question stringlengths 16 1.73k | answer stringlengths 1 6.02k | source stringlengths 13 50 | Rationale stringlengths 7 2.01k ⌀ | annotated_formula stringlengths 9 409 ⌀ | linear_formula stringlengths 11 357 ⌀ |
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b'Suppose -203 = -5*l - 4*f, 185 = 4*l + l - 5*f. Suppose t + 12 = -l. Let r be (6/(-4))/(t/850). Solve c - 6*c = -3*q + r, q = 0 for c.\n' | b'-5\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let b(f) = -2*f**3 + 19*f**2 + 5*f - 22. Let g be b(9). Let s = g - 98. Solve -s = 2*r + m, 24 = -5*r - m + 3*m for r.\n' | b'-4\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let o(v) = 79*v**2 - 2*v - 3. Let p be o(-1). Let t = p + -73. Solve -2*y + 4*l + 0 = 10, t*l = -4*y + 6 for y.\n' | b'-1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let i(t) = -2*t**2 - 20*t. Let s be i(-10). Suppose -12 = -3*p - s*p. Solve 2*v = -4*c + 2*c - p, 5*v = -2*c - 7 for v.\n' | b'-1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let z(x) = x**3 + 9*x**2 + 13*x - 5. Suppose 0 = 10*f - 7*f + 21. Let u be z(f). Solve u*q - 2*r = -2*q - 4, r = -3*q - 3 for q.\n' | b'-1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let y be 66/20 - 1/10*3. Solve k + 8 = -3*v + 15, 3*v - y = 0 for k.\n' | b'4\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let h = -1936 - -1937. Solve 0 = -z + h, 0*l - 14 = 3*l - 5*z for l.\n' | b'-3\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose -55 - 66 - 89 = -70*b. Solve 0 = -5*o - 2*n - 16, 6 = -o - b*n + 4*n for o.\n' | b'-4\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose 61*q = 266 + 100. Solve 5*h + 4*b + b - 20 = 0, -h - q = -b for h.\n' | b'-1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let g = -176 + 230. Suppose g*l - 42*l = 36. Solve 2*f + 2*f = l*v - 32, -4*v = 2*f - 6 for f.\n' | b'-5\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let q(l) = 33*l. Let a(y) = -y**2 + 2*y - 2. Let p be a(1). Let d be q(p). Let n = 38 + d. Solve -5*v - 11 = -3*c - 0*v, -4*c = n*v + 32 for c.\n' | b'-3\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose 2*x - 3*s - 37 = -6, 5*x = -2*s + 30. Let m = 9 + -2. Solve -r + m = 4*y, -3*r - y + 2*y = -x for r.\n' | b'3\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let r be (5 - 44/10)/((-3)/(-25)). Solve j = r*k + 12, 3*k - 4 = -4*j + k for j.\n' | b'2\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose -2*p = 4*k - 26, 4*p - 19*k - 41 = -16*k. Solve 5*s - 4*q + 23 = 0, 4*q + 7 = 6*s - p*s for s.\n' | b'-3\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let d(j) = -j**3 + j**2 + 4*j - 3. Let l be d(2). Suppose -3*u + 9 = -o - l, 5*o + 2*u = 18. Solve 3*b = i - 5, 3 + 1 = o*i for b.\n' | b'-1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let i(s) = 80*s + 84. Let w be i(-1). Solve 4*d = -w*v, -3 = -4*d + 6*d + 5*v for d.\n' | b'1\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let p(i) = -4*i**2 + 6*i + 1. Let s be p(5). Let k = -69 - s. Solve 0*d - 5*d - 3*m + 14 = k, -d - 2*m = 0 for d.\n' | b'4\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let g = 1612 + -1607. Solve 4*k - 20 = -2*h, 7*h - 2*k - 2 = g*h for h.\n' | b'4\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose -90 = -3*b + w + 2*w, 5*w = 2*b - 66. Let a be (-1)/7*-19 - (-8)/b. Let k be (a - 3/1) + 2. Solve -8 = k*n + f - 1, -4*f = -n + 1 for n.\n' | b'-3\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Let n = -68 - -73. Suppose -d + 8 = n*h, 0*d + h = 2*d - 5. Solve -d*z + 15 = -2*z - 4*a, 0 = -5*z - a - 30 for z.\n' | b'-5\n' | math_dataset__algebra__linear_2d_composed | null | null | null |
