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amanrangapur commited on
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4e1e153
·
1 Parent(s): 1ad7d1f

added more instances for old_scans_math

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Files changed (11) hide show
  1. bench_data/old_scans_math.jsonl +129 -4
  2. bench_data/pdfs/old_scans_math/4_pg186.pdf +3 -0
  3. bench_data/pdfs/old_scans_math/4_pg281.pdf +3 -0
  4. bench_data/pdfs/old_scans_math/4_pg355.pdf +3 -0
  5. bench_data/pdfs/old_scans_math/4_pg380.pdf +3 -0
  6. bench_data/pdfs/old_scans_math/4_pg396.pdf +3 -0
  7. bench_data/pdfs/old_scans_math/4_pg433.pdf +3 -0
  8. bench_data/pdfs/old_scans_math/4_pg451.pdf +3 -0
  9. bench_data/pdfs/old_scans_math/4_pg48.pdf +3 -0
  10. bench_data/pdfs/old_scans_math/4_pg512.pdf +3 -0
  11. bench_data/pdfs/old_scans_math/4_pg98.pdf +3 -0
bench_data/old_scans_math.jsonl CHANGED
@@ -10,8 +10,6 @@
10
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\therefore u=a^{2} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x-\\int x . x(a^{2}-x^{2})^{\\frac{n-2}{2}} d x", "case_sensitive": true, "first_n": null, "last_n": null}
11
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "=a^{2} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x+\\frac{x(a^{2}-x^{2})^{\\frac{n}{2}}}{n}-\\frac{u}{n}", "case_sensitive": true, "first_n": null, "last_n": null}
12
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\therefore u=\\frac{x(a^{2}-x^{2})^{\\frac{n}{2}}}{n+1}+\\frac{n a^{2}}{n+1} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x", "case_sensitive": true, "first_n": null, "last_n": null}
13
- {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_00", "type": "present", "max_diffs": 0, "checked": "rejected", "url": null, "text": "log\u2061x2+1+1x2+1\u221214(x2+1)2", "case_sensitive": true, "first_n": null, "last_n": null}
14
- {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_01", "type": "present", "max_diffs": 0, "checked": "rejected", "url": null, "text": "=4x2+34(x2+1)2+log\u2061x2+1.", "case_sensitive": true, "first_n": null, "last_n": null}
15
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(22.)\\int \\frac{x^2 dx}{x^4+1}1", "case_sensitive": true, "first_n": null, "last_n": null}
16
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(x^m+1) = (x^2-2x \\cos \\frac{\\pi}{m}+1)(x^2-2x \\cos \\frac{3\\pi}{m}+1)\\dots", "case_sensitive": true, "first_n": null, "last_n": null}
17
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(x^2-2x \\cos \\frac{m-1}{m}\\pi+1)", "case_sensitive": true, "first_n": null, "last_n": null}
@@ -138,7 +136,7 @@
138
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{1}=k \\xi_{2}", "case_sensitive": true, "first_n": null, "last_n": null}
139
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{2}^{2}=1", "case_sensitive": true, "first_n": null, "last_n": null}
140
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3}^{2}=1", "case_sensitive": true, "first_n": null, "last_n": null}
141
- {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_13", "type": "present", "max_diffs": 0, "checked": null, "url": null, "text": "\\xi_{1} \\xi_{2}=\\xi_{2} \\xi_{3}=\\xi_{3} \\xi_{1}=0", "case_sensitive": true, "first_n": null, "last_n": null}
142
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3} \\xi_{1}=-\\xi_{1} \\xi_{3}=0", "case_sensitive": true, "first_n": null, "last_n": null}
143
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_15", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{2} \\xi_{3}=0", "case_sensitive": true, "first_n": null, "last_n": null}
144
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3}=\\pm \\sqrt{\\left({\\xi}_{3}^{2}\\right)} \\xi_{2}=\\pm \\frac{\\xi_{2}}{\\tau}", "case_sensitive": true, "first_n": null, "last_n": null}
@@ -260,7 +258,7 @@
260
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dy}{dx} = sec 2 x \\frac{d}{dx} tan 2 x + tan 2 x \\frac{d}{dx} sec 2 x", "case_sensitive": true, "first_n": null, "last_n": null}
261
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "= sec 2 x sec^2 2 x (2) + tan-2 x sec 2 x tan 2 x (2)", "case_sensitive": true, "first_n": null, "last_n": null}
262
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "= 2 sec 2 x (sec^2 2 x + tan^2 2 x)", "case_sensitive": true, "first_n": null, "last_n": null}
263
- {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": " \\quad \\frac{dy}{dx} = 6 (cos 3 x - sin 2 x).", "case_sensitive": true, "first_n": null, "last_n": null}
264
