Tutor Partner: October 2007

October 15, 2007

Arithmetic: Multiplication of Decimal Numbers

Problem	Multiplicand	Multiplier	Product
1	61.2498	0.0332	2.03349336
2	1.167	2.3948	2.7947316
3	33.0316	226.5675	7483.887033
4	921.9036	0.0758	69.88029288
5	72.6051	9.5657	694.51860507
6	0.8615	49.3484	42.5136466
7	99.978	679.2372	67908.7767816
8	0.2832	7.8516	2.22357312
9	0.087	34.7893	3.0266691
10	0.721	803.2288	579.1279648
11	792.9531	0.0885	70.17634935
12	75.765	21.3374	1616.628111
13	0.098	142.4263	13.9577774
14	0.8008	0.627	0.5021016
15	0.0018	9.6251	0.01732518
16	0.4721	89.0873	42.05811433
17	66.5786	0.2592	17.25717312
18	0.2782	0.0865	0.0240643
19	95.1599	6.438	612.6394362
20	52.4329	4.2871	224.78508559
21	4.905	0.1814	0.889767
22	0.7764	0.4832	0.37515648
23	90.1419	8.451	761.7891969
24	817.1911	58.6662	47941.49651082
25	0.2148	0.0235	0.0050478
26	0.7086	0.6444	0.45662184
27	129.3588	4.8263	624.32437644
28	85.8494	618.4347	53092.24793418
29	113.8792	8.8228	1004.73340576
30	0.0126	19.4473	0.24503598
31	1.5701	347.4133	545.47362233
32	4.7858	0.0269	0.12873802
33	755.7335	0.0465	35.14160775
34	1.105	4.4373	4.9032165
35	0.0229	372.469	8.5295401
36	42.2988	0.0856	3.62077728
37	0.6851	0.8192	0.56123392
38	860.0558	3.8699	3328.32994042
39	16.324	0.0672	1.0969728
40	0.11	0.0839	0.009229
41	0.0884	5.3749	0.47514116
42	466.4827	20.581	9600.6804487
43	0.0009	994.9815	0.89548335
44	0.1641	0.6713	0.11016033
45	3.3912	967.0225	3279.366702
46	7.7892	72.7784	566.88551328
47	0.606	0.2369	0.1435614
48	881.7866	8.4153	7420.49877498
49	7.3634	896.6017	6602.03695778
50	40.4917	895.8552	36274.70000184

Arithmetic: Division of Decimal Numbers

Problem	Dividend	Divisor	Quotient
1	0.0002	0.2	0.001
2	0.878649	0.327	2.687
3	0.01386	0.077	0.18
4	87915.7398	153.444	572.95
5	0.235266	0.694	0.339
6	58.696919	98.983	0.593
7	818906.792515	883.045	927.367
8	1.473054	4.058	0.363
9	62.284677	0.677	92.001
10	37093.809858	43.811	846.678
11	0.020194	0.878	0.023
12	638.956773	780.167	0.819
13	0.096024	0.012	8.002
14	0.019158	0.093	0.206
15	4.210354	4.418	0.953
16	0.496945	0.095	5.231
17	416.076934	842.261	0.494
18	432.755196	319.141	1.356
19	178877.223162	445.059	401.918
20	3.607818	6.199	0.582
21	403.331658	493.674	0.817
22	196.323231	4.511	43.521
23	3.310818	13.911	0.238
24	0.406912	0.544	0.748
25	0.001406	0.037	0.038
26	25859.600228	32.948	784.861
27	5.38539	0.089	60.51
28	1.413468	0.063	22.436
29	0.001014	0.013	0.078
30	3485.31942	600.71	5.802
31	1.581984	0.216	7.324
32	442.141875	1.125	393.015
33	5319.078301	8.399	633.299
34	5.45019	363.346	0.015
35	0.67405	0.793	0.85
36	24562.96272	37.332	657.96
37	0.701018	0.001	701.018
38	9.648128	10.768	0.896
39	0.909106	0.961	0.946
40	0.00955	0.01	0.955
41	12076.328142	41.714	289.503
42	496.151544	0.692	716.982
43	0.160259	0.017	9.427
44	541731.978424	570.892	948.922
45	7.184295	88.695	0.081
46	3.985767	49.207	0.081
47	20.445	32.712	0.625
48	428.244416	863.396	0.496
49	0.09012	0.001	90.12
50	176.173816	9.359	18.824

Arithmetic: Addition of Decimal Numbers

Problem	First Number	Second Number	Total
1	0.2062	971.9982	972.2044
2	0.0096	0.0199	0.0295
3	0.6832	0.0366	0.7198
4	0.5926	0.8564	1.449
5	0.0009	62.1903	62.1912
6	183.4243	591.3829	774.8072
7	0.4896	5.9477	6.4373
8	763.1996	0.0541	763.2537
9	564.7419	0.8738	565.6157
10	719.3425	9.9659	729.3084
11	7.0388	5.5543	12.5931
12	0.3011	5.8915	6.1926
13	0.3588	30.3923	30.7511
14	639.4555	0.0033	639.4588
15	2.2994	9.3268	11.6262
16	260.2303	9.5765	269.8068
17	0.0665	0.1745	0.241
18	0.0944	80.9463	81.0407
19	0.0709	0.0168	0.0877
20	0.3768	8.9772	9.354
21	0.0691	0.5045	0.5736
22	661.5715	0.283	661.8545
23	0.0373	2.785	2.8223
24	8.9024	8.3869	17.2893
25	4.7742	30.7488	35.523
26	627.4408	0.0142	627.455
27	0.1048	0.0531	0.1579
28	0.0812	0.2002	0.2814
29	0.0651	18.5913	18.6564
30	52.9475	0.4585	53.406
31	86.8086	0.0178	86.8264
32	98.9	672.5158	771.4158
33	0.5134	523.1954	523.7088
34	287.0697	0.57	287.6397
35	75.3015	31.3465	106.648
36	4.9884	922.2368	927.2252
37	173.3745	932.6914	1106.0659
38	4.3689	49.4474	53.8163
39	0.7279	0.0099	0.7378
40	35.9213	0.6453	36.5666
41	0.9094	0.2244	1.1338
42	0.697	0.6072	1.3042
43	0.3012	1.9867	2.2879
44	0.0248	0.0229	0.0477
45	0.0971	5.7792	5.8763
46	0.0775	0.416	0.4935
47	0.1644	0.0102	0.1746
48	0.0384	6.4944	6.5328
49	0.5738	105.1179	105.6917
50	961.3984	0.0058	961.4042

