. Grade 12 · Chapter 30

    Substitution and bounds · Exponent factor k=0.25; 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=0.25; Final upper bound B=1.25.

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11. Grade 12 · Chapter 31

    Average function values · Multiplier a=2; Power p=4

    Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2; Power p=4.

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12. Grade 12 · Chapter 32

    Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.3.

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13. Grade 12 · Chapter 33

    Differential growth models · Initial amount a=2; 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=2; Rate k=-0.2.

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14. Grade 12 · Chapter 34

    Binomial probability · Trial count n=5; Success probability p=0.2

    Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.2.

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15. Grade 12 · Chapter 35

    Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=60.

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16. Grade 12 · Chapter 36

    Cubic derivatives · Cubic coefficient a=0; 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; Linear coefficient b=-1.

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17. Grade 12 · Chapter 37

    The product rule · Linear shift a=0; 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=0; Exponential rate b=0.

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18. Grade 12 · Chapter 38

    Implicit circle tangents · Circle radius r=3; Final angle (degrees)=150

    Use angle θ=90°. 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)=150.

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19. Grade 12 · Chapter 39

    Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=2.

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20. Grade 12 · Chapter 40

    Substitution and bounds · Exponent factor k=0.3; 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=0.3; Final upper bound B=1.5.

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