b'Suppose 3*s**5 + 4356*s**4 + 98991*s**3 + 557310*s**2 = 0. What is s?\n' | b'-1429, -13, -10, 0\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -26500*n**2 + 1377976*n + 1248.\n' | b'-4*(n - 52)*(6625*n + 6)\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Find i, given that i**2/3 + 36566*i/3 + 97488 = 0.\n' | b'-36558, -8\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -2*u**4 - 100966*u**3 - 302872*u**2 + 403864*u + 1211520 = 0 for u.\n' | b'-50480, -3, -2, 2\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -r**4/7 + 3632*r**3/7 + 29180*r**2/7 - 218256*r/7 - 74880 = 0 for r.\n' | b'-12, -2, 6, 3640\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -n**3/2 + 28821*n**2 + 115290*n + 115292 = 0.\n' | b'-2, 57646\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'What is r in -4*r**5/5 + 477416*r**4/5 - 477404*r**3/5 - 954824*r**2/5 = 0?\n' | b'-1, 0, 2, 119353\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -f**3/3 - 91*f**2 - 18290*f/3 - 104832.\n' | b'-(f + 27)*(f + 64)*(f + 182)/3\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -j**3 - 22210*j**2 + 155509*j - 222170.\n' | b'-(j - 5)*(j - 2)*(j + 22217)\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Let -4*k**4/3 - 343828*k**3/3 + 16*k**2/3 + 1375312*k/3 = 0. What is k?\n' | b'-85957, -2, 0, 2\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine z, given that -2875*z**3/2 + 14372*z**2 + 80530*z + 168 = 0.\n' | b'-4, -6/2875, 14\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine a so that -2*a**3 - 8874*a**2 - 70878*a - 62006 = 0.\n' | b'-4429, -7, -1\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor g**2/4 + 735737*g/4.\n' | b'g*(g + 735737)/4\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -2*m**2/7 - 1338*m/7 - 123876/7.\n' | b'-2*(m + 111)*(m + 558)/7\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -2*q**2 - 2102*q + 110100 = 0 for q.\n' | b'-1101, 50\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor 2*n**3/15 + 20176*n**2/5 - 1252834*n/5 + 58286572/15.\n' | b'2*(n - 31)**2*(n + 30326)/15\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine x, given that -2*x**5 - 45370*x**4 - 257236544*x**3 + 772118016*x**2 = 0.\n' | b'-11344, 0, 3\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -m**3/4 - 24703*m**2/2 + 3462095*m/4 - 15152025 = 0.\n' | b'-49476, 35\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -j**3 + 162437*j**2 - 6595876176*j - 46179092988.\n' | b'-(j - 81222)**2*(j + 7)\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -442041*d**2/2 + 21*d.\n' | b'-3*d*(147347*d - 14)/2\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Let 5*x**2/2 + 2012890*x + 4025775/2 = 0. What is x?\n' | b'-805155, -1\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor v**3/4 + 1433*v**2 + 22876*v + 68592.\n' | b'(v + 4)*(v + 12)*(v + 5716)/4\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Factor -2*u**3 - 9598*u**2 + 231554*u + 241150.\n' | b'-2*(u - 25)*(u + 1)*(u + 4823)\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Find k, given that k**4/4 + 323*k**3/2 + 960*k**2 = 0.\n' | b'-640, -6, 0\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Find l such that 4*l**5 - 1608*l**4 + 166140*l**3 - 869416*l**2 - 7135920*l + 7840800 = 0.\n' | b'-5, 1, 10, 198\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Find v such that 2*v**2/13 + 6468*v/13 - 328400/13 = 0.\n' | b'-3284, 50\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Solve -3*q**4/4 - 80995*q**3 - 1295893*q**2/12 + 197985*q/2 - 53996/3 = 0 for q.\n' | b'-107992, -2, 1/3\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine i so that i**4/4 + 1055*i**3/2 - 46839*i**2/4 + 34814*i + 360308 = 0.\n' | b'-2132, -4, 13\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine n so that 3*n**4 - 1218*n**3 + 163467*n**2 - 7189332*n - 7354020 = 0.\n' | b'-1, 115, 146\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Determine x, given that 4*x**2 + 1530168*x + 6120608 = 0.\n' | b'-382538, -4\n' | math_dataset__algebra__polynomial_roots | null | null | null |