Arithmetic: Subtraction of Decimal Numbers

Problem	Minuend	Subtrahend	Difference
1	8.4689	5.0048	3.4641
2	89.3151	57.1919	32.1232
3	73.3005	0.0929	73.2076
4	704.2784	0.0442	704.2342
5	0.8495	0.0299	0.8196
6	736.492	17.6512	718.8408
7	4.9833	0.0625	4.9208
8	3.0938	0.5741	2.5197
9	42.698	0.0586	42.6394
10	439.8766	23.9916	415.885
11	32.1274	0.0177	32.1097
12	0.9906	0.1685	0.8221
13	73.8926	0.0199	73.8727
14	188.8515	0.0009	188.8506
15	699.3155	24.2184	675.0971
16	412.283	15.3365	396.9465
17	289.8301	63.2924	226.5377
18	0.5646	0.0831	0.4815
19	4.6822	0.6168	4.0654
20	47.2381	22.5258	24.7123
21	708.9366	677.3255	31.6111
22	423.8846	0.0182	423.8664
23	260.7031	5.7613	254.9418
24	0.0289	0.001	0.0279
25	0.409	0.0283	0.3807
26	8.593	4.2104	4.3826
27	754.0625	53.6559	700.4066
28	856.3614	0.0691	856.2923
29	4.8381	0.0139	4.8242
30	49.7488	0.0453	49.7035
31	725.8358	0.6919	725.1439
32	357.9651	7.8646	350.1005
33	19.6024	0.0661	19.5363
34	65.5374	0.0636	65.4738
35	335.3471	0.0635	335.2836
36	1.215	0.0509	1.1641
37	0.1914	0.1523	0.0391
38	79.1584	0.3587	78.7997
39	2.2397	0.0009	2.2388
40	8.9153	0.0723	8.843
41	23.2325	0.3777	22.8548
42	0.0826	0.003	0.0796
43	0.9044	0.001	0.9034
44	830.6473	79.9167	750.7306
45	44.2427	0.0291	44.2136
46	473.8336	0.0731	473.7605
47	45.2832	0.0894	45.1938
48	4.8813	1.7042	3.1771
49	53.6837	0.0462	53.6375
50	0.6878	0.0669	0.6209

Algebra: Least Common Multiple (LCM)

Solution Set	Given Numbers	LCM
1	23,5,13	1495
2	15,14,13	2730
3	18,22,23	4554
4	17,28,14	476
5	23,14,12	1932
6	8,24,7	168
7	20,24,6	120
8	3,15,19	285
9	10,12,14	420
10	13,19,23	5681
11	9,24,3	72
12	2,10,21	210
13	24,14,12	168
14	21,23,16	7728
15	10,17,16	1360
16	13,24,16	624
17	10,9,22	990
18	5,11,7	385
19	4,13,21	1092
20	4,20,17	340
21	15,8,6	120
22	8,5,15	120
23	19,6,22	1254
24	22,10,8	440
25	6,12,7	84
26	13,21,5	1365
27	3,16,24	48
28	18,17,8	1224
29	2,5,4	20
30	3,2,11	66
31	5,18,8	360
32	13,6,19	1482
33	3,2,10	30
34	23,15,7	2415
35	19,6,12	228
36	19,13,15	3705
37	20,7,13	1820
38	11,10,6	330
39	19,12,24	456
40	24,21,4	168
41	15,12,9	180
42	4,22,20	220
43	4,9,3	36
44	21,18,10	630
45	10,17,11	1870
46	17,20,12	1020
47	2,8,15	120
48	15,20,18	180
49	14,30,7	210
50	21,10,20	420

Algebra: Greatest Common Divisor (GCD)

Solution Set	Given Numbers	GCD
1	44,11,66	11
2	570,133,323	19
3	63,56,14	7
4	48,12,72	12
5	55,33,66	11
6	63,18,45	9
7	84,60,12	12
8	45,20,35	5
9	21,12,18	3
10	11,33,55	11
11	12,84,48	12
12	36,16,28	4
13	63,36,45	9
14	54,30,18	6
15	40,48,72	8
16	60,30,70	10
17	56,70,42	14
18	50,30,60	10
19	207,253,368	23
20	18,12,10	2
21	35,70,14	7
22	45,36,72	9
23	55,11,33	11
24	44,55,77	11
25	48,12,60	12
26	84,98,56	14
27	28,7,35	7
28	340,187,527	17
29	56,14,84	14
30	60,40,10	10
31	60,10,50	10
32	65,39,299	13
33	45,20,10	5
34	70,98,84	14
35	77,66,33	11
36	30,18,6	6
37	66,44,33	11
38	527,85,221	17
39	63,28,56	7
40	81,90,63	9
41	39,169,403	13
42	35,10,25	5
43	63,54,36	9
44	63,28,49	7
45	456,133,361	19
46	81,27,45	9
47	42,7,28	7
48	551,145,667	29
49	138,713,299	23
50	51,34,391	17

Analytic Geometry: Equation of a Line

Given two points, the equation of a line whose points are equidistant from the two given points is determined.