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dx}{dt} = C_1", "case_sensitive": true, "first_n": null, "last_n": null}
265
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dy}{dt} = -gt + C_2", "case_sensitive": true, "first_n": null, "last_n": null}
266
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dx}{dt}", "case_sensitive": true, "first_n": null, "last_n": null}
@@ -313,3 +311,130 @@
313
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^{\\frac{1}{2}} + y^{\\frac{1}{2}} = a^{\\frac{1}{2}}", "case_sensitive": true, "first_n": null, "last_n": null}
314
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_17", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x + y = a", "case_sensitive": true, "first_n": null, "last_n": null}
315
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_18", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "PQR \\cdot \\Delta x = X \\Delta x", "case_sensitive": true, "first_n": null, "last_n": null}
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\therefore u=a^{2} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x-\\int x . x(a^{2}-x^{2})^{\\frac{n-2}{2}} d x", "case_sensitive": true, "first_n": null, "last_n": null}
11
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "=a^{2} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x+\\frac{x(a^{2}-x^{2})^{\\frac{n}{2}}}{n}-\\frac{u}{n}", "case_sensitive": true, "first_n": null, "last_n": null}
12
  {"pdf": "1_pg72.pdf", "page": 1, "id": "1_pg72_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\therefore u=\\frac{x(a^{2}-x^{2})^{\\frac{n}{2}}}{n+1}+\\frac{n a^{2}}{n+1} \\int(a^{2}-x^{2})^{\\frac{n-2}{2}} d x", "case_sensitive": true, "first_n": null, "last_n": null}
 
 
13
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(22.)\\int \\frac{x^2 dx}{x^4+1}1", "case_sensitive": true, "first_n": null, "last_n": null}
14
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(x^m+1) = (x^2-2x \\cos \\frac{\\pi}{m}+1)(x^2-2x \\cos \\frac{3\\pi}{m}+1)\\dots", "case_sensitive": true, "first_n": null, "last_n": null}
15
  {"pdf": "1_pg40.pdf", "page": 1, "id": "1_pg40_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(x^2-2x \\cos \\frac{m-1}{m}\\pi+1)", "case_sensitive": true, "first_n": null, "last_n": null}
 
136
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{1}=k \\xi_{2}", "case_sensitive": true, "first_n": null, "last_n": null}
137
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{2}^{2}=1", "case_sensitive": true, "first_n": null, "last_n": null}
138
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3}^{2}=1", "case_sensitive": true, "first_n": null, "last_n": null}
139
+ {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{1} \\xi_{2}=\\xi_{2} \\xi_{3}=\\xi_{3} \\xi_{1}=0", "case_sensitive": true, "first_n": null, "last_n": null}
140
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3} \\xi_{1}=-\\xi_{1} \\xi_{3}=0", "case_sensitive": true, "first_n": null, "last_n": null}
141
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_15", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{2} \\xi_{3}=0", "case_sensitive": true, "first_n": null, "last_n": null}
142
  {"pdf": "3_pg634.pdf", "page": 1, "id": "3_pg634_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\xi_{3}=\\pm \\sqrt{\\left({\\xi}_{3}^{2}\\right)} \\xi_{2}=\\pm \\frac{\\xi_{2}}{\\tau}", "case_sensitive": true, "first_n": null, "last_n": null}
 
258
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dy}{dx} = sec 2 x \\frac{d}{dx} tan 2 x + tan 2 x \\frac{d}{dx} sec 2 x", "case_sensitive": true, "first_n": null, "last_n": null}
259
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "= sec 2 x sec^2 2 x (2) + tan-2 x sec 2 x tan 2 x (2)", "case_sensitive": true, "first_n": null, "last_n": null}
260
  {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "= 2 sec 2 x (sec^2 2 x + tan^2 2 x)", "case_sensitive": true, "first_n": null, "last_n": null}
261
+ {"pdf": "2_pg65.pdf", "page": 1, "id": "2_pg65_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": " \\quad \\frac{dy}{dx} = 6 (cos 3 x - sin 2 x)", "case_sensitive": true, "first_n": null, "last_n": null}
262
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dx}{dt} = C_1", "case_sensitive": true, "first_n": null, "last_n": null}
263
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dy}{dt} = -gt + C_2", "case_sensitive": true, "first_n": null, "last_n": null}
264
  {"pdf": "2_pg189.pdf", "page": 1, "id": "2_pg189_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{dx}{dt}", "case_sensitive": true, "first_n": null, "last_n": null}
 
