Esercizi per il corso di riallineamento - people.unica.itpeople.unica.it/montaldo/files/2007/09/Esercizi-riallineamento... · FACOLTA DI FARMACIA E BIOLOGIA CORSO DI LAUREA IN BIOLOGIA
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
FACOLTA DI FARMACIA E BIOLOGIA
CORSO DI LAUREA IN BIOLOGIA
CORSO DI RIALLINEAMENTO IN MATEMATICA
Equazioni di primo grado
1. 2(3x− 1) = 3x+ 7
2. 3(x− 1)− 2x = 4(x− 2)− 1
3. 3x+ 2(x− 1) = 5x− 3
4. 4(2− x) + 3x− 1 = −(x+ 2) + 9
5. 2(x− 3) = 4(1− 2x) + 3(x− 1)
6. 2(3x− 7) = 3(1− x)− 8x
7. 6(x+ 2)− 3(x+ 4) + 3 = 2x+ 4(x+ 1)
8. 3(x+ 2)− (2x+ 1) = 10− 3(x− 1)− 4x
9. 2(x− 3)− 5(1 + x)− 1 = x+ 2(1− x)
10. 5 + 2(4− x) + 3(x− 5) = 6(x+ 2)− 3(4x− 7)
11. 1− [2− 3(x− 1) + x] = 2x− 4(x+ 1)
12. 3− 2(x+ 2)− (1 + 4x) = x− 2(2x+ 1)
13. 2− [2x− (3− x)− 4] = 3(1− 2x) + 2− 3x
14. x+ 10 + 2(3x− 5) = −(3x− 1) + 6(1 + 3x) + 1
15. 5− [−(x− 1− 5(2x− 1))] = 2 + x+ 5(2x− 3)
16. x− 1 + 5(x− 3) + 4 = 6(x− 2)
17. 13(x− 3) + 1 = 2
(12x− 1
)+ 4x
3
18.(13− 1
2
)4x− 1
2(1− 6x) + 2x
3= 0
19. 12(x− 1) + 1
4(x+ 1) + x(1
2− 2) = 1− 2x
20. (3x+ 1)(12− 1)+ 1
2(x+ 1) = −x
21. (2x− 1)(13− 1
2
)+ 1
2x = 4 + x
6
22. 13
(2x+12− x−1
4
)− 1
2
(x+13− x
2
)= x− 5
4
2
Equazioni di secondo grado
1. x2 − 16 = 0
2. 3x2 − 27 = 0
3. x2 + 1 = 0
4. x2
4− 1 = 0
5. (2x− 1)2 − (x2 − 1) + 4x = 14
6. 3(2x+5)8− 2x2 = 3x−5
4
7. (x− 1)(x+ 2) + (x− 3)(x+ 1) = (x− 2)(x+ 1)
8. x2 − 8x = 0
9. 3x2 + 5x = 0
10. −x2 − 3x = 0
11. 2x = 52x2
12. (x− 1)2 − 1 = x
13. (x+ 2)2 − 3x = 4
14. (x+ 2)2 = 3(x− 1)2 + 1
15. 2 + (x+ 2)2 = 5x+ 3(2− x)
16. x2 − 7x+ 10 = 0
17. x2 + x− 6 = 0
18. x2 + x+ 3 = 0
19. x2 − 4x− 5 = 0
20. x2 − 12x+ 36 = 0
21. 2x2 − 9x+ 9 = 0
22. 4x2 + 4x+ 1 = 0
23. 2x2 − 2x+ 3 = 0
3
24. x2
4− x+ 7
6
25. x(x2 − 3x) + 2 = x3
26. (x+ 1)2 + (x+ 2)2 − 41 = 0
27. (2x− 1)2 = x2 + 12
28. x− 3 + x(x+ 3) = 2x2 + 1
29. 3(x2 − 1) + 8x(1− x) = (1− 2x)2
30. (2x+ 1)2 + (x+ 2)(x+ 1) = x+ 2
31. 2− 3x(4− x) = x2 − 16
32. 3x−54− x−3
5= 17+x2
20
33. (x+1)2
3− 2x
3= 1−x
2+ 2
3
34. x2−43
+ (x−1)22
= 7x2+512
35. (2− x)(7− x) = 83x− x2+28
6
36. (2x−1)23− (x−2)(1−2x)
6= (1− 2x)2
37. (x+2)(5x+3)4
= (x+1)(x−1)4
+ (x+1)(2−x)2
38. x8+ 1+x
4= x2+12x
32− 1
4
39. x2+115
+ 5x−15
+ (x+2)(2−x)3
+ 3(x−2)5
40. (x+ 1)3 + (x−1)(2−x)2
= (x2 − 1)x
4
Equazioni frazionarie
1. 3x+ 5 = 0
2. 1x+ 1
