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178
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stringclasses 8
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stringclasses 56
values |
|---|---|---|
What are the prime factors of 1369?
37
|
numbers
|
list_prime_factors
|
What are the prime factors of 13221?
3, 13, 113
|
numbers
|
list_prime_factors
|
List the prime factors of 1279.
1279
|
numbers
|
list_prime_factors
|
List the prime factors of 778.
2, 389
|
numbers
|
list_prime_factors
|
What are the prime factors of 5819?
11, 23
|
numbers
|
list_prime_factors
|
List the prime factors of 5194.
2, 7, 53
|
numbers
|
list_prime_factors
|
What are the prime factors of 5527?
5527
|
numbers
|
list_prime_factors
|
What are the prime factors of 1002?
2, 3, 167
|
numbers
|
list_prime_factors
|
What are the prime factors of 420?
2, 3, 5, 7
|
numbers
|
list_prime_factors
|
What are the prime factors of 13871?
11, 13, 97
|
numbers
|
list_prime_factors
|
List the prime factors of 24/(-20)*(-20)/8.
3
|
numbers
|
list_prime_factors_composed
|
Let d = 21 + 81. List the prime factors of d.
2, 3, 17
|
numbers
|
list_prime_factors_composed
|
Suppose -3*v + 33 = 12. Suppose 3*i = 4*b - 40, -4*b = v*i - 2*i - 72. What are the prime factors of b?
13
|
numbers
|
list_prime_factors_composed
|
Let p(b) = -b**2 + 9*b. What are the prime factors of p(7)?
2, 7
|
numbers
|
list_prime_factors_composed
|
Let a be (12/9)/(1/3). Let y be 16 + -10 + 1*-3. Suppose -q + 15 = y*u, 0*q + a*q - 3*u = 0. What are the prime factors of q?
3
|
numbers
|
list_prime_factors_composed
|
Suppose 2 = 2*r, -g + 0*r + 3*r - 3 = 0. Suppose -o + 16 = 5*p, -20 = -5*p - 4*o - 1. Suppose p*a - 2*x = x + 30, -x = g. List the prime factors of a.
2, 5
|
numbers
|
list_prime_factors_composed
|
Suppose -5*q = -2*d + 26, 3*q - 1 - 2 = -5*d. Suppose -g = d*g - 12. Suppose 5*v - 5*l + l = 6, g*v = -5*l + 11. What are the prime factors of v?
2
|
numbers
|
list_prime_factors_composed
|
Suppose 0 = 2*h + 8 - 22. List the prime factors of h.
7
|
numbers
|
list_prime_factors_composed
|
Suppose -2*x + x + 5 = 0. Suppose -40 = -x*c + c. List the prime factors of c.
2, 5
|
numbers
|
list_prime_factors_composed
|
Let z(y) = -y - 6. Let c be z(-7). Let v = -1 + 3. List the prime factors of 10 + c*(v + -3).
3
|
numbers
|
list_prime_factors_composed
|
What is the tens digit of 541?
4
|
numbers
|
place_value
|
What is the tens digit of 4223?
2
|
numbers
|
place_value
|
What is the units digit of 1137?
7
|
numbers
|
place_value
|
What is the units digit of 1750?
0
|
numbers
|
place_value
|
What is the units digit of 1005?
5
|
numbers
|
place_value
|
What is the tens digit of 10513?
1
|
numbers
|
place_value
|
What is the tens digit of 614?
1
|
numbers
|
place_value
|
What is the hundreds digit of 843?
8
|
numbers
|
place_value
|
What is the hundreds digit of 2156?
1
|
numbers
|
place_value
|
What is the thousands digit of 10445?
0
|
numbers
|
place_value
|
Let h(o) = o**3 + 9*o**2 + 13. Let w be h(-9). Suppose -5 = -2*q - w. Let x(y) = 2 - 2*y. What is the units digit of x(q)?
0
|
numbers
|
place_value_composed
|
Let w(y) be the first derivative of -y**3/3 - 5*y**2/2 - y - 1. What is the units digit of w(-4)?
