FINDING THE PATTERN FROM THE GIVEN RULE WORKSHEETS

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}

Solution

Problem 2 :

Double the input number plus two

Output numbers  {2, 4, 10}

Solution

Problem 3 :

Rule : Five times the input number minus three

Output numbers {7, 12, 17}

Solution

Problem 4 :

Rule : Add one to the input number then double the result 

Output numbers  {2, 6, 12}

Solution

Problem 5 :

Rule : Multiply the input number by itself then add one

Output numbers : {2, 5, 17}

Solution

Problem 6 :

Rule : Multiply the input number by one more than itself.

Output numbers {2, 6, 20}

Solution

Part B :

For the following input numbers and output numbers, find the rule in the number crunching machine :

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

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.

Solution

Answer Key

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, .............

Example 1  :

The formula for finding the circumference C of a circle with radius r is C  =  2∏r.

Find :

a) The circumference of a circle of radius 4.2 cm.

b) The radius of a circle with circumference 112 cm.

c) The diameter of a circle with circumference 400 meters.

Example 2  :

When a stone is dropped from the top of a cliff, the total distance fallen is given by the formula

D  =  1/2gt²

where D is the distance in meters and t is the time taken in seconds. Given that g  =  9.8 ms^-2,Find :

a) The total distance fallen in the first 2 seconds of fall

b) The height of the cliff, to the nearest metre, if the stone takes 4.8 seconds to hit the ground.

Example 3  :

When a car travels a distance d kilometers in time t hours, the average speed for the journey is given by the formula

s  =  d/t kmh^-1

Find :

(a) The distance travelled by a car in 2 3/4 hours if its average speed is 80 kmh^-1.

(b) The time taken, to the nearest minute, for a car travel 790 km at an average speed of 95 kmh^-1

Example 4 :

A circle’ s area A is given by

A  =  ∏r²

where r is the length of its radius.

Find :

(a) the area of a circle radius 6.4 cm

(b) the radius of a circular swimming pool which has an area of 160 m²

Example 5 :

A cylinder of radius r and height h has volume given by

V  =  ∏r²h

Find :

(a) the volume of a cylindrical tin can of radius 8 cm and height 21.2 cm.

(b) the height of a cylinder of radius 6 cm and volume 120 cm³

(c) the radius, in mm, of a copper pipe of volume 470 cm³ and length 6 m

Solution

Example 6 :

If p is a positive integer greater than 1, which of the following must be negative? 

(A) 5 - p     (B) 2p - 6    (C) 1 - p    (D) -p + 3   (E) 2p + 3

Solution

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