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Grade 12 practice chapters
1–20 of 600 matching chapters · Page 1 of 30
Clear filtersGrade 12 · Chapter 1
Cubic derivatives · Cubic coefficient a=-2; 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=-2; Linear coefficient b=-3.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 2
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.
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Open practice chapterGrade 12 · Chapter 3
Implicit circle tangents · Circle radius r=1; Final angle (degrees)=30
Use angle θ=18°. 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)=30.
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Open practice chapterGrade 12 · Chapter 4
Signed accumulation · Slope a=0.5; Subtracted intercept b=0
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=0.
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Open practice chapterGrade 12 · Chapter 5
Substitution and bounds · Exponent factor k=0.1; 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=0.1; Final upper bound B=0.5.
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Open practice chapterGrade 12 · Chapter 6
Average function values · Multiplier a=0.5; Power p=1
Use the interval 0≤x≤1.28. Find the endpoint value, integral, and average function height. Givens: Multiplier a=0.5; Power p=1.
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Open practice chapterGrade 12 · Chapter 7
Differential growth models · Initial amount a=0.5; Rate k=-0.5
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=-0.5.
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Open practice chapterGrade 12 · Chapter 8
Binomial probability · Trial count n=2; Success probability p=0.05
Use success count k=1. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=2; Success probability p=0.05.
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Open practice chapterGrade 12 · Chapter 9
Vector components and angles · Vector length r=1; 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=1; Final angle (degrees)=15.
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Open practice chapterGrade 12 · Chapter 10
Cubic derivatives · Cubic coefficient a=-1.5; 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=-1.5; Linear coefficient b=-2.5.
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Open practice chapterGrade 12 · Chapter 11
The product rule · Linear shift a=-1.5; 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=-1.5; Exponential rate b=-0.75.
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Open practice chapterGrade 12 · Chapter 12
Implicit circle tangents · Circle radius r=1.5; Final angle (degrees)=60
Use angle θ=36°. 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)=60.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 13
Signed accumulation · Slope a=1; Subtracted intercept b=0.5
Integrate on 0≤x≤2.4. Find the signed integral, total geometric area, and zero crossing of the line. Givens: Slope a=1; Subtracted intercept b=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 12 · Chapter 14
Substitution and bounds · Exponent factor k=0.15; 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=0.15; Final upper bound B=0.75.
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Open practice chapterGrade 12 · Chapter 15
Washer volumes · Outer radius factor a=1.5; Inner radius factor b=0.1
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=0.1.
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Open practice chapterGrade 12 · Chapter 16
Differential growth models · Initial amount a=1; Rate k=-0.4
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=-0.4.
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Open practice chapterGrade 12 · Chapter 17
Binomial probability · Trial count n=3; Success probability p=0.1
Use success count k=2. Calculate P(X=k), P(X≤k), and the expected count. Givens: Trial count n=3; Success probability p=0.1.
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Open practice chapterGrade 12 · Chapter 18
Vector components and angles · Vector length r=1.5; 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=1.5; Final angle (degrees)=30.
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Open practice chapterGrade 12 · Chapter 19
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.
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Open practice chapterGrade 12 · Chapter 20
Implicit circle tangents · Circle radius r=2; Final angle (degrees)=90
Use angle θ=54°. 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)=90.
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