COMALGE
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Transcript of COMALGE
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7/30/2019 COMALGE
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COMALGE PRACTICE EXERCISES 1
I. Know the structure of the real number system ( rational, irrational, integers, natural numbers, decimals)
Know also the properties of real numbers.
II. Perform the indicated operations
1. Add 22 y5xyx2 and 22 y6xy5x7
2. Subtract 2a + 2b 4c from the sum of 4a 7b + 12c and 5b 3c
3. 9x ( 2y 3x) { y ( 2y - x) } [ 2y + 2 ( 4x - 3y) ]4. }a]3)3a(5a2[4a{a5a2 223
5. a. 465 )35( b. 374343 )yx2()yx4( c. 2870 )y5)(yx5(
d. (25)(2-7)(2-2) e. (3s5t-4)-6 f. (-5m-1n4)3(n-3m-2)-7
6. a.2
6a9
2bc
4
0c
3b
2a3 b. 2
v2
u33
u2
w284
w7
3v
2u3
c.6b3
32b3b
da
)da(.
n2p21p
p1n22n
)yx(
)yx(
7. a.43
3 6
2 232
3 2b.
2 3 7
3 3 0
43a b c
2a b cc.
1 3 5
1 2 3
9 t y
(4 ty )d.
2a 1
a 1 n
9
(3 )
e. 35
1419
1010
1010
f. 3243
4312
zyx6
zyx4
g.
22
22
213
wvu
wvu
8. a. 3xy( 2x 3y ) ( x + 5y ) b. )xy4(yx2)yx3x2(xy3 22
9. a. )3x3x2)(1x4x4( 22 b. )y3xy4x)(yxy3x2( 2222
10. )1x)(10xx2( nn2
11. a. Divide 4x4x5x6 23 by 2x + 3 b. Divide 3x2x4 3 by 2x - 1
12. a. Divide 4x4x5x4243 by x + 2 b. Divide 16a4n - 64a10n by 2a3n
13. a. Divide 1xxx259 by 1xx
2 b. Divide 3x8x4x3 24 by 2x6x3 2
14. a. Divide x3 + y3 by x 2y b. Divide 4x2- 6xy- 3y2 by 2x + 3y
c. Divide 3z3
-11z2
x - 18zx2
- 6x3
by z - 5xIII. Use special product formulas to find the following.
1. ( 7x + 3y ) ( 2x 4y) 12. ( 6m + 5n) ( 6m + 5n )
2. ( 2mn 3r) ( 5mn + 2r ) 13. )2t5( 3 )2t5( 3
3.2)y3x5( 14. 3nn )yx(
4. 232 )y2x3( 15. 2)z2yx5(
5. 243 )z3yx5( 16. 2)c2b6a(
6. 3)yx4( 17. 2)w3z2yx2(
7. 32 )c2xy( 18. ]z4)y2x3[( ]z4)y2x3[(
8. 32 )xx3( 19. ]3)xx2[( 2 ]3)xx2[( 2
9. ( 4x - 3y) ( 4x + 3y) 20. [ 2( x + y) 5] [ 3 ( x + y) + 4 ]
10. )b7a5( 43 )b7a5( 43 21. )]1x()xx2[( 32 )]1x()xx2[( 32
11. )(4c
3
ab)(
4c
3
ab22. )]yx()b2a[( 232 )]yx()b2a[( 232
IV. Factor the following completely.
1. x10x4x2 23 16. 20abba 22
2. 232232 zxy4yzx12zxy6 17. 6x11x102
3. 3y (2x + 5) 4x (2x + 5) 18. 4224 q6qp13p6
4. 22 )y3x(xz6)y3x(x3 19. 456 x9x24x16
5. 22 z16x52 20. 22 y25xy10x
6. 684 zyx4 21. baaba2
7. 643 xd9yx 22. d6c3cd4c22
8. 42 r4)z3x2(81 23. 224 x1x2x
9. 22 )n3m4(4a64 24. yz18xz24xy3x4 2
10. 33 ba27 25. bcacbab2a 22
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11. 63 b8a 26.2233 yxy2xyx
12. 912 yx8 27. 3322 dc8d3cd5c2
13. 33 a)b3x(64 28. )7x4()3x(8)7x4)(3x(2 22
14. acb4a9 223 29. 4)yx(23)yx(62
15. 94 y81yx625 30. 2222 ba9)y9xy12x4(25
V. Reduce the ff fractions to lowest terms.
1.7
52
xy30
yx362.
3a8a4
3a7a62
2
3.x3
27x3
4.3b4bb12
1b432
2
VI. Perform the indicated operations
1.324
23
yx8
xy27
xy24
yx402.
y412
9y6y
9y
15yy 2
2
2
3.
dc
bc
dc
bdbc
dc
dcc
22
22
22
23
4.22
2
22
22
22
33
y9x
y3xy
yxy3x9
y3xy2x
yxy4x3
yx27
5.x
3x
2x
1x6.
x53
yx2
3x5
y2x3
7.22 x4x2
3
3x12
28.
3x
1x
9x
6x6
3x
x2
9.a3
2
3a
110.
8x10x3
3x2
12xx6
3x
6xx2
1x2222
11.1x
1x2x
)x1(x
1x2
2
12.2x
4x
1x
1
2x
3
13.c1
c
3c3
2c
5c3
2c14.
9x6x
x
3x
2x
9x6x
2x3
3x
x322
15.2x3
x
2x5x12
1x56x
216.
x
1
1x
x
1x
2
17.
x2
1
4
1
x
1x
4
2
1
2
3
18.
1x2
x1211x2
3
2x
5
19.
x
11
1xx
1x
xx
2
2
20.
y
x21
11
x
1
21.
q2p
qp2
q2p
1
qp
2
VII. Simplify the ff expressions
1.1
11
)yx(
yx2.
1221
2112
yx2yx
x6yxy3.
223
232
yya
yaa
4. 122 )yx( 5. 2
4
)3x(8
)3x(46.
11vu
vu7.
11
22
xy
yxxy