b'Let q = -25 + 45. Suppose -m - 8 = -5*m, 5*m - q = -5*u. Let -3 + 3 - 3*k**4 - k**2 - 4*k**3 + 6*k**2 + u*k = 0. Calculate k.\n' | b'-2, -1/3, 0, 1\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let u(v) be the first derivative of 4*v**3/3 - 362*v**2 - 728*v - 433. Factor u(o).\n' | b'4*(o - 182)*(o + 1)\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let r(x) be the third derivative of 2*x**2 + 1/360*x**6 + 9 - 1/18*x**4 + 0*x**3 + 1/45*x**5 + 0*x - 1/630*x**7. Suppose r(w) = 0. What is w?\n' | b'-2, 0, 1, 2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let x(g) = g**2 + 460*g - 425. Let r(v) = -4*v**2 - 2298*v + 2134. Let u(p) = -3*r(p) - 14*x(p). Find n, given that u(n) = 0.\n' | b'1, 226\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let s(k) = 3*k**3 + k**2 - 3. Let g(u) = -14*u**3 - 210*u**2 + 896*u + 1122. Let h(t) = -g(t) - 6*s(t). Factor h(c).\n' | b'-4*(c - 46)*(c - 6)*(c + 1)\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Suppose 3 = 2*y + 13. Let l(u) = u**2 + 5*u + 2. Let f be l(y). Factor -11*b - 9*b + 3*b**f + 19*b - b**3 - b**2.\n' | b'-b*(b - 1)**2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let h be 2/10 - (856/(-20) + 41). Factor -3*n + 66/5*n**h - 42/5 - 9/5*n**3.\n' | b'-3*(n - 7)*(n - 1)*(3*n + 2)/5\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let l(k) be the first derivative of 8/7*k - 8/21*k**3 - 42 + 1/14*k**2 - 1/28*k**4. Factor l(c).\n' | b'-(c - 1)*(c + 1)*(c + 8)/7\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let d be 30/(-18)*18/(-5). Let k(v) = 3*v**2 + 3*v - 6. Let m(o) = 20*o**2 + 17*o - 36. Let s(i) = d*m(i) - 39*k(i). Factor s(l).\n' | b'3*(l - 3)*(l - 2)\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Factor -711*t - 3/4*t**2 - 168507.\n' | b'-3*(t + 474)**2/4\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let v(a) be the third derivative of a**6/300 - 19*a**5/50 - 59*a**4/30 - 70*a**2 + 4. Let v(f) = 0. Calculate f.\n' | b'-2, 0, 59\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Suppose -4*u = -3*g + 18, -5 = 4*g + 3*u - 4. Let l(s) = -s**3 + 2*s**2 - 18*s - 99. Let q be l(-3). Factor 3/5*x**g + 6/5*x + q.\n' | b'3*x*(x + 2)/5\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Suppose 4*y - 9*y = -30. Let l = -5 + y. Factor 1 - 2 - l + 4*h**2 - 2.\n' | b'4*(h - 1)*(h + 1)\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let i = -4 - -10. Let v(z) = -2*z + 14. Let r be v(i). Factor 7 - 5*c**r + 4 - 31*c + 10*c + 25*c**3 - 2.\n' | b'(c + 1)*(5*c - 3)**2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let 28*n + 237/4*n**2 - 48 - 63/4*n**3 + n**4 = 0. Calculate n.\n' | b'-1, 3/4, 8\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let y = 328/47 + -8813/1081. Let j = y - -265/69. Determine u, given that -j + 4*u - 4/3*u**2 = 0.\n' | b'1, 2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let n(p) be the second derivative of -1/3*p**4 + 9*p + 1/10*p**5 + 1/15*p**6 + 0 + p**2 - 1/6*p**3 - 1/42*p**7. Factor n(r).\n' | b'-(r - 2)*(r - 1)**2*(r + 1)**2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let g(w) be the third derivative of w**6/40 - 52*w**5/15 - 353*w**4/24 - 71*w**3/3 + 1245*w**2. What is i in g(i) = 0?\n' | b'-1, -2/3, 71\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let z(c) be the third derivative of 0 - 5/16*c**4 + 25/6*c**3 - c**2 + c - 1/24*c**5. Factor z(l).\n' | b'-5*(l - 2)*(l + 5)/2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'What is k in -16*k**2 + 468 + 7693*k**3 - 504*k - 4*k**4 - 3785*k**3 - 3852*k**3 = 0?\n' | b'-3, 1, 3, 13\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let 0 + 4*v**3 + 2/3*v**4 - 24*v**2 + 80/3*v = 0. Calculate v.\n' | b'-10, 0, 2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let j(z) be the third derivative of -1/120*z**5 + 49*z**2 + 0 + 0*z**3 + 0*z + 1/960*z**6 - 5/192*z**4. Factor j(k).\n' | b'k*(k - 5)*(k + 1)/8\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Factor -1/4*g**4 - 153*g**2 - 1323/4 + 945/2*g + 23/2*g**3.