Unit 3 Booklet

Checkup for algebraic operations
x Ð1/4 x x 3/4
x Ð1/2
1. Factorise the numerator and/or denominator if possible, then simplify:
(a)
7v
9a
(b) b
6
14v
(c)
3ab 2 6x Ð 18
(d)
(e)
3x + 3y
a Ð 8
(f) (g)
v 2 + 3v + 2
6x + 9y
a 2 Ð 64
v 2 Ð 4
v 2 Ð vw
v
2. Simplify:
(a) b 3 2 (b) a 2 x (c) z (d)
x
x
2 ¸
z
a 2 ¸
a
4 b
x a
2 6
b b
(e) c
(f) (g) (h) x + 1 x + 2
+
c
3u 2v
3
Ð
+
1
2
Ð
4 8
4 5
k m
5
3. Change the subject of each formula to x.
(a) 5 + x = 6 (b) x Ð a = w (c) ax + m = p (d) x / z = p /w
(e) N = 2px 2 (f) T = 4x + 3 (g) w = 1 / 2 (x + y) (h) M =
5
8x 2
4. Express each of these in its simplest form:
(a) Ö32 (b) Ö1000 (c) 2Ö45 (d) Ö45 Ð Ö20
9
(e) Ö50 Ð Ö18 (f) Ö72 + Ö50 (g)
(h) 2Ö8 Ð Ö2
2
a
5. If x = 1 + Ö3 and y = 1 Ð Ö3, simplify:
(a) 2x + 2y (b) 5xy (c) x 2 + y 2
6. Rationalise the denominators in the following and simplify where possible:
(a) 1 /Ö5 (b) 8 / Ö2 (c) 15 /Ö5 (d) Ö2/ Ö6
7. Write in their simplest form:
(a) 5 6 x 5 8 (b) x 8 ¸ x 6 (c) (d) (a 2 ) 3
(e) (4a 3 b) 2 (f) (g) (p 2 ) 0 (h) x 3 (x 2 Ð x)
8. Write with positive indices:
(a) 5 Ð2 (b) ab Ð3 (c) (y Ð3 ) Ð2 (d)
9. Write these in root form: 10. Write these in index form:
(a) b 1/2 (b) c Ð3/2 (a) 3 Öx
4 (b) 1 / Öa
3
11. Evaluate:
(a) 36 3/2 (b) 32 Ð2/5 (c) (x 8 ) 1/2 (d) (y 7/2 ) Ð2
(e) a Ð3/2 (a 1/2 Ð a Ð5/2 ) (f) 2s 1/2 ¸ 4s Ð1/2
(g)
Mathematics Support Materials: Mathematics 3 (Int 2) Ð Student Materials 13