Review: Numbers and Patterns

The figure has radial/rotational symmetry. What is its angle of rotation?

• 45 degrees

• 60 degrees

• 90 degrees

• 180 degrees

Answer explanation

If you rotate it by 90 degrees, the part in corner will not be the same as the original... Thus, you need to roe it by 180 degrees to obtain the same figure as the original.

Which of the following is not a positional number system?

• Hindu-Arabic

• Egyptian

• Babylonian

• Ancient Chinese

• Existence of Multiplicative Identity

• Existence of Additive Identity

• Existence of Multiplicative Inverse

• Existence of Additive Inverse

What is the result of the following modular addition?

8 +₆ 9 =

• 3

• 5

• 7

• 17

Answer explanation

(8+9)(mod 6)=17 (mod 6) = 5

17/6 = 2 remainder 5

• TRUE

• FALSE

• Cannot be determined

Answer explanation

For encoding equation y=ax+b, we cannot use an even number for a because it does not have a multiplicative inverse in Z₂₆

• TRUE

• FALSE

• Cannot be determined

Answer explanation

Its a subset but not a proper subset because they are equal.

• Associativity

• Commutativity

• Distributivity

• Closure

Based on the axis of reflectional symmetry, which of the following does not belong to the group?

• 
• 
• 
• 
• 

Answer explanation

All have vertical axis of symmetry, only the last one, does not have vertical symmetry.

TRUE or FALSE: In Roman Number System, when a symbol appears before a larger symbol it is subtracted.

• TRUE

• FALSE

• Cannot be determined.

Answer explanation

Example: in XL, the value is 40 since X(10) is subtracted from the larger symbol L which has a value 50

What is the result of the following modular multiplication?

12  X₇ 5 =  

• 11

• 4

• 6

• 60

Answer explanation

(12 * 5) mod 7

= 60 mod 7

= 4

since 60/7 = 8 remainder 4