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Grade 12 practice chapters

1. Grade 12 · Chapter 181

   Differential growth models · Initial amount a=1.5; Rate k=0

   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.

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2. Grade 12 · Chapter 182

   Binomial probability · Trial count n=7; Success probability p=0.35

   Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=7; Success probability p=0.35.

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3. Grade 12 · Chapter 183

   Vector components and angles · Vector length r=2; Final angle (degrees)=90

   Evaluate at the signed angle θ=54° (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)=90.

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4. Grade 12 · Chapter 184

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

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5. Grade 12 · Chapter 185

   The product rule · Linear shift a=-0.5; 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=-0.5; Exponential rate b=0.25.

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6. Grade 12 · Chapter 186

   Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=180

   Use angle θ=108°. 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)=180.

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7. Grade 12 · Chapter 187

   Signed accumulation · Slope a=2; Subtracted intercept b=3

   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=3.

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8. Grade 12 · Chapter 188

   Substitution and bounds · Exponent factor k=0.2; 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=0.2; Final upper bound B=1.25.

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9. Grade 12 · Chapter 189

   Average function values · Multiplier a=2; Power p=3

   Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2; Power p=3.

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10. Grade 12 · Chapter 190

    Binomial probability · Trial count n=8; Success probability p=0.4

    Use success count k=5. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=8; Success probability p=0.4.

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11. Grade 12 · Chapter 191

    Vector components and angles · Vector length r=2.5; 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=2.5; Final angle (degrees)=105.

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12. Grade 12 · Chapter 192

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

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13. Grade 12 · Chapter 193

    The product rule · Linear shift a=0; 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; Exponential rate b=0.5.

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14. Grade 12 · Chapter 194

    Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=3.5.

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15. Grade 12 · Chapter 195

    Substitution and bounds · Exponent factor k=0.25; 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=0.25; Final upper bound B=1.5.

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16. Grade 12 · Chapter 196

    Washer volumes · Outer radius factor a=2; Inner radius factor b=0.6

    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=0.6.

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17. Grade 12 · Chapter 197

    Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=0.2.

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18. Grade 12 · Chapter 198

    Binomial probability · Trial count n=9; Success probability p=0.45

    Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=9; Success probability p=0.45.

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19. Grade 12 · Chapter 199

    Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=120.

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20. Grade 12 · Chapter 200

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

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