Lq Unit 3 Indices, Surds And Number Systems

Math/CE LQ Ex.3

Unit 3 Indices, Surds and Number Systems 2006 CE Exam Syllabus Syllabus Topics

Notes (Whole Syllabus)

Law of indices

Notes (Foundation Part) Using law of integral indices to simplify algebraic expressions up to 2 variables.

Including rational indices. Manipulation of surds, including the rationalization of denominators in the form of a . Inter-convert between simple binary / hexadecimal numbers to decimal numbers.

1.

Laws of Indices Assume a ≠ 0 and b ≠ 0 . (a)

a m × a n = a m+n

(b)

(c)

(a m ) n = a mn

(d)

(e)

a0 = 1

(f)

(g)

am = m a

(h)

a m = (m a ) n = m a n

1

n

2.

a m ÷ a n = a m−n

a am ( )m = m b b 1 a −m = m a

m , n are integers and m is positive.

Binary System: Two digits ( 0, 1 only) 10110102 = 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 2 + 0 = 64 + 16 + 8 + 2 = 9010 2510 ⇒

2 25 … 1 2 12 … 0 2 6 …0 2 3 …1 1

Remainder

Bottom Up

∴2510 = 110012

1

Math/CE LQ Ex.3

3.

Hexadecimal System: Sixteen digits ( 0, 1, 2, … , 9, A, B, C, D, E, and F) 5E4A16 = 5 × 163 + 15 × 162 + 4 × 16 + 10 = 20480 + 3840 + 64 + 10 = 2439410 Remainder

16 6759 … 7 16 422 … 6 16 26 … 10 1

675910

Bottom Up

∴675910 = 1A6716

Section A

1. Simplify

a

, expressing your answer in index form.

[CE 90]

a

2. (a)

If

x

9 = 3 , find x. (b) Simplify and express with positive indices

3. Simplify 9 3 − 75 . 4. Simplify

(a 4 b −2 ) 2 ab

 x −1  x 2   y   

−3

.

[CE 93]

[CE 94]

and express your answer with positive indices.

[CE 94]

Exam. report: Fair. Some candidates did not give

Exam. Tips: make sure the completion of

answer using positive indices only.

simplification

5. Simplify (a + b)2 - (a - b)2. 6. Solve without using a calculator: 3 x =

[CE 95] 1 27

.

[CE 95]

5

a 4 4 a3 . 7. Simplify a −2 8. Simplify

9. Simplify

27 − 12 .

x3 y 2 and express your answer with positive indices. x −3 y

[CE 96]

[CE 97]

[CE 97] 2

Math/CE LQ Ex.3

10. Simplify

a 3a 4 and express your answer with positive indices. b −2

[CE 98]

11. Simplify

(a −3 ) 2 and express your answer with positive indices. a

[CE 99]

12. Simplify

x −3 y and express your answer with positive indices. x2

[CE 00]

13. Simplify

m3 and express your answer with positive indices. (mn) 2

[CE 01]

14. Simplify

(ab 2 ) 2 and express your answer with positive indices. a5

[CE 02]

15. Solve the equation 4x+1 = 8.

[CE 03]

16. Simplify

(a −1b) 3 and express your answer with positive indices. b2

[CE 04]

17. Simplify

( x 3 y) 2 and express your answer with positive indices. y5

[CE 05]

~ End of Unit 3 LQ ~ 3