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

Attempt · Explain · Animate

Grade 12 practice chapters

1. Grade 12 · Chapter 481

   Substitution and bounds · Exponent factor k=0.4; 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=0.4; Final upper bound B=1.

   Question · Worked solution · Animated example

   Open practice chapter

2. Grade 12 · Chapter 482

   Binomial probability · Trial count n=5; Success probability p=0.4

   Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.4.

   Question · Worked solution · Animated example

   Open practice chapter

3. Grade 12 · Chapter 483

   Cubic derivatives · Cubic coefficient a=-1; 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; Linear coefficient b=1.5.

   Question · Worked solution · Animated example

   Open practice chapter

4. Grade 12 · Chapter 484

   The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=1.

   Question · Worked solution · Animated example

   Open practice chapter

5. Grade 12 · Chapter 485

   Substitution and bounds · Exponent factor k=0.45; 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=0.45; Final upper bound B=1.25.

   Question · Worked solution · Animated example

   Open practice chapter

6. Grade 12 · Chapter 486

   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.

   Question · Worked solution · Animated example

   Open practice chapter

7. Grade 12 · Chapter 487

   Binomial probability · Trial count n=6; Success probability p=0.45

   Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=6; Success probability p=0.45.

   Question · Worked solution · Animated example

   Open practice chapter

8. Grade 12 · Chapter 488

   Vector components and angles · Vector length r=2; Final angle (degrees)=15

   Evaluate at the signed angle θ=9° (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)=15.

   Question · Worked solution · Animated example

   Open practice chapter

9. Grade 12 · Chapter 489

   Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=2.

   Question · Worked solution · Animated example

   Open practice chapter

10. Grade 12 · Chapter 490

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

    Question · Worked solution · Animated example

    Open practice chapter

11. Grade 12 · Chapter 491

    Substitution and bounds · Exponent factor k=0.5; 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=0.5; Final upper bound B=1.5.

    Question · Worked solution · Animated example

    Open practice chapter

12. Grade 12 · Chapter 492

    Differential growth models · Initial amount a=3; 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=3; Rate k=-0.1.

    Question · Worked solution · Animated example

    Open practice chapter

13. Grade 12 · Chapter 493

    Binomial probability · Trial count n=7; Success probability p=0.5

    Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=7; Success probability p=0.5.

    Question · Worked solution · Animated example

    Open practice chapter

14. Grade 12 · Chapter 494

    Vector components and angles · Vector length r=2.5; Final angle (degrees)=30

    Evaluate at the signed angle θ=18° (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)=30.

    Question · Worked solution · Animated example

    Open practice chapter

15. Grade 12 · Chapter 495

    Cubic derivatives · Cubic coefficient a=0; Linear coefficient b=2.5

    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=2.5.

    Question · Worked solution · Animated example

    Open practice chapter

16. Grade 12 · Chapter 496

    The product rule · Linear shift a=-0.5; Exponential rate b=-0.75

    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=-0.75.

    Question · Worked solution · Animated example

    Open practice chapter

17. Grade 12 · Chapter 497

    Substitution and bounds · Exponent factor k=0.55; Final upper bound B=1.75

    Integrate from x=0 to x=1.05. Find the transformed upper bound under u=kx² and the exact integral, then give a decimal approximation. Givens: Exponent factor k=0.55; Final upper bound B=1.75.

    Question · Worked solution · Animated example

    Open practice chapter

18. Grade 12 · Chapter 498

    Binomial probability · Trial count n=8; Success probability p=0.55

    Use success count k=5. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=8; Success probability p=0.55.

    Question · Worked solution · Animated example

    Open practice chapter

19. Grade 12 · Chapter 499

    Vector components and angles · Vector length r=3; 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=3; Final angle (degrees)=45.

    Question · Worked solution · Animated example

    Open practice chapter

20. Grade 12 · Chapter 500

    Cubic derivatives · Cubic coefficient a=0.5; Linear coefficient b=3

    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=3.

    Question · Worked solution · Animated example

    Open practice chapter