6= −2
3
3. 1x+3
+ 2 = 0
4. xx+1
= 2x+1x− 1
5. 2x−2 = 5
x+3− 1
2−x
6. 5xx+6− 2 = 2x− 1− x(2x+3)
x+6
7. x2−1x+1− 2(x+ 3) = 0
8. 3x+2
+ 52−x = 0
9. 16− 1
1−x = 1+x2−2x
10. 4+x3
= 5x+ 1 + 1−x
6
11. 2x+1
+ 1− 1x−1 = 8
x2−1
12. 12x−1 −
2x= x− 2
x(x+ 1)
13. xx−6 −
x−16
= 23+ x+6
6−x
14. 11−x −
43= x
x+1− 1+x
x−1
15. 1x−1 = 5
x2− 3
x2−x
16. xx−1 +
5−2xx2−3x+2
+ 1x−2 = 0
17. x2−4x+6x2−3x+2
− 27x−2 = 1− 26+x
x−1
18. 2x+1x−5 + 3x−1
x−3 = 64x2−8x+15
19. 4x+32x−1 +
8x−14x+2
= 474x2−1
20. 2x−1 = 3
4+ 2
x2−1
5
Equazioni di grado superiore al secondo
1. (x2 − 2x)(3x+ 6) = 0
2. (x2 − 3x)(x2 + 4x) = 0
3. x3 − 5x2 + 6x = 0
4. 2x3 + x2 − x = 0
5. 3x3 − 2x2 + x = 0
6. x3 + 5x2 + 3x− 9 = 0
7. x3 + 7x2 + 15x+ 9 = 0
8. 4x4 − x2 = 0
9. 16x4 − 1 = 0
10. x4 + 5x3 + 5x2 − 5x− 6 = 0
11. 8x4 − 16x3 + x− 2 = 0
12. x3 − 5x2 + 2x+ 8 = 0
13. 5x3 + 4x2 + 4x− 1 = 0
14. x3 + 5x2 − 9x− 45 = 0
15. x3 + x2 − 6x = 0
16. 3x4 − 10x3 + 10x− 3 = 0
17. 2x4 + 5x3 − 5x− 2 = 0
18. x4 − x2 − 12 = 0
19. x4 − 13x2 + 36 = 0
20. x6 − 9x3 + 8 = 0
21. 3x3 − 15x2 − 6x+ 72 = 0
22. 4x3 + 13x2 − 13x− 4 = 0
23. 12x3 + 13x2 − 13x− 12 = 0
6
24. 2x4 − 5x3 + 4x2 − 5x+ 2 = 0
25. x4 + x3 − x− 1 = 0
26. x3 + 3x2 + 3x+ 1 = 0
27. 4x3 − 21x2 + 21x− 4 = 0
28. 6x3 − 7x2 − 7x+ 6 = 0
29. 3x3 − 2x2 − 2x+ 3 = 0
30. 2x4 − 3x3 + 3x− 2 = 0
31. 3x3 − (4√2− 3)x2 − (4
√2− 3)x+ 3 = 0
32. 5x3 + 4x2 + 4x− 1 = 0
33. x4 − 3x3 + x2 − 2x− 3 = 0
34. x4
3− x3
2+ x2 − x+ 1
6= 0
35. 2x4 − 7x3 + 3x2 + 8x− 4 = 0
36. x3 + 5x2 − 9x− 45 = 0
37. 8x3 − 18x2 + x+ 6 = 0
38. 2x4 − 11x3 − 6x2 − 7x = 0
39. x4 − 6x3 + 13x2 − 12x+ 4 = 0
40. 4x4 − 5x2 + 1 = 0
7
Equazioni irrazionali
1.√2x− 1 = 2
2.√2x+ 3 = 3
3.√3x+ 1 = 2
4.√x+ 2 = 6
5.√10− 3x = −5
6.√3− x = 4
7.√x+ 1 = 10
8. 3 +√4− x = 0
9.√x+ 1 = 1
10.√x− 1 = 3
11.√28− x− x2 = 4
12.√x2 + 1 = 4
13.√x2 − 9x+ 23− 3 = 0
14.√4x− 7 = x− 3
15.√8− x = 2x− 6
16.√x+ 2 = x+ 2
17.√5 + 2x− 5 = 2x
18.√2x− 5 + 2 = x
19.√x+ 5 + 6 = x+ 5
20.√3x2 + 5x− 3 = x
21.√2x2 − 3x− 10− x = 0
22.√5− 3x =
√5x− 35
23.√3x+ 7 =
√4x+ 5
8
24.√8− 7x =
√6x2 + 5
25.√x2 + 3x− 3 =
√x
26.√3x2 + 3x− 1 =
√x
27.√x+ 2 +
√1− 3x = 0
28.√x+ 1 +
√3x+ 1 = 0
29.√x+ 1−
√x− 1 = 1
30.√4− 2x−
√2x− 3 = 1
31.√x− 9−
√x− 18 = 1
32.√6− 2x+
√4x− 3 = 3
33.√x+ 4 +
√x− 8 = 6
34.√4− x+
√x− 3 = 1
35.√5− x+
√x− 3 = 2
36.√x− 1 + 2 = 6−
√x− 7