Problem	Given Points	Equation of the Line
1	P1(3,3) P2(9,-1)	3x-2y-16=0
2	P1(7,6) P2(-4,7)	11x-1y-10=0
3	P1(-7,8) P2(-1,-3)	12x-22y+103=0
4	P1(8,-7) P2(-9,-6)	17x-1y+2=0
5	P1(-9,4) P2(-2,-4)	14x-16y+77=0
6	P1(9,7) P2(1,-3)	4x+5y-30=0
7	P1(3,-5) P2(-8,-2)	11x-3y+17=0
8	P1(-7,2) P2(-3,-4)	2x-3y+7=0
9	P1(6,9) P2(-1,1)	14x+16y-115=0
10	P1(4,8) P2(-5,7)	9x+1y-3=0
11	P1(4,-6) P2(-9,-9)	13x+3y+55=0
12	P1(1,9) P2(-5,-5)	3x+7y-8=0
13	P1(6,2) P2(7,-5)	1x-7y-17=0
14	P1(-7,8) P2(-6,-2)	2x-20y+73=0
15	P1(7,-3) P2(-8,-9)	10x+4y+29=0
16	P1(3,9) P2(-7,8)	20x+2y+23=0
17	P1(5,8) P2(-1,3)	12x+10y-79=0
18	P1(-2,6) P2(-3,-5)	1x+11y-3=0
19	P1(8,7) P2(-3,-2)	11x+9y-50=0
20	P1(-8,8) P2(-5,-5)	3x-13y+39=0
21	P1(-4,4) P2(5,-1)	9x-5y+3=0
22	P1(-3,7) P2(7,-1)	5x-4y+2=0
23	P1(5,8) P2(-9,-8)	7x+8y+14=0
24	P1(3,7) P2(-9,-8)	8x+10y+29=0
25	P1(9,7) P2(-9,-1)	9x+4y-12=0
26	P1(3,7) P2(8,-1)	10x-16y-7=0
27	P1(1,2) P2(-1,1)	4x+2y-3=0
28	P1(4,6) P2(-2,-1)	12x+14y-47=0
29	P1(4,-9) P2(-5,-9)	2x-0y+1=0
30	P1(-2,1) P2(-5,-8)	1x+3y+14=0
31	P1(9,9) P2(6,-8)	3x+17y-31=0
32	P1(2,9) P2(9,-2)	7x-11y+0=0
33	P1(9,5) P2(-5,-4)	28x+18y-65=0
34	P1(8,6) P2(-4,8)	6x-1y-5=0
35	P1(-7,4) P2(6,-6)	26x-20y-7=0
36	P1(8,9) P2(-9,-2)	17x+11y-30=0
37	P1(4,8) P2(-7,9)	11x-1y+25=0
38	P1(-5,8) P2(1,-7)	4x-10y+13=0
39	P1(-4,8) P2(8,-1)	8x-6y+5=0
40	P1(-6,3) P2(-7,-6)	1x+9y+20=0
41	P1(6,6) P2(9,-6)	2x-8y-15=0
42	P1(1,1) P2(6,-2)	5x-3y-19=0
43	P1(6,-2) P2(-2,-6)	2x+1y-0=0
44	P1(-4,1) P2(7,-8)	11x-9y-48=0
45	P1(-6,9) P2(1,-3)	14x-24y+107=0
46	P1(4,1) P2(-6,-5)	5x+3y+11=0
47	P1(3,-1) P2(-8,-5)	22x+8y+79=0
48	P1(-4,7) P2(1,-4)	5x-11y+24=0
49	P1(9,-8) P2(-9,-8)	1x-0y-0=0
50	P1(3,3) P2(-2,3)	2x-0y-1=0

Analytic Geometry: Distance Between Two Points

Given two points, their distance and the slope of the line joining them are solved.

