## Thursday, August 13, 2009

### [Mathematic SPM] Number Bases

1. Which of the following are the numbers in base eight?
A. 1, 2, 3, 4, 5, 6, 7
B. 0, 1, 2, 3, 4, 5, 6, 7
C. 1, 2, 3, 4, 5, 6, 7, 8
D. 0, 1, 2, 3, 4, 5, 6, 7, 8

2. Which of the following is not the number in base five?
A. 2
B. 3
C. 4
D. 5

3. State, in base ten, the value of digit 2 in the number 24418
A. 100
B. 512
C. 1200
D. 1024

4. What is the value of the red digit of 10011012
A. 25
B. 27
C. 26
D. 28

5. The value of first digit 1 in 1110001012
A. 102
B. 128
C. 225
D. 256

6. The expanded notation of 43528
A. 2 x 83 + 5 x 82 + 3 x 81 + 4 x 80
B. 2 x 84 + 5 x 83 + 3 x 82 + 4 x 81
C. 4 x 83 + 3 x 82 + 5 x 81 + 2 x 80
D. 4 x 84 + 3 x 83 + 5 x 82 + 2 x 81

7. State the number in base two for (1 x 26) + (1 x 25) + (1 x 24) + (0 x 23) + (0 x 22)
+ (1 x 21) + ( 0 x 20)
A. 11010112
B. 11010102
C. 11100102
D. 11101102

8. Express 100100112 as a number in base ten.
A. 13610
B. 12810
C. 14710
D. 25610

9. Express 10568 as a number in base ten.
A. 51210
B. 52410
C. 55810
D. 56810

10. Express 23610 as a number in base two.
A. 1001112
B. 10011112
C. 100111102
D. 110111012

11. Express 31010 as a number in base five.
A. 20025
B. 20205
C. 22235
D. 22205

12. State the value of m and n for 344215 = 3 x 5m + 4 x 53 + 4 x 52 + 2 x 5n + 1 x 50
A. m = 2, n = 1
B. m = 4, n = 1
C. m = 2, n = 0
D. m = 4, n = 0

13. Express 83 + 82 + 80 as a number in base eight.
A. 11018
B. 10158
C. 10558
D. 14508

14. Given that 2x + 21 + 20 = 1000112, the value of x is
A. 5
B. 6
C. 7
D. 8

15. Given that 100111012 = y10. The value of y is
A. 135
B. 129
C. 148
D. 157

16. Given that 111110102 = y8, the value of y is
A. 761
B. 372
C. 552
D. 231

17. Given that 1005 = m2, the value of m is
A. 101112
B. 11001002
C. 110012
D. 10101012

18. Given that m910 = 3445. The value of m is
A. 6
B. 7
C. 8
D. 9

19. Given that 2148 = T5. The value of T is
A. 1030
B. 1300
C. 1320
D. 1303

20. Express 26 + 23 + 22 + 1 as a number in base two.
A. 11001112
B. 10010102
C. 11010012
D. 10011012

21. Calculate the value of 1101112 + 1110112
A. 1100102
B. 11100102
C. 11101102
D. 1111102

22. 10110102 - 111012
A. 1111012
B. 1101012
C. 1110002
D. 1011012

23. Given that 10102 + m2 = 110012, find the value of m.
A. 10112
B. 11102
C. 11012
D. 11112

24. Given that 100002 < x2 < equiv="Content-Type" content="text/html; charset=utf-8">2, the possible value of x is
A. 100012
B. 111102
C. 100112
D. 100102

25. Express 11010012 as a number in base eight.
A. 136
B. 115
C. 151
D. 321

26. Express 3415 as a number in base eight
A. 1008
B. 1408
C. 1558
D. 5258

27. Given that x2 = 1258. The value of x is
A. 11011102
B. 11100012
C. 10101012
D. 10101102

28. Given that y5 = 10010001102. The value of y is
A. 43125
B. 44315
C. 40045
D. 12345

29. Calculate the value of 1101112 + 1110112.
A. 1100102
B. 11100102
C. 11101102
D. 1111102

30. Given that 324m = 1318, so the value of m is
A. 2
B. 5
C. 8
D. 10