Number Base System – Mathematics JAMB & WAEC Past Questions and Answers

1

If 23x=325, find the value of x.

A.

7

6

5

4

The sum of 110112, 111112, and 100002 is 10m10n02. Find the values of m and n.

m=0,n=0

m=1,n=0

m=0,n=1

m=1,n=1

The subtraction below is in base seven. Find the missing number. 5 1 6 2Seven - 2 6 4 4seven 2 x 1 5

2

3

4

5

Convert $42_5$ to a base three numeral.

$201_3$

$210_3$

$211_3$

$222_3$

If $23_{x}$ + $101_{x}$ = $130_{x}$ , find the value of x.

7

6

5

4

Given that $124_{x}$ = 7( $14_{x}$ ), find the value of x.

12

11

9

8

Evaluate $(111_{two})^2$ and leave your answer in base 2.

$111001_{two}$

$110001_{two}$

$101001_{two}$

$10010_{two}$

Convert $35_{10}$ to a number in base 2.

1011

10011

100011

11001

Arrange the following numbers in descending order of magnitude: $22_{\operatorname{\mathrm{th}}ree}34_{five}21_{six}$

A.

$21_{six}22_{\operatorname{\mathrm{th}}ree}34_{five}$

B.

$22_{six}34_{five}22_{\operatorname{\mathrm{th}}ree}$

C.

$22_{\operatorname{\mathrm{th}}ree}34_{five}21_{six}$

D.

$34_{five}21_{six}22_{\operatorname{\mathrm{th}}ree}$

10

In what number base is the addition 465 + 24 + 225 = 1050?

Ten

Nine

Eight

Seven

In what number base was the addition 1 + nn = 100, where n > 0, done?

n - 1

n

n + 1

n + 2

Find the value of x for which $32_{four}=22_{x}$

three

five

six

seven

Convert $101101_{two}$ to a number in base ten.

61

46

45

44

Two numbers $24_{x}$ and $31_{y}$ are equal in value when converted to base ten. Find the equation connecting x and y.

2x = 3 (y - 1)

4x - y = 1

3y + 2x = 3

3y = 2 (x + 3)

Find $(101_2)^2$ , expressing the answer in base 2

10101

11001

10010

11101

Simplify: $11011_{two}$ − $1101_{two}$

$101000_{two}$

$1100_{two}$

$1110_{two}$

$1011_{two}$

Find the missing number in the addition of the following numbers, in base seven. 4 3 2 1 1 2 3 4 * * * * 1 2 3 4 1

3453

5556

6016

13453

If $104_{x}$ = 68, find the value of x

5

7

8

9

Arrange in ascending order of magnitude: $26_8$ , $36_7$ and $25_9$ .

$25_926_836_7$

$26_825_936_7$

$36_726_825_9$

$36_725_926_8$

Evaluate $(20_{\operatorname{\mathrm{th}}ree})^2$ - $(11_{\operatorname{\mathrm{th}}ree})^2$ in base three

101

121

202

2020

Convert 77 to a number in base two

1001101

111001

100110

10101

If $M5_{ten}$ = $1001011_{two}$ find the value of M.

5

6

7

8

Given, that $4P4_5$ = $119_{10}$ find the value of P

1

2

3

4

Evaluate $(111_{two})^2$ - $(101_{two})^2$

$10_{two}$

$100_{two}$

$1100_{two}$

$11000_{two}$

Evaluate $202^2_{\operatorname{\mathrm{th}}ree}$ - $112^2_{\operatorname{\mathrm{th}}ree}$

21120

21121

21112

21011

If y = $23_{five}$ + $101_{\operatorname{\mathrm{th}}ree}$ find y, leaving your answer in base two

1110

10111

11101

111100

Convert the decimal number 89 to a binary number.

101101

111001

1001001

1011001

Convert 35 to a number in base two.

$10011_{two}$

$100011_{two}$

$110010_{two}$

$1011_{two}$

Convert 89ten to a number in base two.

1101001

1011001

1001101

101101

If $23_{y}$ = $1111_{two}$ , 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑦.

4

5

6

7

If $101_{two}$ + $12_{y}$ = $23five$ , find the value of y.

8

7

6

5

Simplify: $(11_{two})^2$

$1001_{two}$

$1101_{two}$

$101_{two}$

$10001_{two}$

Change $432_{five}$ to a number in base three.

$10100_{three}$

$11100_{three}$

$11101_{three}$

$10110_{three}$

Express $413_7$ in base 5.

$1131_5$

$1311_5$

$2311_5$

$2132_5$

Arrange the following numbers in ascending order of magnitude: $110_{two}$ , $31_{eight}$ , $42_{five}$ .

A.

$110_{two},31_{eight},42_{five}$

B.

$110_{two},42_{five},31_{eight}$

C.

$31_{eight},42_{five},110_{two}$

D.

$42_{five},31_{eight},110_{two}$

36

The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.

Seven

Eight

Nine

Ten

Given that $21_5$ = $14_{x}$ . Find the value of x.

4

5

6

7