Teste de vericação tirado do livro Cálculo, volume 1, de James Stewart.
Teste de Álgebra.
1. Calcule cada expressão sem usar calculadora.
(a)
(−3)4
(b)
−34
3−4
(c)
(d)
523
521
(e)
−2
2
3
(f )
16−3/4
2. Simplique cada expressão. Escreva suas respostas sem expoentes negativos.
√
(a)
√
200 − 32
(b)
3 3
2 2
(3a b )(4ab )
(c)
3x3/2 y 3
x2 y −1/2
−2
3. Expanda e simplique.
(a)
3(x + 6) + 4(2x − 5)
(d)
(2x + 3)2
(e)
(b)
(x + 3)(4x − 5)
(c)
√ √
√
√
( a + b)( a − b)
(x + 2)3
4. Fatore cada expressão.
(a)
4x2 − 25
(b)
2x2 + 5x − 12
(d)
x4 + 27x
(e)
3x3/2 − 9x1/2 + 6x−1/2
(c)
x3 − 3x2 − 4x + 12
(f )
x3 y − 4xy
5. Simplique as expressões racionais.
(a)
x2 + 3x + 2
x2 − x − 2
y
x
(d) 1
y
−
−
(b)
2x2 − x − 1 x + 3
·
x2 − 9
2x + 1
(c)
x2
x+1
−
2
x −4 x+2
x
y
1
x
6. Racionalize a expressão e simplique
(a)
√
10
√
5−2
√
(b)
4+h−2
h
7. Reescreva completando o quadrado.
(a)
x2 + x + 1
(b)
2x2 − 12x + 11
8. Resolva a equação. (Encontre apenas as soluções reais)
2x
2x − 1
=
x+1
x
4
2
x − 3x + 2 = 0
(a)
x + 5 = 14 − x/2
(b)
(d)
2x2 + 4x + 1 = 0
(e)
(g)
√
2x(4 − x)−1/2 − 3 4 − x = 0
(c)
(f )
x2 − x − 12 = 0
3|x − 4| = 10
9. Resolva cada desigualdade. Escreva suas respostas usando a notação de intervalos.
(a)
−4 < 5 − 3x ≤ 17
(d)
|x − 4| < 3
(b)
(e)
x2 < 2x + 8
2x − 3
≤1
x+1
1
(c)
x(x + 1)(x + 2) > 0
10. Diga se cada equação é verdadeira ou falsa.
(a)
(p + q)2 = p2 + q 2
(d)
1 + TC
=1+T
C
(b)
(e)
√
√ √
ab = a b
(c)
√
a2 + b 2 = a + b
1
1 1
= −
x−y
y x
Respostas teste de álgebra.
1. (a)
2. (a)
81
(b)
√
6 2
−81
(b)
(c)
1/81
48a5 b7
(d)
25
(c)
x
9y 7
(e)
2
11x − 2
(b) 4x + 7x − 15
3
2
(e) x + 6x + 12x + 8
3. (a)
9/4
(c)
(f )
1/8
a−b
(d)
4x2 + 12x + 9
(2x − 5)(2x + 5) (b) (2x − 3)(x + 4) (c) (x − 3)(x − 2)(x + 2)
2
−1/2
(d) x(x + 3)(x − 3x + 9)
(e) 3x
(x − 1)(x − 2) (f ) xy(x − 2)(x + 2)
4. (a)
5. (a)
6. (a)
7. (a)
x−1
1
x+2
(b)
(c)
(d) −(x + y)
x−2
x−3
x−2
√
√
1
5 2 + 2 10 (b) √
4+h+2
2
3
1
2
+
x+
(b) 2(x − 3) − 7
2
4
√
6 (b) 1
(g) 12/5
8. (a)
9. (a)
[−4, 3[
10. (a) Falso
(b)
2
2
√
±1, ± 2
−3, 4
(d)
−1 ±
] − 2, 4[
(c)
] − 2, 0[ ∪ ]1, ∞[
(c)
(b) Verdadeiro
(e)
(c) Falso
(d) Falso
2
(d)
(f )
2/3, 22/3
]1, 7[
(e) Falso
(e)
] − 1, 4]