311
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^{\\frac{1}{2}} + y^{\\frac{1}{2}} = a^{\\frac{1}{2}}", "case_sensitive": true, "first_n": null, "last_n": null}
312
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_17", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x + y = a", "case_sensitive": true, "first_n": null, "last_n": null}
313
  {"pdf": "2_pg238.pdf", "page": 1, "id": "2_pg238_equation_18", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "PQR \\cdot \\Delta x = X \\Delta x", "case_sensitive": true, "first_n": null, "last_n": null}
314
+ {"pdf": "4_pg433.pdf", "page": 1, "id": "4_pg433_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\begin{vmatrix} \na_1 \\pm mb_1 & b_1 & c_1 \\\\ \na_2 \\pm mb_2 & b_2 & c_2 \\\\ \na_3 \\pm mb_3 & b_3 & c_3 \n\\end{vmatrix} = \n\\begin{vmatrix} \na_1 & b_1 & c_1 \\\\ \na_2 & b_2 & c_2 \\\\ \na_3 & b_3 & c_3 \n\\end{vmatrix} \\pm \n\\begin{vmatrix} \nmb_1 & b_1 & c_1 \\\\ \nmb_2 & b_2 & c_2 \\\\ \nmb_3 & b_3 & c_3 \n\\end{vmatrix}\n", "case_sensitive": true, "first_n": null, "last_n": null}
315
+ {"pdf": "4_pg433.pdf", "page": 1, "id": "4_pg433_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "m\\begin{vmatrix} b_1 & b_1 & c_1 \\\\ b_2 & b_2 & c_2 \\\\ b_3 & b_3 & c_3 \\end{vmatrix}", "case_sensitive": true, "first_n": null, "last_n": null}
316
+ {"pdf": "4_pg433.pdf", "page": 1, "id": "4_pg433_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\begin{vmatrix} 4244 & 4245 \\\\ 4246 & 4247 \\end{vmatrix}", "case_sensitive": true, "first_n": null, "last_n": null}
317
+ {"pdf": "4_pg433.pdf", "page": 1, "id": "4_pg433_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\begin{vmatrix} 4244 & 4245 \\\\ 2 & 2 \\end{vmatrix} = \\begin{vmatrix} 4244 & 1 \\\\ 2 & 0 \\end{vmatrix} = -2", "case_sensitive": true, "first_n": null, "last_n": null}
318
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "50 (11-x) + 10 x = 310", "case_sensitive": true, "first_n": null, "last_n": null}
319
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "550-50 x + 10 x = 310", "case_sensitive": true, "first_n": null, "last_n": null}
320
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "- 50 x + 10 x = - 550 + 310", "case_sensitive": true, "first_n": null, "last_n": null}
321
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "- 40 x = - 240", "case_sensitive": true, "first_n": null, "last_n": null}
322
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x = 6", "case_sensitive": true, "first_n": null, "last_n": null}
323
+ {"pdf": "4_pg98.pdf", "page": 1, "id": "4_pg98_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "11-x=5", "case_sensitive": true, "first_n": null, "last_n": null}
324
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^3-3x^2 - 18 x + 40 = 0", "case_sensitive": true, "first_n": null, "last_n": null}
325
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(x-a) Q(x) + R=f(x)", "case_sensitive": true, "first_n": null, "last_n": null}
326
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "R=f(a)", "case_sensitive": true, "first_n": null, "last_n": null}
327
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(x) = x^4 - 2 x^3 - 9 x^2 + 2", "case_sensitive": true, "first_n": null, "last_n": null}
328
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(4) = - 14", "case_sensitive": true, "first_n": null, "last_n": null}
329
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^4 - 2 x^3 - 9 x^2 + 0x + 2", "case_sensitive": true, "first_n": null, "last_n": null}
330
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_06", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^4 =4x^3", "case_sensitive": true, "first_n": null, "last_n": null}
331
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_07", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "2 x^3 =8x^2", "case_sensitive": true, "first_n": null, "last_n": null}
332
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_08", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "-x^2=-4x", "case_sensitive": true, "first_n": null, "last_n": null}
333
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "-4x=-16", "case_sensitive": true, "first_n": null, "last_n": null}
334
+ {"pdf": "4_pg451.pdf", "page": 1, "id": "4_pg451_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(4) = - 14", "case_sensitive": true, "first_n": null, "last_n": null}
335
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a+[b-(a - b)]", "case_sensitive": true, "first_n": null, "last_n": null}