37.√x2 + 3x− 3 =
√x
38.√6x2 − 2x− 1 =
√1− x
39.√14x2 − 2x− 1 =
√3x
40.√x2 + 2x− 14 =
√x− 2
9
Equazioni esponenziali
1. 3x = 27
2. 2x = 116
3. 2x+1 = 8
4. (3x+1)2 = 9
5. 25x−2 = 18
6. 32x+1
9= 3x−2
7. x−1√9 = 3x−1
√3
8. 2x−3 · 4x+1 = 4
9. 23x = 82x+2
10. 8x2+2x = 1
8
11. 43x2−5x+1 = 1
4
12. (2x−1)x+1 = 8
13. (81+x)x = 1
14.3√32x−1 · x
√9 = 3x
15. x+1√8x · 2x
√22−x =
x√2x+2
16. (52−x)3+x
25x−1 = (5x−2)2x−3
252x·1253
17.x+2√28 · x−1
√8 =
2x−1√83 · x−1
√4
18. 2x−1 · 3 = 51+x
19. 5 · 2x+3 = 320 · 3x−3
20. 3x−2 · 7x−2 = 4x+3
21. 2x + 2x−1 + 2x−2 + 2x−3 + 2x−4 = 62
22. 3x + 3x−3 − 3x−4 + 3x−5 = 250
23. 22x+1 − 6 = 4x − 22x−1
10
24. 3x+1 + 3x−1 = 4x + 22x−1
25. 2 · 3x+1 − 3 · 5x+1 = 6 · 5x − 3x+2
26. 7x+1 − 52+x = 7x−1 − 51+x
27. 32x+1 − 52x−1 = 25x − 9x−1
28. 432−x − 4 · 51+x = 2 · 5x − 6
31−x
29. 2 · 3x−1 + 5 · 3x+1 = 23x+2 − 23x−1
30. 4x+2 − 5x−1 = 5x+1 − 22x−1
11
Equazioni logaritmiche
1. log(x− 1) = log(4− 3x)
2. log(3x+ 2) = 3 log 2
3. log(x− 2) + log(2x− 3) = log 3
4. 13log(x2 + 7) = log(x+ 1)
5. 12log(2x− 3) = log 5
6. 2 log x+ log 3 = log(5x− 2)
7. log(x−√1− x2) = 0
8. log x = 2 log(x− 2)
9. log(x+ 2) + log(3x+ 1) = 3 log 4
10. log(x+ 2)− 2 log 3 = log 6− log(x− 1)
11. 12log x+ log 3 = 1
2log 4 + log(x− 1)
12. 2 log x− log(x+ 1) = log 9− 2 log 2
13. log x+ log(2x− 1)− log 3 = log(2x+ 5)
14. log(3x+ 1) + log 3 = 4 log 2 + log(x− 2)
15. 3 log 2 + log(x− 1) = 2 log(x+ 1)
16. log(2− x) + log(x+ 1) = log 2
17. 12log x+ 1
2log(x− 1) = log 2 + 1
2log 5
18. 1 + log(x− 1) = log 5
19. 1 + log√x− 2 = log 5 + 1
2log(2x− 1)
20. 12log(12x+ 16) = log(x+ 3)
21. 12log(3x+ 4) = log(x+ 3)− log 2
22. log(3x+ 1) + log(x+ 1) = log 2 + log(9x2 − 1)
23. 2 + log x = 12log(x+ 2)− log 0.01
12
24. log(x− 1) + log√2 = 1
2log(x2 + 7)
25. log2(x2 + 2)− 2 log2 x = log2 3− log2(x
2 − 2)
26. logx(2x+ 3) = 2
27. logx2+2(x+ 1) = 12
28. log3(√x− 1− 2) = 1
29. log2(3x− 2) = 1 + 12log2(5x
2 − 14x+ 1)
30. 2 log3(x+ 2) + log3(x− 1)2 = 2 log3(5x− 2)
13
Equazioni trigonometriche
1. cos(x) =√32
2. sin(x) = 0
3. sin(x) = 1
4. sin(x) = 12
5. sin(x) = −12
6. 2 sin(x) = 3
7. 3 cos(x) = −5
8. cos(x) = −√22
9. 5 sin(x) = 6
10. tan(x) =√3
11. cot(x) = −√3
12. sin(x) = −√22
13. cos(x) = −12
14. sin(x)−√32
= 0
15. tan(x) = 1
16. 2 cos2(x)− 1 = 0
17. 5− 2 sin2(x) = 0
