instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let u = -14/3 + 59/12. Factor 1/4*h**4 - 1/4*h**2 - 1/4*h**5 + 0*h + u*h**3 + 0.\n | -h**2*(h - 1)**2*(h + 1)/4\n | ibivibiv/math_instruct | |
Is 78095 a multiple of 128?\n | False\n | ibivibiv/math_instruct | |
Let r(o) = -o**3 + 6*o**2 - o + 8. Let h be r(6). Suppose -h*b = -3*l + 8, -4*l - l + 11 = -b. Let w(t) = 12*t - 2. Is 22 a factor of w(l)?\n | True\n | ibivibiv/math_instruct | |
Let z(w) = -19*w**2 + 2*w. Let x(l) = -21*l**2 + 2*l. Determine 3*x(c) - 4*z(c).\n | 13*c**2 - 2*c\n | ibivibiv/math_instruct | |
Sort 1/258, -3, -5, 0.3 in descending order.\n | 0.3, 1/258, -3, -5\n | ibivibiv/math_instruct | |
Let y be 84/45 - 4/(-30). Solve 2*o - 4 = i, 2*i + 0*o = y*o for i.\n | 4\n | ibivibiv/math_instruct | |
Let h = -73.14 - -155.11. Let g = h - 80. Round g to the nearest integer.\n | 2\n | ibivibiv/math_instruct | |
Evaluate ((-1)/(-5))/(798/1995).\n | 1/2\n | ibivibiv/math_instruct | |
What is the fifth root of 34030735 to the nearest integer?\n | 32\n | ibivibiv/math_instruct | |
Let g(v) = 0*v + 24 - v + v**2 - 23. Calculate g(0).\n | 1\n | ibivibiv/math_instruct | |
Let l(v) = 8*v - 1. Let o(c) = 84*c + 8. Give -6*l(b) - o(b).\n | -132*b - 2\n | ibivibiv/math_instruct | |
What is the remainder when 600 - (96/(-30) + 8/(-10)) is divided by 95?\n | 34\n | ibivibiv/math_instruct | |
Express (0*n + n - 4*n)*(-10*n + 15*n + 11*n)*(11 - 11*n - 11) in the form b*n + x*n**3 + t*n**2 + o and give x.\n | 528\n | ibivibiv/math_instruct | |
Solve -3*j - 2*b = 13, -j = -15275*b + 15276*b + 6 for j.\n | -1\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 6601 and 574?\n | 287\n | ibivibiv/math_instruct | |
Let i(y) = -y. Let u(c) be the third derivative of -c**4/6 + 4*c**3/3 - 2*c**2 + 33*c. Calculate u(i(b)).\n | 4*b + 8\n | ibivibiv/math_instruct | |
Solve 0 = 313*v - 1399 + 354 - 1772 for v.\n | 9\n | ibivibiv/math_instruct | |
Simplify (((m**(-1/3)/m)**(-2/27)/(m**(-8)*m**(2/23)))**(-7))**20 assuming m is positive.\n | m**(-2089640/1863)\n | ibivibiv/math_instruct | |
How many minutes are there between 10:22 AM and 7:28 PM?\n | 546\n | ibivibiv/math_instruct | |
What is next in -2039, -2046, -2063, -2096, -2151?\n | -2234\n | ibivibiv/math_instruct | |
What is the fifth biggest value in -11/30, 2, 0.2, 102, 1/2?\n | -11/30\n | ibivibiv/math_instruct | |
Let h(s) be the second derivative of s**4/12 + s**3/3 + 6*s**2 - 4*s. What is the lowest common multiple of h(0) and 8?\n | 24\n | ibivibiv/math_instruct | |
What is the product of 18.2 and -0.28?\n | -5.096\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 2 and 8 - 740/(-11 + 6).\n | 156\n | ibivibiv/math_instruct | |
Rearrange -12*x + 15*x**2 + 12*x to r + t*x + q*x**2 and give q.\n | 15\n | ibivibiv/math_instruct | |
Let n(r) = r**2 - 9*r - 10. Let v be n(10). Suppose a + a = v. Solve w - 5*w + 16 = a for w.\n | 4\n | ibivibiv/math_instruct | |