Problem	Given Points	Distance	Slope
1	P1(2,4) P2(-9,1)	sqrt of 130	-3/-11
2	P1(-5,3) P2(7,-6)	sqrt of 225	-3/4
3	P1(4,-7) P2(-5,-2)	sqrt of 106	5/-9
4	P1(2,3) P2(-1,-5)	sqrt of 73	-8/-3
5	P1(3,5) P2(9,4)	sqrt of 37	-1/6
6	P1(4,7) P2(6,2)	sqrt of 29	-5/2
7	P1(3,2) P2(1,9)	sqrt of 53	7/-2
8	P1(1,3) P2(4,6)	sqrt of 18	1/1
9	P1(4,-2) P2(-7,-5)	sqrt of 130	-3/-11
10	P1(6,1) P2(3,8)	sqrt of 58	7/-3
11	P1(7,4) P2(3,3)	sqrt of 17	-1/-4
12	P1(3,1) P2(8,8)	sqrt of 74	7/5
13	P1(2,-8) P2(-4,-2)	sqrt of 72	1/-1
14	P1(6,7) P2(3,6)	sqrt of 10	-1/-3
15	P1(-7,4) P2(6,-6)	sqrt of 269	-10/13
16	P1(6,4) P2(7,1)	sqrt of 10	-3/1
17	P1(-6,3) P2(-2,-1)	sqrt of 32	-1/1
18	P1(8,4) P2(3,9)	sqrt of 50	1/-1
19	P1(9,5) P2(5,4)	sqrt of 17	-1/-4
20	P1(-5,6) P2(-6,-8)	sqrt of 197	-14/-1
21	P1(8,9) P2(-2,7)	sqrt of 104	-1/-5
22	P1(5,6) P2(-4,1)	sqrt of 106	-5/-9
23	P1(5,7) P2(7,8)	sqrt of 5	1/2
24	P1(-2,3) P2(-7,-9)	sqrt of 169	-12/-5
25	P1(9,5) P2(-8,-3)	sqrt of 353	-8/-17
26	P1(6,3) P2(9,6)	sqrt of 18	1/1
27	P1(7,4) P2(1,-9)	sqrt of 205	-13/-6
28	P1(-3,6) P2(2,-5)	sqrt of 146	-11/5
29	P1(7,6) P2(2,3)	sqrt of 34	-3/-5
30	P1(-7,2) P2(4,-7)	sqrt of 202	-9/11
31	P1(-8,7) P2(-2,-2)	sqrt of 117	-3/2
32	P1(5,-9) P2(-4,-8)	sqrt of 82	1/-9
33	P1(8,4) P2(1,8)	sqrt of 65	4/-7
34	P1(7,1) P2(-5,-4)	sqrt of 169	-5/-12
35	P1(8,2) P2(4,-7)	sqrt of 97	-9/-4
36	P1(-8,6) P2(3,-1)	sqrt of 170	-7/11
37	P1(8,3) P2(6,9)	sqrt of 40	3/-1
38	P1(6,7) P2(8,-2)	sqrt of 85	-9/2
39	P1(8,3) P2(-6,2)	sqrt of 197	-1/-14
40	P1(7,9) P2(5,-6)	sqrt of 229	-15/-2
41	P1(2,6) P2(9,2)	sqrt of 65	-4/7
42	P1(3,8) P2(-1,-6)	sqrt of 212	-7/-2
43	P1(4,7) P2(7,4)	sqrt of 18	-1/1
44	P1(-5,8) P2(-8,-9)	sqrt of 298	-17/-3
45	P1(5,2) P2(-9,-9)	sqrt of 317	-11/-14
46	P1(6,-5) P2(-2,-6)	sqrt of 65	-1/-8
47	P1(9,5) P2(-6,9)	sqrt of 241	4/-15
48	P1(8,1) P2(5,-2)	sqrt of 18	-1/-1
49	P1(9,3) P2(3,9)	sqrt of 72	1/-1
50	P1(9,4) P2(8,2)	sqrt of 5	-2/-1

October 3, 2007

Algebra: Linear Equations in Two Unknown

Given two linear equations, the two equations are solved simultaneously for x and y.

Problem	Given Equations	Solution
1	x+5y = 56; 4x+7y = 94	x = 6; y = 10
2	5x+3y = 25; 6x+8y = 52	x = 2; y = 5
3	6x+4y = 84; 6x+7y = 102	x = 10; y = 6
4	7x-8y = -14; 5x+6y = 154	x = 14; y = 14
5	4x+5y = 108; x+5y = 72	x = 12; y = 12
6	4x+y = 53; 2x+2y = 46	x = 10; y = 13
7	x+4y = 54; 4x+3y = 60	x = 6; y = 12
8	3x+y = 29; 2x+3y = 38	x = 7; y = 8
9	3x+2y = 29; 7x+3y = 76	x = 13; y = -5
10	4x+6y = 140; 9x+8y = 238	x = 14; y = 14
11	9x+4y = 62; x+6y = 68	x = 2; y = 11
12	8x+8y = 144; 3x+7y = 74	x = 13; y = 5
13	8x+8y = -56; 7x+4y = -16	x = 4; y = -11
14	7x+6y = 176; 6x+7y = 175	x = 14; y = 13
15	9x+8y = -59; 4x+6y = -14	x = -11; y = 5
16	2x+8y = 100; 7x+2y = 38	x = 2; y = 12
17	9x-3y = 96; 7x+4y = 100	x = 12; y = 4
18	8x+4y = 52; x+4y = 10	x = 6; y = 1
19	2x+3y = 48; 9x+8y = 161	x = 9; y = 10
20	2x+5y = 57; 3x+6y = 69	x = 1; y = 11
21	6x+3y = 90; 2x+5y = 62	x = 11; y = 8
22	3x+2y = 45; x+4y = 35	x = 11; y = 6
23	6x+9y = 180; 5x+3y = 87	x = 9; y = 14
24	9x+9y = 144; 3x+9y = 60	x = 14; y = 2
25	4x+7y = 87; 8x+7y = 111	x = 6; y = 9
26	5x+y = 34; 2x+3y = 37	x = 5; y = 9
27	6x+3y = -42; 9x+7y = -58	x = -8; y = 2
28	9x+4y = 121; x+y = 14	x = 13; y = 1
29	x+2y = 24; 7x+5y = 96	x = 8; y = 8
30	4x+2y = 38; 8x+6y = 74	x = 10; y = -1
31	2x+3y = 24; 5x+4y = 39	x = 3; y = 6
32	8x+7y = 122; 8x+3y = 98	x = 10; y = 6
33	2x+4y = 44; 6x+y = 55	x = 8; y = 7
34	x+9y = 119; 2x+8y = 118	x = 11; y = 12
35	9x-6y = 12; x+7y = 55	x = 6; y = 7
36	4x+5y = 30; 6x+5y = 40	x = 5; y = 2
37	x+2y = 31; x+8y = 115	x = 3; y = 14
38	7x+8y = 52; 6x+8y = 48	x = 4; y = 3
39	4x+2y = 36; 7x+3y = 60	x = 6; y = 6
40	3x+9y = 75; 2x+2y = 22	x = 4; y = 7
41	7x+4y = 11; 7x+4y = 11	x = 1; y = 1
42	2x+9y = 110; 3x+6y = 75	x = 1; y = 12
43	7x+2y = 37; 7x+9y = 93	x = 3; y = 8
44	2x+4y = -44; 5x+5y = -40	x = 6; y = -14
45	8x+y = 54; x+y = 12	x = 6; y = 6
46	3x+9y = 54; 9x+6y = 78	x = 6; y = 4
47	2x+6y = -64; 6x+3y = 18	x = 10; y = -14
48	6x+9y = 90; 3x+y = 24	x = 6; y = 6
49	3x+7y = 101; 6x+8y = 118	x = 1; y = 14
50	4x-7y = 1; 5x+3y = 13	x = 2; y = 1

