10,000 ways to practice.
One idea at a time.

Attempt · Explain · Animate

Grade 12 practice chapters

1. Grade 12 · Chapter 161

   Signed accumulation · Slope a=0.5; 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=0.5; Subtracted intercept b=1.5.

   Question · Worked solution · Animated example

   Open practice chapter

2. Grade 12 · Chapter 162

   Substitution and bounds · Exponent factor k=1; 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=1; Final upper bound B=1.5.

   Question · Worked solution · Animated example

   Open practice chapter

3. Grade 12 · Chapter 163

   Average function values · Multiplier a=0.5; Power p=4

   Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=0.5; Power p=4.

   Question · Worked solution · Animated example

   Open practice chapter

4. Grade 12 · Chapter 164

   Washer volumes · Outer radius factor a=2.5; 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=2.5; Inner radius factor b=0.6.

   Question · Worked solution · Animated example

   Open practice chapter

5. Grade 12 · Chapter 165

   Differential growth models · Initial amount a=0.5; 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=0.5; Rate k=-0.2.

   Question · Worked solution · Animated example

   Open practice chapter

6. Grade 12 · Chapter 166

   Binomial probability · Trial count n=5; Success probability p=0.25

   Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.25.

   Question · Worked solution · Animated example

   Open practice chapter

7. Grade 12 · Chapter 167

   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.

   Question · Worked solution · Animated example

   Open practice chapter

8. Grade 12 · Chapter 168

   The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=-0.25.

   Question · Worked solution · Animated example

   Open practice chapter

9. Grade 12 · Chapter 169

   Implicit circle tangents · Circle radius r=3; 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=3; Final angle (degrees)=240.

   Question · Worked solution · Animated example

   Open practice chapter

10. Grade 12 · Chapter 170

    Substitution and bounds · Exponent factor k=0.1; Final upper bound B=0.75

    Integrate from x=0 to x=0.45. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.1; Final upper bound B=0.75.

    Question · Worked solution · Animated example

    Open practice chapter

11. Grade 12 · Chapter 171

    Washer volumes · Outer radius factor a=3; 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=3; Inner radius factor b=0.7.

    Question · Worked solution · Animated example

    Open practice chapter

12. Grade 12 · Chapter 172

    Differential growth models · Initial amount a=1; 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=1; Rate k=-0.1.

    Question · Worked solution · Animated example

    Open practice chapter

13. Grade 12 · Chapter 173

    Binomial probability · Trial count n=6; Success probability p=0.3

    Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=6; Success probability p=0.3.

    Question · Worked solution · Animated example

    Open practice chapter

14. Grade 12 · Chapter 174

    Vector components and angles · Vector length r=1.5; 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=1.5; Final angle (degrees)=75.

    Question · Worked solution · Animated example

    Open practice chapter

15. Grade 12 · Chapter 175

    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.

    Question · Worked solution · Animated example

    Open practice chapter

16. Grade 12 · Chapter 176

    The product rule · Linear shift a=-1; 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; Exponential rate b=0.

    Question · Worked solution · Animated example

    Open practice chapter

17. Grade 12 · Chapter 177

    Implicit circle tangents · Circle radius r=1; 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=1; Final angle (degrees)=150.

    Question · Worked solution · Animated example

    Open practice chapter

18. Grade 12 · Chapter 178

    Signed accumulation · Slope a=1.5; 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=1.5; Subtracted intercept b=2.5.

    Question · Worked solution · Animated example

    Open practice chapter

19. Grade 12 · Chapter 179

    Substitution and bounds · Exponent factor k=0.15; 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=0.15; Final upper bound B=1.

    Question · Worked solution · Animated example

    Open practice chapter

20. Grade 12 · Chapter 180

    Washer volumes · Outer radius factor a=1; Inner radius factor b=0.4

    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=1; Inner radius factor b=0.4.

    Question · Worked solution · Animated example

    Open practice chapter