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# Calculus Questions - All Grades

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What are the next 2 numbers in the sequence $1, 5, 9...$?
1. $45,225$
2. $14,18$
3. $13,17$
4. $32,128$
College Calculus
Find the following indefinite integral
$int(-7x^2+ 4/x- 5/x^4) dx$
1. $-7x^3 + 4 ln(|x|) -5x^-3 +C$
2. $1/3x^3 + 4ln (|x|) + 5/3 x^-3 +C$
3. $-7/3x^3 + 4ln(|x|) + 5/3x^-3 +C$
4. $-14x - 4x^-2 + 20x^-5 +C$
The standard form of a quadratic equation is the following:
1. y = mx + b
2. $y = ax^2 + bx + c$
3. $y = a(x - h)^2 + k$
4. y = a(x - p)(x - q)
On $f(x)=2x^5+x^3-3x$
1. $(-0.65,1.4)$ is a relative and absolute maximum.
2. $(0.65,-1.4)$ is a relative and absolute minimum.
3. $(-0.65,1.4)$ is a relative maximum.
4. $(0.65,-1.4)$ is a relative minimum.
5. Both A and B.
6. Both C and D.
7. None of the above.
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. $int_-5^5(3x^3+2x^2)dx=500$
On what intervals is the function $f(x)=3x^3+2x^2$ concave upwards and downwards?
1. concave upward $(-2/9, oo)$, concave downward $(-oo, -2/9)$
2. concave upward $(-oo, -2/9)$, concave downward $(-2/9, -oo)$
3. concave upward $(0, oo)$, concave downward $(-oo, 0)$
4. concave upward $(-oo, 0)$, concave downward $(0, oo)$
What is the second derivative of $f(x)=3x^3+2x^2$?
1. $f''(x)=18x+4$
2. $f''(x)=9x^2+4x$
3. $f''(x)=18$
4. $f''(x)=0$
On what intervals is the function $f(x)=3x^3+2x^2$ increasing or decreasing?
1. increasing: $(-oo,-4/9) uu (0, oo)$, decreasing: $(-4/9, 0)$
2. increasing: $(-oo,-4/9)$, decreasing: $(-4/9, 0)$
3. increasing: $(-oo,0) uu (-4/9, oo)$, decreasing: $(-4/9, 0)$
4. increasing: $(-4/9, 0)$, decreasing: $(-oo,-4/9) uu (0, oo)$
What are the critical numbers of the following equation?
$f(x)=3x^3+2x^2$
1. $x=-4/9, 0$
2. $x=4/9, 0$
3. $x=-9/4, 0$
4. $x=9/4, 0$
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
What is the sum of the first 12 numbers in the series $8,24,72,216,648...$ ?
1. $2 125 760$
2. $6.87 xx10^10$
3. $531441$
4. $-2 125 760$
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. $78125$
The sum to infinity of the geometric sequence $16, 8, 4, 2, ...$ is
1. $8$
2. $16$
3. $32$
4. $64$
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. $183$
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