Collect the terms in -32348*u + 16182*u + 16164*u.\n | -2*u\n | ibivibiv/math_instruct | |
Let h(i) be the first derivative of -i**8/1344 + i**7/840 + i**6/480 - i**5/240 - 2*i**2 + 3. Let f(x) be the second derivative of h(x). Factor f(u).\n | -u**2*(u - 1)**2*(u + 1)/4\n | ibivibiv/math_instruct | |
Which is the nearest to -1/22? (a) 1/3 (b) -1/4 (c) -173 (d) -29/5\n | b\n | ibivibiv/math_instruct | |
Simplify (1*sqrt(3159))/((sqrt(3) + sqrt(27))*4).\n | 9*sqrt(13)/16\n | ibivibiv/math_instruct | |
Let z(x) = -2*x**2 + 2 + 3*x + x**2 + 4 - 3. Let y be z(0). Solve 4*p + 0*i = 2*i + 18, 0 = y*p - i - 14 for p.\n | 5\n | ibivibiv/math_instruct | |
What is the value of (2/42)/((-912)/(-13680))?\n | 5/7\n | ibivibiv/math_instruct | |
Suppose -24 = -n - 4*o, -5*o + 0 = -25. Solve -u + 12 = 2*u - f, -u + 15 = -n*f for u.\n | 3\n | ibivibiv/math_instruct | |
What is prob of sequence ud when two letters picked without replacement from bbqbbudbb?\n | 1/72\n | ibivibiv/math_instruct | |
Suppose 4*d + 3*d = -49. Let v(z) = -z**2 - 9*z + 6. List the prime factors of v(d).\n | 2, 5\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 21 and 33?\n | 231\n | ibivibiv/math_instruct | |
What is the next term in 85, 344, 775, 1378, 2153?\n | 3100\n | ibivibiv/math_instruct | |
Factor 5*t**5/2 + 5150*t**4 + 2626375*t**3 - 26651250*t**2 + 133903125*t/2.\n | 5*t*(t - 5)**2*(t + 1035)**2/2\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 123 and 18122.\n | 41\n | ibivibiv/math_instruct | |
Calculate ((0/(-24))/12)/4.\n | 0\n | ibivibiv/math_instruct | |
Let y = 49.1 - 54. Let a = y - -0.9. Sort a, 2/13, 0.4 in ascending order.\n | a, 2/13, 0.4\n | ibivibiv/math_instruct | |
Calculate the remainder when 16/(-56) + 363/21 is divided by 3.\n | 2\n | ibivibiv/math_instruct | |
List the prime factors of 921989760.\n | 2, 3, 5, 480203\n | ibivibiv/math_instruct | |
Let h = -2 - -3. Suppose 0 = -0*x - 2*x - 6, 5*o = -5*x. What is the tens digit of (-2 - h)/(o/(-14))?\n | 1\n | ibivibiv/math_instruct | |
Evaluate 19 - (-38 + 3 - -86).\n | -32\n | ibivibiv/math_instruct | |
What is 1017 to the power of 1/3, to the nearest integer?\n | 10\n | ibivibiv/math_instruct | |
Suppose 0 - 3 = -3*t. Let p be (-12)/16*t - 26/(-24). Factor -p*k - 2/3 + 8/3*k**2 - 5/3*k**3.\n | -(k - 1)**2*(5*k + 2)/3\n | ibivibiv/math_instruct | |
Let b(o) = 2*o**2 - o. Suppose 4*v + 13 = 5*d - 2*d, 0 = 4*v - 4*d + 12. Let j(p) = 9*p**2 + 6*p + 25. Let c(f) = v*b(f) + j(f). Let c(l) = 0. What is l?\n | -5\n | ibivibiv/math_instruct | |
Find the second derivative of -4*i*w**3*x**2 - 39*i*w**3*x - i*w - 5*i*x + 2086829*w**3*x**2 + 422*w**2*x wrt x.\n | -8*i*w**3 + 4173658*w**3\n | ibivibiv/math_instruct | |
In base 3, what is -1200 + 12001?\n | 10101\n | ibivibiv/math_instruct | |
What is 17932.4 rounded to the nearest 1000?\n | 18000\n | ibivibiv/math_instruct | |
496131295 divided by 99226259\n | 5\n | ibivibiv/math_instruct | |
Rearrange (19 - 17 - 4*p**4 + 6)*(3 - 7 - 1) to y + d*p + s*p**2 + m*p**3 + h*p**4 and give h.\n | 20\n | ibivibiv/math_instruct | |
