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Grade 12 College

Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 Derivatives
Identify and classify the extrema of the given function.
f(x)=x3+x2-x
  1. Relative maximum: (-1,32); relative minimum: (13,-1)
  2. Relative maximum: (-1,1); absolute minimum: (13,-527)
  3. Relative maximum: (-1,1); relative minimum: (13,-527)
  4. Relative maximum: (-1,32); no relative or absolute minimums
Grade 12 Derivatives
f(x)=2x5+x3-3x is
  1. increasing on (-,).
  2. decreasing on (-,-0.65)(0.65,) and increasing on (-0.65,0.65).
  3. increasing on (-,-0.65)(0.65,) and decreasing on (-0.65,0.65).
  4. decreasing on (-,-1.4)(1.4,) and decreasing on (1.4,-1.4).
Grade 12 Derivatives
An equation of the line tangent to the graph of y=cos(2x) at x=π4 is which of the following?
  1. y-1=-(x-π4)
  2. y-1=-2(x-π4)
  3. y=2(x-π4)
  4. y=-(x-π4)
  5. y=-2(x-π4)
Grade 12 Integrals
Find the indefinite integral. csc(x2-2)cot(x2-2)x dx
  1. 12tan(x2-2)+C
  2. cot(x2-2)+C
  3. -12csc(x2-2)+C
  4. -sec(x2-2)+C
Grade 12 Derivatives
Find the derivative for this function: f(x)=x2+5x+3.
  1. f(x)=2x+5
  2. f(x)=2x+3
  3. f(x)=2x+5x
Grade 12 Derivatives
Differentiate. f(x)=x-32
  1. f(x)=x-52
  2. f(x)=-32x-52
  3. f(x)=-32x-12
  4. f(x)=-23x-2
Grade 12 Derivatives
Differentiate. f(x)=3x-2+5x-3-2x-5
  1. f(x)=-6x-1-15x-2+10x-4
  2. f(x)=3x-3+5x-4-2x-6
  3. f(x)=3x-1+5x-2-2x-4
  4. f(x)=-6x-3-15x-4+10x-6
Grade 12 Integrals
Find the indefinite integral. cos4(x)sin(x) dx
  1. cos5(x)+C
  2. -15sin5(x)+C
  3. sin5(x)+C
  4. -15cos5(x)+C
  5. -5cos5(x)+C
Grade 12 Integrals
Find the indefinite integral. 3x2dx
  1. 6x+C
  2. x3+C
  3. 12x+C
  4. 23x3+C
Grade 12 Derivatives
Find the derivative of the following function. f(x)=3x5-10x2+5x+7+13x-3x3
  1. f(x)=15x4-20x+5+7x-9x4
  2. f(x)=15x4-20x+18-9x2
  3. f(x)=15x4-20x+5-13x2+9x4
  4. f(x)=3x3-23-3x2
Grade 12 Derivatives
Find the derivative. f(x)=3x4
  1. f(x)=3x3
  2. f(x)=12x
  3. f(x)=12x3
  4. f(x)=4x3
Grade 12 Derivatives
Differentiate. f(x)=3x4+9x-73x4
  1. f(x)=12x3+9x+743x3
  2. f(x)=12x3+92x+2143x
  3. f(x)=12x3+92x+2833x7
  4. f(x)=12x3+9-734x3
Grade 12 Integrals
What is the area under the curve for the function f(x)=3x3+2x2 on the closed interval [-5,5]?
  1. 5-5(3x3+2x2)dx=5003
  2. 5-5(3x3+2x2)dx=3500
  3. 5-5(3x3+2x2)dx=3
  4. 5-5(3x3+2x2)dx=500
Grade 12 Derivatives
What is ddx(xlnx)?
  1. xlnx
  2. (lnx)x
  3. (2x)(lnx)(xlnx)
  4. (lnx)(xlnx-1)
  5. 2(lnx)(xlnx)
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