Analytic Geometry: Equation and Slope of a Line

Given two points each for line P1P2 and line AB, the equations and slopes of the lines are determined. Through their slopes, it's determined whether the lines are parallel or perpendicular to each other.

Problem	Given Points	Equations of the Line	Slopes of the Line
1	P1(7,9) P2(6,3); A(8,5) B(2,6)	6x-y-33=0, x+6y-38=0	perpendicular lines: m1=-6/-1 m2=1/-6
2	P1(4,5) P2(9,8); A(3,2) B(0,7)	3x-5y+13=0, 5x+3y-21=0	perpendicular lines: m1=3/5 m2=5/-3
3	P1(2,6) P2(7,0); A(2,2) B(8,7)	6x+5y-42=0, 5x-6y+2=0	perpendicular lines: m1=-6/5 m2=5/6
4	P1(6,1) P2(2,5); A(5,0) B(9,4)	x+y-7=0, x-y-5=0	perpendicular lines: m1=1/-1 m2=1/1
5	P1(-9,4) P2(9,6); A(12,13) B(3,12)	x-9y+45=0, x-9y+105=0	parallel lines: m1=1/9 m2=-1/-9
6	P1(9,2) P2(5,8); A(3,0) B(9,4)	3x+2y-31=0, 2x-3y-6=0	perpendicular lines: m1=3/-2 m2=2/3
7	P1(1,5) P2(0,2); A(9,1) B(6,2)	3x-y+2=0, x+3y-12=0	perpendicular lines: m1=-3/-1 m2=1/-3
8	P1(2,8) P2(7,5); A(5,4) B(8,9)	3x+5y-46=0, 5x-3y-13=0	perpendicular lines: m1=-3/5 m2=5/3
9	P1(-2,0) P2(4,9); A(6,7) B(10,13)	3x-2y+6=0, 3x-2y-4=0	parallel lines: m1=3/2 m2=3/2
10	P1(5,7) P2(1,1); A(6,5) B(0,9)	3x-2y-1=0, 2x+3y-27=0	perpendicular lines: m1=-3/-2 m2=2/-3
11	P1(-4,9) P2(9,6); A(1,11) B(14,8)	3x+13y-105=0, 3x+13y-146=0	parallel lines: m1=-3/13 m2=-3/13
12	P1(-1,6) P2(9,0); A(10,3) B(0,9)	3x+5y-27=0, 3x+5y-45=0	parallel lines: m1=-3/5 m2=3/-5
13	P1(-6,1) P2(2,9); A(7,12) B(1,6)	x-y+7=0, x-y+5=0	parallel lines: m1=1/1 m2=-1/-1
14	P1(9,7) P2(0,9); A(6,0) B(8,9)	2x+9y-81=0, 9x-2y-54=0	perpendicular lines: m1=2/-9 m2=9/2
15	P1(-2,0) P2(3,7); A(4,7) B(9,14)	7x-5y+14=0, 7x-5y+7=0	parallel lines: m1=7/5 m2=7/5
16	P1(7,1) P2(8,4); A(7,0) B(4,1)	3x-y-20=0, x+3y-7=0	perpendicular lines: m1=3/1 m2=1/-3
17	P1(-3,4) P2(2,0); A(6,0) B(1,4)	4x+5y-8=0, 4x+5y-24=0	parallel lines: m1=-4/5 m2=4/-5
18	P1(-8,3) P2(2,8); A(1,6) B(7,9)	x-2y+14=0, x-2y+11=0	parallel lines: m1=1/2 m2=1/2
19	P1(6,2) P2(7,0); A(6,7) B(8,8)	2x+y-14=0, x-2y+8=0	perpendicular lines: m1=-2/1 m2=1/2
20	P1(-6,6) P2(5,3); A(12,6) B(1,9)	3x+11y-48=0, 3x+11y-102=0	parallel lines: m1=-3/11 m2=3/-11
21	P1(-5,6) P2(1,3); A(6,4) B(12,1)	x+2y-7=0, x+2y-14=0	parallel lines: m1=-1/2 m2=-1/2
22	P1(5,3) P2(9,5); A(3,7) B(5,3)	x-2y+1=0, 2x+y-13=0	perpendicular lines: m1=1/2 m2=-2/1
23	P1(-6,2) P2(4,1); A(14,2) B(4,3)	x+10y-14=0, x+10y-34=0	parallel lines: m1=-1/10 m2=1/-10
