8/11/2019 Number bases 1.docx

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Number bases 1

1Express 2310as a number in base 2.

A 100002

B 100112

C 101112

D 111112

2 What is the value of 6, in base ten, in

the number 6 1455?

A 5B 125

C 750

D 6 000

3 Which of the following is true?

A 102+12= 1102

B 1112102= 102

C 1002+ 112= 1102

D 100212= 112

4 What is the value of 24+2 + 2

5, as a

number in base two?A 1100102

B 1010102

C 1100002

D 1011002

5 Express 5 22 + 2 2

3 + 2

5 as a

number in base two.

A 10000002

B 10001002

C 10010002

D 11000002

6 What is the place value of the digit 0

in the number 10435?

A 0

B 5

C 25

D 100

7 Express 62+7

2as a number in base

eight.

A 448

B 618

C 858D 1258

8 Express 44+ 8as a number in base

five.

A 2645

B 20205

C 20115

D 20245

9 2(83) +8

2+16=

A 10248

B 11048

C 21208

D 22208

10 111112+1110102=

A 1000110

B 1011001

C 1111001

D 1111110

11 Express 32+3

3+ 3

5+1 as a number

in base 8.

A 2808

B 4308

C 4508

D 53218

12 110101210112=

A 1110112

B 1000002

C 1100002

D 1010102

13 Given 1001m = 51310, what is the

value of m?A 2 C 8

B 5 D 16

14 Express 1110001012 as a number in

base 8.

A 7008

B 7058

C 7508

D 8008

15 Given 110002+k2=1010102, what

is the value of k?A 100002

B 100102

C 101002

D 100012

16 Given that 2 53 + 5

2 + 3(5) = k5,

find the value of k.

A 2905

B 21005

C 21305

D 21505

17 Given 4q48 is a 3-digit number inbase 8, find the value of q if 4q48=

1001111002.

A 4

B 5

C 6

D 7

18 Given 648 = 2f + 2

g + 2

h, find the

value off +g +h.

A 4

B 5

C 9D 11

19 Given y2 = 1005 + 1112, find the

value ofy.

A 100012

B 100102

C 110012

D 1000002

20 Given 101112< k< 110012, find the

value of kas a number in base 8.

A 278

B 308

C 318

D 328

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MATRICES 1

3 (a) GivenHis matrix ( )3 81 4 and the inverse matrixofH

is k 4 8

3p

. Find the values of kand ofp.

(b) Using matrices, find the value of xand ofy which

satisfy the following matrix equation.

H( )xy = 3

1

[6 marks]

4 (a) The inverse matrix of ( )5 34 2 is1

p

3

4 5

q

.

Find the value ofpand of q.

(b) Using matrices, solve the following simultaneous

equations:

5x+ 3y= 41

4x+ 2y= 30

[6 marks]

5 (a) M 2 3

3 5

= ( )1 00 1 whereMis a 2 2 matrix.

Find the matrixM.

(b) Using matrices, solve the following simultaneous

equations:

2x3y= 3

3x+ 5y=3 [6 marks]

6 (a) Find the matrixL such that

1 4

2 5

3 6

( )1 2 34 5 6 =L.

(b) It is given M= ( )7 918a and N= ( )5

2 7

b . If 5M

6N =

( )

11 15

43 48, find the value of a and of b.

[6 marks]

7(a) Given matrix P=

2

3

4 5

3 3

x

and matrix Q=5 2

4 y

,

find the value ofxand ofy ifPQ= ( )1 00 1 .

(b) Using matrices, calculate the value of a and of b

that satisfy the following matrix equation:

5 2

4 1

( )a

b=

95

67

[6 marks]

8 (a)3

12

4m

is the inverse matrix of ( )8 211 3 . Find the

value of m.

(b) Write the following simultaneous linear equations

as matrix equation:

8x+ 2y= 2

11x+ 3y= 2

Hence, using matrix method, calculate the value of x

and ofy.

[6 marks]

9 (a) The invers e matrix of 2 1

3 4

is

1

d

1

3 2

e

.

Find the value of dand of e.

(b) Using matrices, calculate the value of x and of y

that satisfy both of the following equations:

2xy= 11

3x4y= 9 [6 marks]

10 (a) Matrix V = 3 5

1 2

and matrix W = h 2 5

1 a

such that VW = ( )1 00 1 . Find the value of aand of h.

(b) Using matrices, find the value of x and of y that

satisfy the following simultaneous equations:

3x5y=17

x+ 2y= 53 [6 marks]

11 (a) GivenA= ( )14 7m andB= ( )4 95 n , find the value

of mand of nifAB=3 19

51 29

.

(b) Using matrices, solve the equationA( )pq = ( )1016 .[6 marks]

12 (a) Pis a 2 2 matrix andP( )1 23 4 = ( )1 0

0 1. Find

the matrixP.

(b) Hence, solve the following simultaneous linear

equations using matrices:

x+ 2y= 14

3x+ 4y= 16 [6 marks]