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# Calculus Questions - All Grades

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