Math With Amar · Guided practice
10,000 ways to practice.
One idea at a time.
Each chapter gives you a distinct mathematical scenario: one question to attempt, a hint, a worked solution, and an animated example you can control.
10,000 questions · 10,000 animated scenarios · 14 study levels
Choose a starting point
Practice at your level.
Grade labels are starting points; school sequences vary. Advanced chapters assume the prerequisites listed on their pages.
Attempt · Explain · Animate
Grade 12 practice chapters
521–540 of 600 matching chapters · Page 27 of 30
Clear filtersGrade 12 · Chapter 521
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 chapterGrade 12 · Chapter 522
Substitution and bounds · Exponent factor k=0.85; 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=0.85; Final upper bound B=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 523
Binomial probability · Trial count n=14; Success probability p=0.85
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=14; Success probability p=0.85.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 524
Cubic derivatives · Cubic coefficient a=-1; 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=-1; Linear coefficient b=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 525
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 chapterGrade 12 · Chapter 526
Substitution and bounds · Exponent factor k=0.9; 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=0.9; Final upper bound B=1.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 527
Binomial probability · Trial count n=15; Success probability p=0.9
Use success count k=9. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=15; Success probability p=0.9.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 528
Cubic derivatives · Cubic coefficient a=-0.5; 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=-0.5; Linear coefficient b=2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 529
The product rule · Linear shift a=-1; 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=-1; Exponential rate b=-0.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 530
Substitution and bounds · Exponent factor k=0.95; Final upper bound B=2
Integrate from x=0 to x=1.2. 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=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 531
Binomial probability · Trial count n=16; Success probability p=0.95
Use success count k=10. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=16; Success probability p=0.95.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 532
Cubic derivatives · Cubic coefficient a=0; 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; Linear coefficient b=3.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 533
The product rule · Linear shift a=-0.5; 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=-0.5; Exponential rate b=-0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 534
Binomial probability · Trial count n=2; Success probability p=0.3
Use success count k=1. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=2; Success probability p=0.3.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 535
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 chapterGrade 12 · Chapter 536
The product rule · Linear shift a=0; 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; Exponential rate b=-0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 537
Substitution and bounds · Exponent factor k=0.1; 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=0.1; Final upper bound B=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 538
Binomial probability · Trial count n=3; Success probability p=0.35
Use success count k=2. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=3; Success probability p=0.35.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 539
Cubic derivatives · Cubic coefficient a=1; 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=1; Linear coefficient b=-2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 540
The product rule · Linear shift a=0.5; 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=0.5; Exponential rate b=0.
Question · Worked solution · Animated example
Open practice chapter