18.√2 sin2(x)− sin(x) = 0
19. cos(x)(sin(x)−
√22
)= 0
20. 4 sin2(x)− 1 = 0
21. −2cos2(x) + 1 = 0
22. sin(2x) = 12tan(x)
23. sin(2x) + 2 cos2(π4− x) = 3
14
24. cos(2x) + sin2(x) = 12
25. cos(2x) = cos(x)
26. sin(x) cos(x) = 32
27. sin(x) cos(x) = 1
28. cos(2x) = 1− sin2(x)
29. sin(x) = cos(2x)
30. cos(x) = 2 sin2(x)− 1
31. 3 sin2(x) + 2 cos(x) = 2
32. 2− sin(x) = cos2(x) + 7 sin2(x)
33. cos(2x) + 2 sin2(x) = 1
34. cos(2x)− 2 sin2(x) = 1
35. 2 sin(2x) + 2 sin2(x) = 3
36. sin(2x) + sin2(x) = 1
37. sin4(x)− sin2(x) cos2(x)− 2 cos4(x) = 0
38. 3 sin(x) +√3 sin(x) = −
√3
39. cos2(x) + 2 = 3 cos(x)
40. cos(2x) + 1 = 2 cos(x)
15
Disequazioni razionali intere di primo grado
1. 12x− 1 < 1 + 2(x+ 4)
2. 3 + 4(1 + x)− (1 + 3x) > −2
3. 3(x− 1)− 2 < 5x+ 1
4. 4(2x− 1)− 3(1− 2x) > 5
5. x3− (x−4)
2> 5−x
6+ 1
6. 3 + 2(x− 1) > 7 + 5(x− 2)
7. 8(5− x) + 3(x− 5) > 0
8. 9(20− 5x) + 27 > 8(5x− 6)
9. x−13− 1
2< 2(x+ 1) + 1
3
10. 1+3x3− (x−1)
4< x+6
6− 1
3
11. 2+3x4− x−2
3> 1
12. 12x+ x+3
3− x
4< 8
13. 12[2x− (1 + x)] > x− 1
3(1− 3x)
14. 13
(x− 1
2
)− 1
2
(x− 1
3
)< x−4
2
15. 1−x4− 2x−1
2> 3x−1
4− 5
(x+ 1
3
)16. 2
3
[3(x− 2) + 1−2x
4− x
2
]< x+ 1
2
17. 12− 1
3[x− 2(1− 3x)] < x−1
6− x+1
5
18. 4[x−23− 2
(x−16− 1−x
9
)]< x− 8
19.2− 1
3x
5− 1− 2
3x
4< 2−
12−3x10
20. 2−x1+ 1
2
− 3−x2− 1
2
> 2(1+6x)3
16
Disequazioni razionali intere di secondo grado
1. x(9− 2x) ≤ 0
2. x(x− 4) < 0
3. (2x+ 5)(x− 1) < 0
4. (x+ 4)(2x+ 5) > 0
5. 12x2 − 4x+ 3 < 0
6. −5 + 4x− 3x2 < 0
7. x2 − 5x+ 4 > 0
8. 2x2 − 7x− 15 ≥ 0
9. x2 + 4x < 0
10. 12x2 − 17x− 105 < 0
11. x2 + 6x+ 9 ≤ 0
12. x2 − 14x+ 49 < 0
13. 3x2 − 5x+ 9 > 0
14. 2x2 − 9 > 0
15. 9x2 − 25 < 0
16. x2 − 4x < 0
17. x2 − 10x+ 25 > 0
18. x2 − 81 ≥ 0
19. 25− x2 ≤ 0
20. x(x− 4) ≤ 0
21. (x− 2)(x− 3) > 0
22. (2x− 1)(x+ 1) > 0
23. (1− x)(x+ 1) > 0
17
24. (x− 2)(2 + x) < 0
25. x2 − 9 > 0
26. 4x2 − 1 < 0
27. 1− 25x2 < 0
28. 9− 49x2 > 0
29. (5 + 2x)(3 + x) < 0
30. (4− x)(1 + 2x) < 0
31. (3x+ 1)(1− x) > 0
32. x(x+ 5)− 7(x+ 8) < 7
33. 2− 2(2x− 1) + 4x2 − 3 > 0
34. (x− 2)2 − 4(x− 3) > 0
35. 2x2 − 4(x− 3)− 2x+ 7(4x− 1) < (x+ 1)2
36. x2+4−4x3− x−5
2< 5−3x
2+ x−3
2
37. 3−2x2− (x−1)2
4< 3
38. x2+164− x−3
2< 1− x
39. x2
4− (x+ 4)(x− 5) > (2x+1)
2
40. (x+1)2−(x−3)23
> (x+2)2
2− x
18
Disequazioni razionali intere di grado superiore al secondo