336
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a+b -[(b+d) - (a - b)]", "case_sensitive": true, "first_n": null, "last_n": null}
337
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "m-(n-p) +[3m-\\overline{3n-6 m}]", "case_sensitive": true, "first_n": null, "last_n": null}
338
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a-[a-\\{a-(-a)\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
339
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x-[3y+\\{3 z - (z - x) + y\\} - 2x]", "case_sensitive": true, "first_n": null, "last_n": null}
340
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "-[m-(m+n) - (m-n) - (- m + n)]", "case_sensitive": true, "first_n": null, "last_n": null}
341
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_06", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "12a -\\{(a+b) - [b - (a - b)] - a\\}", "case_sensitive": true, "first_n": null, "last_n": null}
342
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_07", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "2 x -\\{x - (x - y) - [x -\\overline{x - y}] - y\\}", "case_sensitive": true, "first_n": null, "last_n": null}
343
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_08", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "12-2a-\\{- a - [2a - (a-\\overline{7-a})]\\}", "case_sensitive": true, "first_n": null, "last_n": null}
344
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "14-3 a -\\{9 a - [10 a - (11 a -\\overline{6 - 6 a})]\\}", "case_sensitive": true, "first_n": null, "last_n": null}
345
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a-[-\\{-(-a)\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
346
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a-3-[-\\{-(-a + \\overline{a + b})\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
347
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x + y -[-(x - y) + \\{ - x + (x -\\overline{x - y}) \\} ]", "case_sensitive": true, "first_n": null, "last_n": null}
348
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "1 - \\{ - a -(a+1)-[-a-(a -\\overline{a - 1})]\\}", "case_sensitive": true, "first_n": null, "last_n": null}
349
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a-(-{\\{-[-(-a)]\\}})", "case_sensitive": true, "first_n": null, "last_n": null}
350
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_15", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "1-(-{\\{a+(-a +1)\\} }) - \\{a-\\overline{a-1}\\}", "case_sensitive": true, "first_n": null, "last_n": null}
351
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "6m+\\{4m-[8n- (2m +4 n) - 22 n]-7 n\\}+[9m-(3n+ 4 m) +14 n]", "case_sensitive": true, "first_n": null, "last_n": null}
352
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_17", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "1247 - [1722-\\{1722+(933 - 1247)\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
353
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_18", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a +\\{(4 - b) + (a - 4) -\\overline{a-7}\\}", "case_sensitive": true, "first_n": null, "last_n": null}
354
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_19", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a -\\{(6-b)+(6\u0430 - 6) - (5\u0430 - 7)\\}", "case_sensitive": true, "first_n": null, "last_n": null}
355
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_20", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a + \\{a-(b - c)\\}", "case_sensitive": true, "first_n": null, "last_n": null}
356
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_21", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "- a+[4a-(5 b + c)]", "case_sensitive": true, "first_n": null, "last_n": null}
357
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_22", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "4a-[6b+(3\u0430-\u0441) - \\{5b-\\overline{c- a}\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
358
+ {"pdf": "4_pg48.pdf", "page": 1, "id": "4_pg48_equation_23", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "9a-[-7a+\\{56 - (a - b) + \\overline{a -b}\\}]", "case_sensitive": true, "first_n": null, "last_n": null}
359
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "OA=a", "case_sensitive": true, "first_n": null, "last_n": null}
360
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a + bi", "case_sensitive": true, "first_n": null, "last_n": null}
361
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "-4-2 i", "case_sensitive": true, "first_n": null, "last_n": null}