Let s be 3*(-14)/(-63)*(-6)/(-10). Let p = 37/6 + -395/66. Sort p, s, 0.3 in increasing order.\n | p, 0.3, s\n | ibivibiv/math_instruct | |
b"What is the jth term of 1002754, 1002734, 1002714, 1002694, 1002674?\n" | -20*j + 1002774\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 6 and (-1)/(3/292)*33/(-44).\n | 438\n | ibivibiv/math_instruct | |
Let g = 4.4 - -1.6. Let w = 5.9 - g. Which is the closest to w? (a) -0.4 (b) 3 (c) -1\n | a\n | ibivibiv/math_instruct | |
Suppose 6*r - 2*r - n + 12 = 0, 0 = n + 4. Let k(o) = o**2 + 3*o + 4. Let u(t) = -t - 1. What is r*u(j) - k(j)?\n | -j**2 + j\n | ibivibiv/math_instruct | |
What is 520 minutes before 2:23 AM?\n | 5:43 PM\n | ibivibiv/math_instruct | |
Solve -150*s + 2 = -153*s + 5*w, w - 22 = 3*s for s.\n | -9\n | ibivibiv/math_instruct | |
Let r be (-12)/8 - (-1)/2. Let p be -21*3*r/(-3). Is (1 - 0)/((-3)/p) prime?\n | True\n | ibivibiv/math_instruct | |
What is 135 minus 302.04738?\n | -167.04738\n | ibivibiv/math_instruct | |
Let d = -1.1 - 1.3. Let y = d - -2.5. Put -1/4, 2/5, y in decreasing order.\n | 2/5, y, -1/4\n | ibivibiv/math_instruct | |
Is 272 a multiple of 6?\n | False\n | ibivibiv/math_instruct | |
Two letters picked without replacement from iiiibiiiibbbiibi. What is prob of picking 2 i?\n | 11/24\n | ibivibiv/math_instruct | |
What is the second derivative of 2291*x**3 - 6440*x?\n | 13746*x\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). O... | zbMATH is a powerful online database specifically designed for mathematical research. It serves as the primary resource for mathematicians, researchers, and students looking for literature in pure and applied mathematics. This platform offers advanced search features that enable users to find precise and relevant info... | ibivibiv/math_instruct | |
Collect the terms in -5*n**2 + 1 + n**2 + 8*n**2 + 625*n.\n | 4*n**2 + 625*n + 1\n | ibivibiv/math_instruct | |
What comes next: 88, 310, 682, 1210, 1900, 2758, 3790?\n | 5002\n | ibivibiv/math_instruct | |
What is the product of -0.65 and -552?\n | 358.8\n | ibivibiv/math_instruct | |
Let w(l) be the first derivative of l**4/4 + 7*l**3/3 + 5*l**2/2 - 3*l - 3. What are the prime factors of w(-5)?\n | 2, 11\n | ibivibiv/math_instruct | |
b"What is the zth term of -33, -4, 45, 114, 203, 312, 441?\n" | 10*z**2 - z - 42\n | ibivibiv/math_instruct | |
Which is the closest to -13? (a) -2 (b) 1 (c) -7\n | c\n | ibivibiv/math_instruct | |
Let z be (0/41)/(2/(-2)). Solve z = 4*y + y + 5 for y.\n | -1\n | ibivibiv/math_instruct | |
b"What is the mth term of 20, 54, 110, 194, 312, 470, 674, 930?\n" | m**3 + 5*m**2 + 12*m + 2\n | ibivibiv/math_instruct | |
What is 5482551 to the power of 1/2, to the nearest integer?\n | 2341\n | ibivibiv/math_instruct | |
Let a(q) = 37205*q**2. Let r(h) = -15*h. Determine r(a(k)).\n | -558075*k**2\n | ibivibiv/math_instruct | |
