Part A :
Given the following output numbers and rules, calculate the corresponding input numbers :
Problem 1 :
Rule : the input number plus four
Output numbers {5, 7, 15}
Problem 2 :
Double the input number plus two
Output numbers {2, 4, 10}
Problem 3 :
Rule : Five times the input number minus three
Output numbers {7, 12, 17}
Problem 4 :
Rule : Add one to the input number then double the result
Output numbers {2, 6, 12}
Problem 5 :
Rule : Multiply the input number by itself then add one
Output numbers : {2, 5, 17}
Problem 6 :
Rule : Multiply the input number by one more than itself.
Output numbers {2, 6, 20}
Part B :
For the following input numbers and output numbers, find the rule in the number crunching machine :
Problem 1 :
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
Problem 6 :
Part C :
Use the rules to list the first six terms of the sequence
(1) Start with 1 and add 2 each time
(2) Start with 3 and multiply by 2 each time
(3) Start with 24 and subtract 8 each time
(4) Start with 32 and divide by 2 each time
(5) Start with 5 and double each time
(6) Start with 1 and 2 and add the previous two numbers to get the next one.
Part A answers :
(1) 1 ==> 5, 3 ==> 7, 11 ==> 15
(2) 0 ==> 2, 1 ==> 4, 4 ==> 10
(3) 7 ==> 2, 3 ==> 12, 4 ==> 17
(4) 0 ==> 2, 2 ==> 6, 5 ==> 12
(5) ±1 ==> 2, ±2 ==> 5, ±4 ==> 17
(6) 1 and -2 ==> 2, 2 and -3 ==> 6 and 4 and -5 ==> 20
Part B answers :
(1) y = 3x
(2) y = 2x+1
(3) y = 2x+5.
(4) y = 4x+1.
(5) y = 5x-2
(6) y = 3x+4
Part C answers :
(1) 1, 3, 5, 7, 9, 11, ........
(2) 3, 6, 12, 24, 48, 96, ................
(3) 24, 16, 8, 0, -8, -16, ...............
(4) 32, 16, 8, 4, 2, 1, ..........
(5) 5, 10, 20, 40, 80, 160, .........
(6) 1, 2, 3, 5, 8, 13, .............
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