082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 1 51
3 Removethe brackets and simplify:
( ) −1
(a) (2x 2 y) 3 (b) (6a 2 b 3√ c) 2 (c)
y −2
2
(d) (x 2 y −1 ) 0.5
( )
3 −1 x −2 −2
(e)
y −3
4 Expressthe following astheir partialfractions:
(a)
(c)
(e)
3x+11
(x −3)(x +7)
6x 2 −2
2x 2 −x
4x−11
2x 2 +15x+7
(b)
(d)
−3−x
x 2 −x
2x 2 −x−7
(x +1)(x −1)(x +2)
5 Convert the following intoasingle fraction:
(a)
(b)
(c)
1
x + 3
x +2 + 6
8x+4
1
s + 2 s 2 + 3s+4
8s+6
6
s + 10
s 2 − s +1
(s +2)(s +3) + s −1
(s +4)(s +3)
6 Expressthe following aspartialfractions:
(a)
(c)
(e)
(f)
(g)
(i)
(k)
(m)
(o)
(q)
(s)
5x
(x +1)(2x −3)
y +3
y 2 +3y+2
2z 2 +15z +30
(z +2)(z +3)(z +6)
(b)
(d)
24x 2 +33x +11
(2x +1)(3x +2)(4x +3)
3x+2
x 2 +5x+6
1
t 2 +3t+2
s +3
(s +1) 2 (h) 2k2 +k+1
k 3 −k
x 3
x 2 +1
s 2
s 2 +1
6d 2 +15d+8
(d +1) 2 (d +2)
−y−1
(y 2 +1)(y −1)
t 2 +t−2
(t −2) 2 (t +1)
x 3 +4x 2 +7x+5
x 2 +3x+2
(j)
(l)
t +5
(t +3) 2
8x−15
4x 2 −12x+9
(n) 2x2 +x+3
x 2 +2x+1
(p)
s 2 −8s−5
(s 2 +s+1)(s−4)
(r) 2s3 +3s 2 −s−4
s 2 +s−1
7 Solve the following quadraticequationsusingthe
quadraticformula:
(a) x 2 +10x+2=0
(b) y 2 −6y−3=0
(c) 2t 2 +2t−9=0
(d) 3z 2 −9z−1=0
(e) 5v 2 +v−6=0
8 Solve the quadratic equationsin Question7by
completing the square.
9 Solve
x 3 −4x 2 −25x+28=0
givenx = 7 is aroot.
10 Solve the following inequalities:
(a) 6t−14
(c) 1−2v<v+4
(e) (x−2) 2 36
x −3
(g)
x +1 0
x
(i)
2 3 x
(b) −63r6
(d) 2 x −2
3
(f)x 2 −2x−3<0
(h)x2 −8x+50
(j) x2 −2x−3
x −5
11 Express eachfraction in its simplestform.
3ab 2
(a)
12ab
3x 2 +3x
(d)
6x 2 −3x
(b) 6x2 y 2 z
3xy 3 (c)
z
xyz −2x 2 y 2 z
(e)
x 2 y 2 −2x 3 y 3
12 Express eachfraction in its simplestform.
x 2 +2x−15
(a)
x 2 −2x−3
2x 2 +7x−4
(c)
2x 2 −3x+1
(e)
x 3 −2x 2 +x−2
x 3 +x 2 +x+1
> 0
9t+6
12−3t
y 2 +4y−12
(b)
y 2 +13y+42
3x 2 t +3xt −3t
(d)
4x 2 z+4xz−4z
13 Express asasingle fraction in itssimplestform.
x +1
(a)
x +6 × x +6
x +2
3x−6
(b)
xy+2y × xy+3y
4x−8
(c)
(d)
(e)
x 2 −1
4
÷ x −1
6
x 2 −9x
x +1 ÷ x −9
x 3 +x 2
x 2 −5x−6
x 2 +x−42 ÷ x2 −1
x 2 +6x−7