362
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a + bi = OB", "case_sensitive": true, "first_n": null, "last_n": null}
363
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "4 - 2 i = \\sqrt{4^2 + 2^2} = 2\\sqrt{5}", "case_sensitive": true, "first_n": null, "last_n": null}
364
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "OA = OB = OC = OD = 1", "case_sensitive": true, "first_n": null, "last_n": null}
365
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_06", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\angle AOB = \\angle BOC = \\angle COD = 60\u00b0", "case_sensitive": true, "first_n": null, "last_n": null}
366
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_07", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "OB = x", "case_sensitive": true, "first_n": null, "last_n": null}
367
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_08", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^3 = - 1", "case_sensitive": true, "first_n": null, "last_n": null}
368
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x=\\sqrt[3]{-1}", "case_sensitive": true, "first_n": null, "last_n": null}
369
+ {"pdf": "4_pg396.pdf", "page": 1, "id": "4_pg396_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\sqrt[3]{- 1} = \\frac{1}{2} + \\frac{1}{2}\\sqrt{3} \\cdot i", "case_sensitive": true, "first_n": null, "last_n": null}
370
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a:b=c:d", "case_sensitive": true, "first_n": null, "last_n": null}
371
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{a}{b} = \\frac{c}{d}", "case_sensitive": true, "first_n": null, "last_n": null}
372
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "ad = bc", "case_sensitive": true, "first_n": null, "last_n": null}
373
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a : b = b : c", "case_sensitive": true, "first_n": null, "last_n": null}
374
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "b^{2}=ac", "case_sensitive": true, "first_n": null, "last_n": null}
375
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "b=\\sqrt{ac}", "case_sensitive": true, "first_n": null, "last_n": null}
376
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_06", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "mn=pq", "case_sensitive": true, "first_n": null, "last_n": null}
377
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_07", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{m}{q} = \\frac{p}{n}", "case_sensitive": true, "first_n": null, "last_n": null}
378
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_08", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x=12: 7", "case_sensitive": true, "first_n": null, "last_n": null}
379
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "12 x = 42", "case_sensitive": true, "first_n": null, "last_n": null}
380
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x = \\frac{4}{1}\\frac{2}{2} = 3\\frac{1}{2}", "case_sensitive": true, "first_n": null, "last_n": null}
381
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "8:5=7:4\\frac{3}{8}", "case_sensitive": true, "first_n": null, "last_n": null}
382
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "8 \\times 4\\frac{3}{8} = 35", "case_sensitive": true, "first_n": null, "last_n": null}
383
+ {"pdf": "4_pg186.pdf", "page": 1, "id": "4_pg186_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "5 \\times 7 = 35", "case_sensitive": true, "first_n": null, "last_n": null}
384
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "5+\\sqrt{x}=2", "case_sensitive": true, "first_n": null, "last_n": null}
385
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "(-3)^{2}=(+3)^{2}", "case_sensitive": true, "first_n": null, "last_n": null}
386
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x = a", "case_sensitive": true, "first_n": null, "last_n": null}
387
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^{2} = a^{2}", "case_sensitive": true, "first_n": null, "last_n": null}
388
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x+4=\\sqrt{x}", "case_sensitive": true, "first_n": null, "last_n": null}
389
+ {"pdf": "4_pg281.pdf", "page": 1, "id": "4_pg281_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x=\\sqrt{x}-4", "case_sensitive": true, "first_n": null, "last_n": null}
390
+ {"pdf": "4_pg355.pdf", "page": 1, "id": "4_pg355_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "a \\text{ and } 5 a", "case_sensitive": true, "first_n": null, "last_n": null}
391