24	P1(0,5) P2(3,8); A(6,4) B(7,5)	x-y+5=0, x-y-2=0	parallel lines: m1=1/1 m2=1/1
25	P1(4,3) P2(2,8); A(1,3) B(6,5)	5x+2y-26=0, 2x-5y+13=0	perpendicular lines: m1=5/-2 m2=2/5
26	P1(-6,6) P2(2,1); A(0,5) B(8,0)	5x+8y-18=0, 5x+8y-40=0	parallel lines: m1=-5/8 m2=-5/8
27	P1(-6,1) P2(3,2); A(14,13) B(5,12)	x-9y+15=0, x-9y+103=0	parallel lines: m1=1/9 m2=-1/-9
28	P1(-8,4) P2(4,0); A(6,4) B(3,5)	x+3y-4=0, x+3y-18=0	parallel lines: m1=-1/3 m2=1/-3
29	P1(-4,7) P2(0,4); A(5,11) B(9,8)	3x+4y-16=0, 3x+4y-59=0	parallel lines: m1=-3/4 m2=-3/4
30	P1(7,5) P2(6,2); A(5,8) B(8,7)	3x-y-16=0, x+3y-29=0	perpendicular lines: m1=-3/-1 m2=-1/3
31	P1(-1,3) P2(4,2); A(8,10) B(3,11)	x+5y-14=0, x+5y-58=0	parallel lines: m1=-1/5 m2=1/-5
32	P1(7,2) P2(9,5); A(1,7) B(4,5)	3x-2y-17=0, 2x+3y-23=0	perpendicular lines: m1=3/2 m2=-2/3
33	P1(-2,6) P2(4,1); A(1,7) B(7,2)	5x+6y-26=0, 5x+6y-47=0	parallel lines: m1=-5/6 m2=-5/6
34	P1(-3,9) P2(7,7); A(0,12) B(10,10)	x+5y-42=0, x+5y-60=0	parallel lines: m1=-1/5 m2=-1/5
35	P1(-2,2) P2(3,5); A(6,9) B(1,6)	3x-5y+16=0, 3x-5y+27=0	parallel lines: m1=3/5 m2=-3/-5
36	P1(2,8) P2(4,0); A(1,7) B(9,9)	4x+y-16=0, x-4y+27=0	perpendicular lines: m1=-4/1 m2=1/4
37	P1(2,7) P2(8,3); A(1,1) B(5,7)	2x+3y-25=0, 3x-2y-1=0	perpendicular lines: m1=-2/3 m2=3/2
38	P1(-4,1) P2(1,5); A(10,14) B(5,10)	4x-5y+21=0, 4x-5y+30=0	parallel lines: m1=4/5 m2=-4/-5
39	P1(-4,1) P2(1,4); A(9,7) B(14,10)	3x-5y+17=0, 3x-5y+8=0	parallel lines: m1=3/5 m2=3/5
40	P1(7,6) P2(6,4); A(4,6) B(2,7)	2x-y-8=0, x+2y-16=0	perpendicular lines: m1=-2/-1 m2=1/-2
41	P1(0,4) P2(1,2); A(6,7) B(8,8)	2x+y-4=0, x-2y+8=0	perpendicular lines: m1=-2/1 m2=1/2
42	P1(-9,5) P2(1,0); A(10,8) B(6,10)	x+2y-1=0, x+2y-26=0	parallel lines: m1=-1/2 m2=1/-2
43	P1(9,1) P2(0,9); A(0,0) B(8,9)	8x+9y-81=0, 9x-8y-0=0	perpendicular lines: m1=8/-9 m2=9/8
44	P1(-2,4) P2(8,0); A(9,8) B(14,6)	2x+5y-16=0, 2x+5y-58=0	parallel lines: m1=-2/5 m2=-2/5
45	P1(1,2) P2(2,4); A(4,2) B(6,1)	2x-y-0=0, x+2y-8=0	perpendicular lines: m1=2/1 m2=-1/2
46	P1(0,5) P2(9,3); A(9,11) B(0,13)	2x+9y-45=0, 2x+9y-117=0	parallel lines: m1=-2/9 m2=2/-9
47	P1(3,8) P2(8,2); A(2,2) B(8,7)	6x+5y-58=0, 5x-6y+2=0	perpendicular lines: m1=-6/5 m2=5/6
48	P1(2,2) P2(1,4); A(3,0) B(5,1)	2x+y-6=0, x-2y-3=0	perpendicular lines: m1=2/-1 m2=1/2
49	P1(7,8) P2(0,3); A(8,2) B(3,9)	5x-7y+21=0, 7x+5y-66=0	perpendicular lines: m1=-5/-7 m2=7/-5
50	P1(0,7) P2(4,0); A(2,2) B(9,6)	7x+4y-28=0, 4x-7y+6=0	perpendicular lines: m1=-7/4 m2=4/7