Suppose -g + 12 = 48. Suppose -5*d + 403 = 4*t, 3*t - 336 = -5*d + 8*d. Let f = g + t. List the prime factors of f.\n | 71\n | ibivibiv/math_instruct | |
Three letters picked without replacement from gififvfiigva. What is prob of sequence vag?\n | 1/330\n | ibivibiv/math_instruct | |
69688 divided by -7\n | -69688/7\n | ibivibiv/math_instruct | |
How many minutes are there between 4:42 PM and 12:50 AM?\n | 488\n | ibivibiv/math_instruct | |
Solve -2*c + 48 = 44 for c.\n | 2\n | ibivibiv/math_instruct | |
Let q = -246 - -248. Suppose 15 = 2*u - q*l - 829, -u - 4*l = -437. Is 15 a factor of u?\n | False\n | ibivibiv/math_instruct | |
Let k(a) = 1718855 + 3*a + 9*a - 1718863 + 10*a - 9*a. Give k(3).\n | 31\n | ibivibiv/math_instruct | |
Calculate -11 divided by 434094.\n | -11/434094\n | ibivibiv/math_instruct | |
Let h = -56049 - -84526. Let d = -41277 + h. What is d rounded to the nearest 1000?\n | -13000\n | ibivibiv/math_instruct | |
Let n(t) = t + 8. Let x be n(-6). Let u be (-9)/(-12) - (-81)/36. Put x, u, 4 in decreasing order.\n | 4, u, x\n | ibivibiv/math_instruct | |
Simplify (sqrt(1375) + -3*sqrt(1375) + sqrt(1375))/((-2*sqrt(5) - sqrt(5))*-3) + -2.\n | -2 - 5*sqrt(11)/9\n | ibivibiv/math_instruct | |
Let d(g) = g**2 - g + 105. What is d(0)?\n | 105\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 357355?\n | 3\n | ibivibiv/math_instruct | |
Let z be (-2270)/(-40) + ((-273)/12)/13. What is the greatest common factor of 1705 and z?\n | 55\n | ibivibiv/math_instruct | |
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"Review question
If this cubic has two equal roots, what can $p$ be? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Ref: R5196
Solution
A p... | Polynomials are fundamental objects of study in algebra and calculus. A univariate polynomial is defined as a function of the form:
f(x) = a\_n x^n + a\_{n-1} x^{n-1} + ... + a_2 x^2 + a_1 x + a\_0, where n is a non-negative integer and the coefficients a\_i belong to some field, typically the real numbers or complex... | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 1113 and 2226.\n | 2226\n | ibivibiv/math_instruct | |
Let g be (-430)/50 + 8 + (-803)/(-5). Suppose 10*x = -22*x + g. Solve x*o + 45 = 25 for o.\n | -4\n | ibivibiv/math_instruct | |
Let b = 4 - -1. Let v be (2/(-5))/((-1)/b). What is the units digit of 9 - 6 - v/1?\n | 1\n | ibivibiv/math_instruct | |
Let m = 1071601/250040 + -1/250040. Let -69/7*y**2 + 9/7*y**4 - m*y**3 - 30/7*y + 0 = 0. Calculate y.\n | -1, -2/3, 0, 5\n | ibivibiv/math_instruct | |
Let w(t) = -996240*t**3 + 10081*t**2 - 40324. Let m(r) = -593*r**3 + 6*r**2 - 24. What is 10081*m(n) - 6*w(n)?\n | -593*n**3\n | ibivibiv/math_instruct | |
Suppose -2*q - 5 = 21. Do -86/7 and q have the same value?\n | False\n | ibivibiv/math_instruct | |
Solve 29*z - 9325 = -54*z - 10155 for z.\n | -10\n | ibivibiv/math_instruct | |
List the prime factors of 1151.\n | 1151\n | ibivibiv/math_instruct |
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