Understanding Engineering Mathematics

(i)

10

12

(ii)

36

9

(iii)

7

3

×

2

5

(iv)

14

15

÷

5

7

(v)

1

2

+

1

4

(vi)

1

3

−

1

7

(vii)

21

5

−

7

10

(viii) 1−

1

2

+

1

3

(ix)

3

5

−

1

2

+

1

6

(x)

(

3

7

−

2

9

)

÷

(

1

5

−

1

2

)

(xi)

12

1 / 2

B.(a) Ifa:b=7:3 determineafor the following values ofb: (i) 4, (ii) 3, (iii)−7,

(iv) 15.

(b) Repeat forbwith the same values fora.

C.Ifa:b=5 : 2 evaluate as fractions

(i)

a

b

(ii)

a

a+b

(iii)

b

a+b

(iv)

a−b

a+b

(v)

a

b

+

b

a

(vi)

a

a+b

−

b

a−b

(vii)

a+b

a−b

+

a−b

a+b

D.Ifais proportional tobanda=6whenb=4, what are the values of the following

(i) awhenb= 3 (ii)

a

b

+

b

a

(iii)

a−b

a+b

(iv) bwhena= 21

1.3.6 Factorial and combinatorial notation – permutations and

combinations

➤➤

416

➤

A.Evaluate

(i) 5! (ii) 10! (iii)

301!

300!

(iv)

18!6!

16!

(v)

14!

(7!)^213

(vi)

10!

4!6!

(vii) 10!+11! (viii)

9!

6!3!

−

8!

5!4!

B.Evaluate

(i)^9 C 2 (ii)^9 C 7 (iii)^11 C 4

(iv)^10 C 4 (v)^100 C 100 (vi)^7 P 3

(vii)^6 P 36 C 3

C.How many combinations of 4 different letters can be chosen fromABCDEFG?

1.3.7 Powers and indices

➤➤

418

➤

A.Evaluate in terms of powers of primes