Algebra: Multiplication of Polynomials

Problem	Given Polynomials	Solution
1	6x+7y and 7x³+2y	42x⁴+12xy+49x³y+14y²
2	4x⁴-8y and 4x³-7y³	16x⁷-28x⁴y³-32x³y+56y⁴
3	7x⁴+4y and 2x³-8y²	14x⁷-56x⁴y²+8x³y-32y³
4	5x²-3 and 7y³-10	35x²y³-50x²-21y³+30
5	2x-5 and 1x+13	2x²+21x-65
6	8x⁴-3y and 7x-5y⁴	56x⁵-40x⁴y⁴-21xy+15y⁵
7	8x²-13 and 3y³-3	24x²y³-24x²-39y³+39
8	2x³+6y⁴ and 5x⁴	10x⁷+30x⁴y⁴
9	2x+6 and 3x²-2	6x³-4x¹+18x²-12
10	4x-12 and 5y²-1	20xy²-4x-60y²+12
11	2x-12 and 3x+13	6x²-10x-156
12	4x+7 and 1x²-10	4x³-40x¹+7x²-70
13	3x-8 and 1y-6	3xy-18x-8y+48
14	8x⁴+6y⁴ and 8x³	64x⁷+48x³y⁴
15	8x+11 and 7x-14	56x²-35x-154
16	3x⁴+12 and 1x²+5	3x⁶+15x⁴+12x²+60
17	8x³-6 and 1y²+5	8x³y²+40x³-6y²-30
18	7x³-1 and 3y²+5	21x³y²+35x³-3y²-5
19	1x³+4y and 7x⁴+5y²	7x⁷+5x³y²+28x⁴y+20y³
20	4x⁴+1y and 8x²+3y⁴	32x⁶+12x⁴y⁴+8x²y+3y⁵
21	6x-8y and 5x+5y³	30x²+30xy³-40xy-40y⁴
22	6x-10 and 7y²-11	42xy²-66x-70y²+110
23	7x+11 and 6x-12	42x²-18x-132
24	1x-5 and 7x-8	7x²-43x+40
25	7x⁴+2y and 3x²	21x⁶+6x²y
26	2x³-9 and 5y²+14	10x³y²+28x³-45y²-126
27	7x⁴-4y² and 3x	21x⁵-12xy²
28	2x²+1y⁴ and 7x²	14x⁴+7x²y⁴
29	8x⁴-8y⁴ and 8x³+1y	64x⁷+8x⁴y-64x³y⁴-8y⁵
30	6x+7 and 5x²-12	30x³-72x¹+35x²-84
31	2x+4 and 7x+2	14x²+32x+8
32	8x⁴+10 and 1x²+1	8x⁶+8x⁴+10x²+10
33	3x+6 and 8x+3	24x²+57x+18
34	5x+4 and 3x-6	15x²-18x-24
35	4x³-7y and 4x+3y²	16x⁴+12x³y²-28xy-21y³
36	7x-2 and 5y-7	35xy-49x-10y+14
37	5x+6y³ and 2x²-6y	10x³-30xy+12x²y³-36y⁴
38	8x³-2y³ and 6x²-4y²	48x⁵-32x³y²-12x²y³+8y⁵
39	6x⁴+13 and 4x²+11	24x⁶+66x⁴+52x²+143
40	3x+7y⁴ and 7x-3y	21x²-9xy+49xy⁴-21y⁵
41	5x²-3 and 3y³-6	15x²y³-30x²-9y³+18
42	3x+7 and 7x+6	21x²+67x+42
43	5x²-7y and 2x³	10x⁵-14x³y
44	3x³+4y⁴ and 6x²	18x⁵+24x²y⁴
45	7x+7y³ and 4x	28x²+28xy³
46	5x²-2y³ and 1x	5x³-2xy³
47	3x-2 and 3x-3	9x²-15x+6
48	7x-2 and 4y²-5	28xy²-35x-8y²+10
49	2x-11 and 2x-1	4x²-24x+11
50	6x-2 and 1x+13	6x²+76x-26

Arithmetic: Multiplication of Fractions

Problem	Multiplicand	Multiplier	Product
1	3/14	5/14	15/196
2	3/10	1/14	3/140
3	3/14	1/18	1/84
4	5/18	7/18	35/324
5	7/22	5/21	5/66
6	5/18	7/22	35/396
7	2/21	1/20	1/210
8	4/15	7/12	7/45
9	7/22	5/24	35/528
10	1/8	1/8	1/64
11	1/14	3/10	3/140
12	2/21	7/22	1/33
13	7/10	4/21	2/15
14	1/14	7/20	1/40
15	7/12	5/24	35/288
16	5/18	7/15	7/54
17	1/7	11/15	11/105
18	3/4	1/20	3/80
19	4/21	7/15	4/45
20	1/5	1/3	1/15
21	1/14	2/15	1/105
22	3/7	2/3	2/7
23	5/8	7/18	35/144
24	7/20	1/20	7/400
25	8/9	1/9	8/81
26	5/24	1/14	5/336
27	3/16	5/18	5/96
28	1/20	5/21	1/84
29	1/18	5/12	5/216
30	7/10	1/18	7/180
31	34/10	10/15	/
32	3/22	5/14	15/308
33	4/15	7/10	14/75
34	5/24	1/16	5/384
35	3/10	5/24	1/16
36	7/10	7/16	49/160
37	1/7	7/9	1/9
38	7/12	5/12	35/144
39	7/16	7/16	49/256
40	4/15	7/12	7/45
41	7/15	5/18	7/54
42	5/21	1/20	1/84
43	7/22	5/24	35/528
44	7/16	8/15	7/30
45	3/20	5/16	3/64
46	7/18	5/12	35/216
47	7/18	3/14	1/12
48	1/15	7/16	7/240
49	2/21	1/14	1/147
50	8/9	2/9	16/81

