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

Attempt · Explain · Animate

Grade 12 practice chapters

1. Grade 12 · Chapter 141

   Implicit circle tangents · Circle radius r=1.5; 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=1.5; Final angle (degrees)=150.

   Question · Worked solution · Animated example

   Open practice chapter

2. Grade 12 · Chapter 142

   Signed accumulation · Slope a=2.5; 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=2.5; Subtracted intercept b=3.

   Question · Worked solution · Animated example

   Open practice chapter

3. Grade 12 · Chapter 143

   Substitution and bounds · Exponent factor k=0.9; 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=0.9; Final upper bound B=1.

   Question · Worked solution · Animated example

   Open practice chapter

4. Grade 12 · Chapter 144

   Average function values · Multiplier a=2.5; Power p=3

   Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=2.5; Power p=3.

   Question · Worked solution · Animated example

   Open practice chapter

5. Grade 12 · Chapter 145

   Washer volumes · Outer radius factor a=1.5; 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=1.5; Inner radius factor b=0.4.

   Question · Worked solution · Animated example

   Open practice chapter

6. Grade 12 · Chapter 146

   Differential growth models · Initial amount a=2.5; 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=2.5; Rate k=0.1.

   Question · Worked solution · Animated example

   Open practice chapter

7. Grade 12 · Chapter 147

   Binomial probability · Trial count n=3; Success probability p=0.15

   Use success count k=2. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=3; Success probability p=0.15.

   Question · Worked solution · Animated example

   Open practice chapter

8. Grade 12 · Chapter 148

   Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=105.

   Question · Worked solution · Animated example

   Open practice chapter

9. Grade 12 · Chapter 149

   Cubic derivatives · Cubic coefficient a=2; 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=2; Linear coefficient b=1.5.

   Question · Worked solution · Animated example

   Open practice chapter

10. Grade 12 · Chapter 150

    The product rule · Linear shift a=2; 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=2; Exponential rate b=-1.

    Question · Worked solution · Animated example

    Open practice chapter

11. Grade 12 · Chapter 151

    Implicit circle tangents · Circle radius r=2; 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=2; Final angle (degrees)=180.

    Question · Worked solution · Animated example

    Open practice chapter

12. Grade 12 · Chapter 152

    Signed accumulation · Slope a=3; 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=3; Subtracted intercept b=3.5.

    Question · Worked solution · Animated example

    Open practice chapter

13. Grade 12 · Chapter 153

    Substitution and bounds · Exponent factor k=0.95; 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=0.95; Final upper bound B=1.25.

    Question · Worked solution · Animated example

    Open practice chapter

14. Grade 12 · Chapter 154

    Average function values · Multiplier a=3; Power p=4

    Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=3; Power p=4.

    Question · Worked solution · Animated example

    Open practice chapter

15. Grade 12 · Chapter 155

    Differential growth models · Initial amount a=3; 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=3; Rate k=0.2.

    Question · Worked solution · Animated example

    Open practice chapter

16. Grade 12 · Chapter 156

    Binomial probability · Trial count n=4; 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=4; Success probability p=0.2.

    Question · Worked solution · Animated example

    Open practice chapter

17. Grade 12 · Chapter 157

    Vector components and angles · Vector length r=0.5; Final angle (degrees)=45

    Evaluate at the signed angle θ=27° (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)=45.

    Question · Worked solution · Animated example

    Open practice chapter

18. Grade 12 · Chapter 158

    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.

    Question · Worked solution · Animated example

    Open practice chapter

19. Grade 12 · Chapter 159

    The product rule · Linear shift a=-2; 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=-2; Exponential rate b=-0.5.

    Question · Worked solution · Animated example

    Open practice chapter

20. Grade 12 · Chapter 160

    Implicit circle tangents · Circle radius r=2.5; Final angle (degrees)=210

    Use angle θ=126°. 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)=210.

    Question · Worked solution · Animated example

    Open practice chapter