\n' | b'-(g - 21)**2*(g - 3)*(g - 1)/4\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let r = -10861/5 - -2173. Let g be 2/(-9) - (-16)/72. Suppose g - r*h - 2/5*h**2 = 0. Calculate h.\n' | b'-2, 0\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let q be ((-34)/(-14) - (-4 - -7))*3/(-4). Let x(g) be the first derivative of 6/7*g**2 - 3/7*g**4 + q*g - 1/7*g**3 - 2. What is b in x(b) = 0?\n' | b'-1, -1/4, 1\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let l(m) be the first derivative of -12 - 7/30*m**4 - 2/75*m**5 - 8/15*m - 2/3*m**3 - 13/15*m**2. Factor l(f).\n' | b'-2*(f + 1)**3*(f + 4)/15\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let h(f) be the third derivative of 7*f**6/40 - 31*f**5/4 + 169*f**4/8 - 21*f**3/2 - f**2 - 188*f. What is g in h(g) = 0?\n' | b'1/7, 1, 21\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let m = 115 - 110. Let g(z) be the third derivative of -1/30*z**m + 1/12*z**4 + 0 + 0*z + 6*z**2 + 2/3*z**3. Find y such that g(y) = 0.\n' | b'-1, 2\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Suppose 121*c = 18*c + 16 + 1735. Let y(p) be the second derivative of 1/15*p**3 - 1/15*p**4 + 1/5*p**2 - c*p + 0. Factor y(u).\n' | b'-2*(u - 1)*(2*u + 1)/5\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'Let c = -23193/19 + 1222. Let a(w) be the second derivative of -1/114*w**4 + 10/57*w**3 - 12*w + 0 - c*w**2. Factor a(x).\n' | b'-2*(x - 5)**2/19\n' | math_dataset__algebra__polynomial_roots_composed | null | null | null |
b'What is the next term in -5806, -12131, -18432, -24697, -30914?\n' | b'-37071\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in 32632, 65494, 98356, 131218?\n' | b'164080\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What comes next: 10133352, 20266705, 30400058?\n' | b'40533411\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in -60585, -60603, -60647, -60729, -60861, -61055, -61323, -61677?\n' | b'-62129\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in 53716, 107726, 161736, 215746, 269756?\n' | b'323766\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is next in 46366092, 46366093, 46366094?\n' | b'46366095\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in 3819, 4903, 7845, 13575, 23023, 37119?\n' | b'56793\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in -22480242, -22480243, -22480244?\n' | b'-22480245\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is next in -1071, -2193, -3471, -4983, -6807, -9021, -11703, -14931?\n' | b'-18783\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in 2843, 7705, 14585, 23483, 34399, 47333?\n' | b'62285\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in -2013, -2103, -2193, -2283, -2373, -2463?\n' | b'-2553\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is next in 23, -10, 7, 74, 191?\n' | b'358\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is next in -8909, -35613, -80141, -142505, -222717, -320789, -436733?\n' | b'-570561\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What comes next: 592, 1182, 1714, 2188, 2604, 2962?\n' | b'3262\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What comes next: 40, -251, -690, -1241, -1868?\n' | b'-2535\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is next in 16792, 17541, 18292, 19045, 19800?\n' | b'20557\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What comes next: 475414, 950806, 1426202, 1901602?\n' | b'2377006\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in -2093437, -2093443, -2093453, -2093467, -2093485, -2093507?\n' | b'-2093533\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in -77626, -155246, -232866, -310486?\n' | b'-388106\n' | math_dataset__algebra__sequence_next_term | null | null | null |
b'What is the next term in 1252078, 5008323, 11268732, 20033305, 31302042?\n' | b'45074943\n' | math_dataset__algebra__sequence_next_term | null | null | null |
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