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Calculus Questions - All Grades

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Grade 12 Calculus
What is [math]d/dx(x^lnx)[/math]?
  1. [math]x^lnx[/math]
  2. [math](lnx)^x[/math]
  3. [math](2/x)(lnx)(x^lnx)[/math]
  4. [math](lnx)(x^(lnx-1))[/math]
  5. [math]2(lnx)(x^lnx)[/math]
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
What is the sum of the first 7 numbers in the series [math]5,25,125,625,...[/math] ?
  1. [math]19531[/math]
  2. [math]9.77 xx10^5[/math]
  3. [math]97655[/math]
  4. [math]78125[/math]
Grade 12 Calculus CCSS: HSF-IF.C.7c
[math]f(x)=2x^5+x^3-3x[/math] is                                                                                               .
  1. Increasing on [math](-oo,oo)[/math]
  2. Decreasing on [math](-oo,-0.65)cup(0.65,oo)[/math] and increasing on [math](-0.65,0.65)[/math]
  3. Increasing on [math](-oo,-0.65)cup(0.65,oo)[/math] and decreasing on [math](-0.65,0.65)[/math]
  4. Decreasing on [math](-oo,-1.4)cup(1.4,oo)[/math] and decreasing on [math](1.4,-1.4)[/math]
Grade 12 Calculus
What is the area under the curve for the function [math]f(x)=3x^3+2x^2[/math] on the closed interval [math][-5,5][/math]?
  1. [math]int_-5^5(3x^3+2x^2)dx=500/3[/math]
  2. [math]int_-5^5(3x^3+2x^2)dx=3/500[/math]
  3. [math]int_-5^5(3x^3+2x^2)dx=3[/math]
  4. [math]int_-5^5(3x^3+2x^2)dx=500[/math]
Grade 11 Sequences and Series
Find the sum of the following finite geometric series: [math]1+4+16+64...+4^9[/math]
  1. [math]516[/math]
  2. [math]2,073.3[/math]
  3. [math]25,347[/math]
  4. [math]349,525[/math]
  5. none of these are correct
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
What is the sum of the first 6 numbers in the series [math]512,2048,8192,...[/math] ?
  1. [math]1.8 xx 10^16[/math]
  2. [math]698,880[/math]
  3. [math]2,096,640[/math]
  4. [math]32,256[/math]
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What is the 61st number in the sequence [math]-3, 0, 3...[/math]?
  1. [math]366[/math]
  2. [math]363[/math]
  3. [math]177[/math]
  4. [math]183[/math]
Grade 11 Sequences and Series
In an arithmetic sequence, if the 4th term is 3 and the 22nd term is 15, then what is the 1st term?
  1. [math]2/3[/math]
  2. [math]1[/math]
  3. [math]-3[/math]
  4. [math]-4/3[/math]
  5. none of these are correct
Grade 12 Calculus
What are all the values of [math]x[/math] for which the function [math]f[/math] defined by [math]f(x)=x^3+3x^2-9x+7[/math] is increasing?
  1. [math]-3< x<1[/math]
  2. [math]-1< x< 1[/math]
  3. [math]x<-3[/math] and [math]x>1[/math]
  4. [math]x<-1[/math] and [math]x>3[/math]
  5. All real numbers
Grade 9 Sequences and Series
Grade 12 Calculus
What is the derivative of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]f'(x)=9x^2+4x[/math]
  2. [math]f'(x)=3x^2+2x[/math]
  3. [math]f'(x)=0[/math]
  4. [math]f'(x)=12x^2+6x[/math]
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What are the fifth and seventh numbers in the sequence [math]1, 6, 36...[/math]?
  1. [math]216,7776[/math]
  2. [math]216,1296[/math]
  3. [math]7776,46656[/math]
  4. [math]1296,46656[/math]
Grade 12 Calculus
Find the indefinite integral. [math]int(4x)/(2x^2-1) \ dx[/math]
  1. [math](2x^2-1)^2+C[/math]
  2. [math]ln 2x^2+C[/math]
  3. [math]ln |2x^2-1|+C[/math]
  4. [math]2/(2x^2-1)^2 +C[/math]
Grade 12 Calculus
Find the indefinite integral. [math]intcsc(x^2-2)cot(x^2-2)x \ dx[/math]
  1. [math]1/2tan( x^2-2)+C[/math]
  2. [math] cot(x^2-2)+C[/math]
  3. [math]-1/2csc( x^2-2)+C[/math]
  4. [math]-sec( x^2-2)+C[/math]
Grade 12 Calculus
Find the indefinite integral. [math]int(5)/(cos5x) \ dx[/math]
  1. [math]ln|sec5x+tan5x|+C[/math]
  2. [math]ln|csc5x+cot5x|+C[/math]
  3. [math]ln|tan5x|+C[/math]
  4. [math]ln|sec5x|+C[/math]
Grade 12 Calculus
Find the indefinite integral. [math]intcot(3x^4+5)12x^3 \ dx[/math]
  1. [math]ln|sin3x^4|+C[/math]
  2. [math]ln|sin(3x^4+5)|+C[/math]
  3. [math]ln|sin12x^3|+C[/math]
  4. [math]ln|sin(12x^3+5)|+C[/math]
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