Arithmetic: Division of Fractions

Problem	Dividend	Divisor	Quotient
1	7/20	3/20	2 1/3
2	8/9	1/14	12 4/9
3	1/10	2/15	3/4
4	5/14	5/16	1 1/7
5	7/22	3/14	1 16/33
6	1/9	7/10	10/63
7	5/24	5/12	1/2
8	5/22	8/21	105/176
9	7/8	1/8	7
10	8/21	1/14	5 1/3
11	7/10	1/14	9 4/5
12	1/24	1/10	5/12
13	8/9	2/9	4
14	5/18	7/22	55/63
15	8/21	5/18	1 13/35
16	7/12	8/21	1 17/32
17	7/20	7/20	1
18	6/7	7/12	1 23/49
19	7/9	1/4	3 1/9
20	4/21	4/15	5/7
21	7/16	7/16	1
22	7/22	1/12	3 9/11
23	7/24	1/12	3 1/2
24	7/15	2/15	3 1/2
25	5/14	7/20	1 1/49
26	1/15	5/18	6/25
27	1/18	3/14	7/27
28	7/8	1/5	4 3/8
29	7/20	3/22	2 17/30
30	3/22	7/15	45/154
31	8/9	5/14	2 22/45
32	3/22	1/10	1 4/11
33	8/15	3/20	3 5/9
34	1/12	5/14	7/30
35	3/22	5/14	21/55
36	1/12	4/15	5/16
37	2/7	3/7	2/3
38	7/16	7/10	5/8
39	3/10	1/14	4 1/5
40	5/9	2/9	2 1/2
41	7/22	7/16	8/11
42	5/18	7/18	5/7
43	7/24	1/14	4 1/12
44	1/14	4/15	15/56
45	1/8	5/9	9/40
46	3/20	3/22	1 1/10
47	7/10	1/14	9 4/5
48	7/22	3/16	1 23/33
49	6/7	1/18	15 3/7
50	7/10	1/18	12 3/5

Arithmetic: Subtraction of Fractions

Problem	Minuend	Subtrahend	Difference
1	5/12	7/12	-1/6
2	5/18	1/10	8/45
3	3/4	5/7	1/28
4	3/10	5/12	-7/60
5	7/18	1/21	43/126
6	2/21	8/15	-46/105
7	7/24	3/20	17/120
8	2/15	7/20	-13/60
9	3/22	3/22	0
10	3/22	1/14	5/77
11	8/9	1/9	7/9
12	3/14	1/20	23/140
13	7/18	3/22	25/99
14	2/15	5/14	-47/210
15	1/8	3/14	-5/56
16	3/10	1/24	31/120
17	1/12	7/20	-4/15
18	1/21	2/15	-3/35
19	3/20	1/10	1/20
20	3/20	7/24	-17/120
21	7/16	1/16	3/8
22	8/9	6/7	2/63
23	8/15	3/16	83/240
24	7/24	1/14	37/168
25	6/7	3/10	39/70
26	7/10	8/15	1/6
27	1/14	3/16	-13/112
28	7/12	5/21	29/84
29	1/9	2/9	-1/9
30	3/7	10/21	-1/21
31	7/24	1/14	37/168
32	7/10	7/10	0
33	6/7	7/12	23/84
34	7/15	7/22	49/330
35	7/18	1/24	25/72
36	5/18	2/15	13/90
37	5/8	2/15	59/120
38	8/9	5/7	11/63
39	7/24	1/14	37/168
40	3/10	1/14	8/35
41	1/12	7/18	-11/36
42	1/15	3/10	-7/30
43	5/14	1/12	23/84
44	7/12	1/18	19/36
45	7/8	10/21	67/168
46	7/22	5/12	-13/132
47	7/24	5/12	-1/8
48	3/10	5/18	1/45
49	7/18	1/20	61/180
50	6/7	4/7	2/7

Arithmetic: Addition of Fractions

Problem	First Number	Second Number	Total
1	1/12	3/10	23/60
2	5/16	7/10	1 1/80
3	3/14	8/15	157/210
4	1/24	3/20	23/120
5	5/14	5/24	95/168
6	2/15	7/18	47/90
7	1/16	7/16	1/2
8	8/9	2/9	1 1/9
9	5/16	1/15	91/240
10	7/10	5/12	1 7/60
11	7/18	7/20	133/180
12	1/12	7/12	2/3
13	5/22	1/15	97/330
14	8/15	1/12	37/60
15	3/22	1/10	13/55
16	7/8	5/18	1 11/72
17	3/14	7/12	67/84
18	4/7	7/10	1 19/70
19	4/5	8/9	1 31/45
20	5/24	7/24	1/2
21	7/9	8/9	1 2/3
22	3/16	5/22	73/176
23	3/22	3/20	63/220
24	2/15	8/21	18/35
25	7/12	1/20	19/30
26	7/16	1/18	71/144
27	5/21	7/10	197/210
28	7/9	1/24	59/72
29	7/9	4/7	1 22/63
30	7/18	1/10	22/45
31	3/16	7/18	83/144
32	4/15	1/14	71/210
33	8/15	7/22	281/330
34	7/12	7/24	7/8
35	7/16	1/24	23/48
36	8/15	8/21	32/35
37	1/21	1/21	2/21
38	7/8	7/9	1 47/72
39	5/24	1/12	7/24
40	7/15	3/20	37/60
41	5/14	7/24	109/168
42	3/5	5/9	1 7/45
43	2/15	5/12	11/20
44	7/16	5/22	117/176
45	7/12	1/12	2/3
46	1/8	7/8	1
47	1/14	1/21	5/42
48	7/18	1/12	17/36
49	6/7	11/24	1 53/168
50	1/22	1/22	11/121