3
|
numbers
|
place_value_composed
|
Suppose -37 = -n - q + 3*q, 3*q - 15 = 0. Suppose -5*k - 3*x = -n, 32 = 4*k - 2*x + 3*x. What is the units digit of k?
7
|
numbers
|
place_value_composed
|
Let k(z) = -z**3 + 7*z**2 + 6*z - 7. What is the units digit of k(7)?
5
|
numbers
|
place_value_composed
|
Suppose -i - 20 = 3*i. Let m(t) be the second derivative of -t**4/12 - t**3 + t**2/2 + t. What is the units digit of m(i)?
6
|
numbers
|
place_value_composed
|
Suppose -5*t = -3*t. Suppose -v + 8 = -t*v. Let c = v - 6. What is the units digit of c?
2
|
numbers
|
place_value_composed
|
Let u(w) = 0 + 0 - 5*w + w**2. Let s be u(5). Suppose s = 4*f - f - 3. What is the units digit of f?
1
|
numbers
|
place_value_composed
|
Suppose -3*w - p + 0*p = 2, 0 = -3*w - 3*p. Let j(g) = -7*g. What is the units digit of j(w)?
7
|
numbers
|
place_value_composed
|
Let l = -11 + 6. Let h be 15/l*(-6 - -1). Let c = -4 + h. What is the tens digit of c?
1
|
numbers
|
place_value_composed
|
Let c(s) = -s**3 + 8*s**2 - 2*s + 11. Let m be c(8). What is the tens digit of 126/10 + (-2)/m?
1
|
numbers
|
place_value_composed
|
What is 0.00033532 rounded to five decimal places?
0.00034
|
numbers
|
round_number
|
What is 0.0014143 rounded to four decimal places?
0.0014
|
numbers
|
round_number
|
What is 0.00535 rounded to 3 dps?
0.005
|
numbers
|
round_number
|
Round 0.0000029 to six decimal places.
0.000003
|
numbers
|
round_number
|
What is 0.00000029 rounded to seven decimal places?
0.0000003
|
numbers
|
round_number
|
What is -0.0852 rounded to two dps?
-0.09
|
numbers
|
round_number
|
Round -4330 to the nearest 1000.
-4000
|
numbers
|
round_number
|
Round -19.8 to the nearest 10.
-20
|
numbers
|
round_number
|
Round 0.15232 to two dps.
0.15
|
numbers
|
round_number
|
Round 0.000022351 to 7 dps.
0.0000224
|
numbers
|
round_number
|
Suppose 0 = -8*s + 12*s + 6280. Round s to the nearest one hundred.
-1600
|
numbers
|
round_number_composed
|
Let u = -0.219 - -0.2190233. What is u rounded to six dps?
0.000023
|
numbers
|
round_number_composed
|
Let h(q) = q**2 + 4*q + 2. Let l be h(-4). Suppose l*n - 1 = 5. Suppose n*v = v - 3200000. What is v rounded to the nearest 1000000?
-2000000
|
numbers
|
round_number_composed
|
Let q = 1.3164 + -1.38. Let c = q + 0.07. What is c rounded to three decimal places?
0.006
|
numbers
|
round_number_composed
|
Let j = 1.90025 - 1.9. What is j rounded to four decimal places?
0.0003
|
numbers
|
round_number_composed
|
Let q = -66.18 + -0.82. Let l = 66.9768 + q. Let w = l + 0.02. Round w to 3 decimal places.
-0.003
|
numbers
|
round_number_composed
|
Let s = -65515799 + 23515773. Let q be s/(-6) - (-2)/(-6). Let z be q/10 - 6/15. Round z to the nearest 100000.
700000
|
numbers
|
round_number_composed
|
Let a = -0.26 - 0.04. What is a rounded to two decimal places?
-0.3
|
numbers
|
round_number_composed
|
Suppose 0 = 9*r - 5*r - 924. What is r rounded to the nearest one hundred?
200
|
numbers
|
round_number_composed
|
Let g = 310.9363 + -311. Let n = 0.06 + g. Round n to three dps.