+ {"pdf": "4_pg355.pdf", "page": 1, "id": "4_pg355_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{1}{a} \\text{ and } \\frac{1}{b}", "case_sensitive": true, "first_n": null, "last_n": null}
392
+ {"pdf": "4_pg355.pdf", "page": 1, "id": "4_pg355_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{x^2-y^2}{x} \\text{ and } \\frac{x^2 + y^2}{x}", "case_sensitive": true, "first_n": null, "last_n": null}
393
+ {"pdf": "4_pg355.pdf", "page": 1, "id": "4_pg355_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{a-b}{2} \\text{ and } \\frac{3a+b}{2}", "case_sensitive": true, "first_n": null, "last_n": null}
394
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_00", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "3x^{2}+2x+1", "case_sensitive": true, "first_n": null, "last_n": null}
395
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_01", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\sqrt{x}", "case_sensitive": true, "first_n": null, "last_n": null}
396
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_02", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "4^{x}+2x^{3}", "case_sensitive": true, "first_n": null, "last_n": null}
397
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_03", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(x) = 2x^{2} + 2x + 3", "case_sensitive": true, "first_n": null, "last_n": null}
398
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_04", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(3)=2\\cdot3^{2}+2\\cdot3+3=27", "case_sensitive": true, "first_n": null, "last_n": null}
399
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_05", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(a) = 2a^{2}+2a+3", "case_sensitive": true, "first_n": null, "last_n": null}
400
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_06", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(0) = 0 + 0 + 3 = 3", "case_sensitive": true, "first_n": null, "last_n": null}
401
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_07", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "y=f(x)", "case_sensitive": true, "first_n": null, "last_n": null}
402
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_08", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "x^{2} + 3 xy + y^{2}", "case_sensitive": true, "first_n": null, "last_n": null}
403
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_09", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\sqrt{x}+\\sqrt{y}", "case_sensitive": true, "first_n": null, "last_n": null}
404
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_10", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "\\frac{x}{y}", "case_sensitive": true, "first_n": null, "last_n": null}
405
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_11", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(x, y) = xy + x", "case_sensitive": true, "first_n": null, "last_n": null}
406
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_12", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(2, 3) = 2^{3} + 2 = 10", "case_sensitive": true, "first_n": null, "last_n": null}
407
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_13", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(x) = x^{2} +3x+2", "case_sensitive": true, "first_n": null, "last_n": null}
408
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_14", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(1)", "case_sensitive": true, "first_n": null, "last_n": null}
409
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_15", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(0)", "case_sensitive": true, "first_n": null, "last_n": null}
410
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_16", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(-1)", "case_sensitive": true, "first_n": null, "last_n": null}
411
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_17", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(x) = 5 x^{3}-2x-3", "case_sensitive": true, "first_n": null, "last_n": null}
412
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_18", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(2)", "case_sensitive": true, "first_n": null, "last_n": null}
413
+ {"pdf": "4_pg380.pdf", "page": 1, "id": "4_pg380_equation_19", "type": "present", "max_diffs": 0, "checked": "verified", "url": null, "text": "f(a)", "case_sensitive": true, "first_n": null, "last_n": null}
414
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415
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