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
541–560 of 600 matching chapters · Page 28 of 30
Clear filtersGrade 12 · Chapter 541
Substitution and bounds · Exponent factor k=0.15; 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=0.15; Final upper bound B=1.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 542
Binomial probability · Trial count n=4; 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=4; Success probability p=0.4.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 543
Cubic derivatives · Cubic coefficient a=1.5; 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=1.5; Linear coefficient b=-2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 544
The product rule · Linear shift a=1; 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; Exponential rate b=0.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 545
Substitution and bounds · Exponent factor k=0.2; 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=0.2; Final upper bound B=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 546
Binomial probability · Trial count n=5; Success probability p=0.45
Use success count k=3. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=5; Success probability p=0.45.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 547
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 chapterGrade 12 · Chapter 548
The product rule · Linear shift a=1.5; 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=1.5; Exponential rate b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 549
Substitution and bounds · Exponent factor k=0.25; Final upper bound B=0.5
Integrate from x=0 to x=0.3. 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=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 550
Binomial probability · Trial count n=6; 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=6; Success probability p=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 551
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 chapterGrade 12 · Chapter 552
The product rule · Linear shift a=2; 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=2; Exponential rate b=0.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 553
Substitution and bounds · Exponent factor k=0.3; 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=0.3; Final upper bound B=0.75.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 554
Binomial probability · Trial count n=7; Success probability p=0.55
Use success count k=4. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=7; Success probability p=0.55.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 555
Cubic derivatives · Cubic coefficient a=-1.5; 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=-1.5; Linear coefficient b=2.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 556
Substitution and bounds · Exponent factor k=0.35; 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=0.35; Final upper bound B=1.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 557
Binomial probability · Trial count n=8; Success probability p=0.6
Use success count k=5. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=8; Success probability p=0.6.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 558
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 559
Substitution and bounds · Exponent factor k=0.4; 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=0.4; Final upper bound B=1.25.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 560
Binomial probability · Trial count n=9; Success probability p=0.65
Use success count k=6. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=9; Success probability p=0.65.
Question · Worked solution · Animated example
Open practice chapter