-0.004
|
numbers
|
round_number_composed
|
Let l(b) be the third derivative of 1/120*b**6 + 0 - 1/30*b**5 + 1/24*b**4 + 0*b + 0*b**3 - 3*b**2. Let u(w) = -2*w**3 + 4*w**2 - 2*w. Give -13*l(i) - 6*u(i).
-i**3 + 2*i**2 - i
|
polynomials
|
add
|
Let u(z) = 7*z**2 + 5*z - 7. Let m(n) = -8*n**2 - 6*n + 8. What is -5*m(l) - 6*u(l)?
2 - 2*l**2
|
polynomials
|
add
|
Let x(b) = b + 1. Let j(n) = -3*n - 9. Let t(o) = j(o) + 6*x(o). Let s(v) = 3 - 2*v. Let i(q) = 2*s(q) + 3*t(q). Let m(l) = 3*l - 2. Determine -5*i(c) + 8*m(c).
-c - 1
|
polynomials
|
add
|
Let s(u) be the first derivative of -7*u**2/2 + 6*u - 2. Suppose -3*j = -f + 14, -4*j + 51 = f + 4*f. Let k(l) = -2*l - 6*l - 5*l + 11. What is f*s(r) - 6*k(r)?
r
|
polynomials
|
add
|
Let j be (-2)/1 + 1 - 0. Let w(d) = -d**2 + d. Let y(s) be the second derivative of -s**4/2 + 2*s**3/3 - s. Let l = 8 - 4. Calculate j*y(i) + l*w(i).
2*i**2
|
polynomials
|
add
|
Suppose x - 10 = -5. Let a(s) = 8 - 2*s**2. Let z(k) = 5 - k**2. Calculate x*a(l) - 8*z(l).
-2*l**2
|
polynomials
|
add
|
Let i(y) = -2*y**2 + y + 9. Let c(g) = g**3 - 4*g**2 + 2*g - 3. Let j be c(4). Let l = 6 + -4. Let n(u) = -2*u**2 + u + u**l + 0*u**2 + 5. Give j*n(q) - 3*i(q).
q**2 + 2*q - 2
|
polynomials
|
add
|
Let l(g) = -14*g + 17 - 2*g - g. Let f(c) = 4 - 10*c. Let s(b) = 29*b - 12. Let a(n) = -17*f(n) - 6*s(n). What is 9*a(z) - 2*l(z)?
2 - 2*z
|
polynomials
|
add
|
Suppose 3*x - 5 + 32 = 0. Let o(j) = 4*j + 5. Let l(k) = 17*k + 21. Determine x*o(w) + 2*l(w).
-2*w - 3
|
polynomials
|
add
|
Let f(o) = -7*o**3 - 4*o**2 - 3. Let t(u) = 7*u**3 + 4*u**2 + 2. Let j(y) = 4*f(y) + 6*t(y). Let x(k) = -5*k**3 - 3*k**2. What is -3*j(p) - 8*x(p)?
-2*p**3
|
polynomials
|
add
|
Express (-3 + 31 - 9)*(3 - 6 + 4)*(0*c - 2*c + 0*c) in the form x*c + p and give x.
-38
|
polynomials
|
coefficient_named
|
Rearrange j + 12 + j - 2*j**2 - 2*j to the form q + d*j + x*j**2 and give q.
12
|
polynomials
|
coefficient_named
|
Rearrange (-2*h + 3*h - 7 - 3*h)*(0 - 1 - 2) to x*h + j and give x.
6
|
polynomials
|
coefficient_named
|
Rearrange (0 + 0 + h)*(-4*h + 4*h - 3*h + 1) - 2*h**2 + 2*h**2 - 5*h**2 to the form p*h**2 + w*h + r and give w.
1
|
polynomials
|
coefficient_named
|
Express 0 - 4 - 7*g**2 + 4 as z + n*g**2 + f*g and give n.
-7
|
polynomials
|
coefficient_named
|
Rearrange 5*k**2 - 4 + 3 + 3*k + 1 - k**3 to l + o*k**3 + f*k**2 + a*k and give a.
3
|
polynomials
|
coefficient_named
|
Rearrange (-3*l - 2 + 2)*((0 + 2 + 0)*(2 - 2 - 2*l) - 2*l + 0*l + 3*l) to the form x + d*l**2 + b*l and give d.
9
|
polynomials
|
coefficient_named
|
Express (2 - 3 + 6)*(-3*h - 1 + 1 - 3) in the form n + b*h and give b.
-15
|
polynomials
|
coefficient_named
|
Express 1 - 2*t**4 - t**2 - 2 - 3*t**4 - 1 as l*t + y + f*t**3 + s*t**2 + c*t**4 and give y.
-2
|
polynomials
|
coefficient_named
|
Express -5*i**3 + 2*i**3 - 12*i**2 + 4*i**3 in the form p*i**2 + l*i + u*i**3 + j and give j.
0
|
polynomials
|
coefficient_named
|
Collect the terms in -2*v**2 - 3*v**2 + 9*v**2 - 5*v**2.
-v**2
|
polynomials
|
collect
|
Collect the terms in 5*q**3 - 29*q**3 + 22*q**3.
-2*q**3
|
polynomials
|
collect
|
Collect the terms in 24*p + 22*p + 29*p.
75*p
|
polynomials
|
collect
|
Collect the terms in 64*k - 64*k - 3*k**2.
-3*k**2
|
polynomials
|
collect
|
Collect the terms in -24*t + 57 - 24*t - 57.
-48*t
|
polynomials
|
collect
|
Collect the terms in o**2 + 4*o**2 - 3*o**3 - 5*o**2.
-3*o**3
|
polynomials
|
collect
|
Collect the terms in 55965 - 55965 - 2*f**3.
-2*f**3
|
polynomials
|
collect
|
Collect the terms in 74*f + 114*f**2 - 74*f.
114*f**2
|
polynomials
|
collect
|
Collect the terms in o**2 + 2717*o - 2717*o.
o**2
|
polynomials
|
collect
|
Collect the terms in -34*v + 19*v + 11*v.
-4*v
|
polynomials
|
collect
|
Let s(w) = w. Let a(t) = 18*t + 7. Let p(r) = -12*r - 5. Let o(z) = 5*a(z) + 7*p(z). Give s(o(u)).
6*u
|
polynomials
|
compose
|
Let j(w) = 78 + 2*w - 42 - 36. Let l(h) be the first derivative of 3*h**2 + 1. Determine j(l(u)).
12*u
|
polynomials
|
compose
|
Let l(y) be the third derivative of -y**4/12 - y**2. Let z(m) = 6*m**2. Let f(s) = -s**2. Let b(r) = -9*f(r) - z(r). What is l(b(g))?
-6*g**2
|
polynomials
|
compose
|
Let n(x) = -7*x**2 - 6*x - 6. Let a(u) = 15*u**2 + 13*u + 13. Let b(t) = 6*a(t) + 13*n(t). Let s(m) be the first derivative of 1 - m**3/3. Determine s(b(i)).
-i**4
|
polynomials
|
compose
|
Let c(x) = -198*x. Let d(w) = -3*w. Calculate c(d(i)).
594*i
|
polynomials
|
compose
|
Suppose -9*r - 12 = -13*r. Let o(b) = -4*b - 4*b + 4*b + r*b. Let g(d) = -2*d. Calculate g(o(l)).
2*l
|
polynomials
|
compose
|
Let d(i) = 229*i. Let a(k) = -2*k**2. Calculate d(a(n)).
-458*n**2
|
polynomials
|
compose
|
Let u(y) = 2*y**2. Let j(n) = -5*n - 9. Let d be j(-6). Let w(h) = 9*h + 0 - 4 - 2*h + 8. Let f(r) = 36*r + 21. Let q(o) = d*w(o) - 4*f(o). Give u(q(l)).
18*l**2
|
polynomials
|
compose
|
Let z be -12 + (-2 - -4 - 1). Let u(w) = 1 + 0 - 8*w + 5. Let m(n) = 15*n - 11. Let s(v) = z*u(v) - 6*m(v). Let k(j) = -j. What is s(k(f))?
2*f
|
polynomials
|
compose
|
Let v(l) = 5*l**2. Let h = 8 - 3. Let d(i) = 5 - h + i. What is v(d(a))?
5*a**2
|
polynomials
|
compose
|
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