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ARCHIVE of PROBLEMS TO PONDER and the ANSWERS for Middle School:
Posted 02/02:
Melvin draws a rectangle with a perimeter of 68 mm. If the length of the rectangle is 20 mm, what is
the area of the rectangle?
A.
B.
C.
D.
400 square millimeters
320 square millimeters
280 square millimeters
196 square millimeters
SOLUTION:
THE MATH BLACKBOARD
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through interactive, online tutoring and academic support
www.mathblackboard.com
[email protected]
218-310-1940
Posted 01/30:
Which rule can be used to find the value of any term in the sequence below where n represents the
position of the term?
Position Value of term
1
6
2
10
3
14
4
18
5
22
n
A. 2n + 4
B. 8n – 2
C. 3n + 3
D. 4n + 2
Two approaches to the solution:
1. Test each rule to see if you get each ‘value’ by plugging in each ‘position’ to the rule. For
example, using rule A., we plug n=1 into it and get 2(1) + 4 = 6, which is true. BUT, using n=2
gives 2(2) + 4 = 8, which is NOT 10. So rule A is not the correct answer. Do this for each rule
until you find the one that fits ALL table entries.
2. Notice each term value increases by 4. This is the “rate of change” or slope. Decreasing
position 1’s value by 4 gets us 2 (at position 0), which is the y-intercept. The only rule that fits
this information is D.
THE MATH BLACKBOARD
Emboldening students to reach their true math potential
through interactive, online tutoring and academic support
www.mathblackboard.com
[email protected]
218-310-1940
Posted 01/28:
Which number comes next in the pattern?
14, 16, 20, 28, ….
A. 38
B. 40
C. 44
notice there is an increase in value of 2 then 4 then 8 as the
numbers increase from 14 to 16 to 20 to 28. The values of
2, 4, and 8 are “powers of 2”. That is, 2 = 2𝟏 , 4 = 22 , and 8 = 23 .
So the next increase is by 16 = 24 . This gives 28 + 16 = 44.
D. 48
Posted 01/22:
Math quiz scores (the number correct) for 11 students are:
7, 10, 5, 7, 9, 10, 8, 6, 8, 10, 4
Find the minimum, maximum, range, mode, median, and mean for this set of data.
ANSWERS:
Minimum: 4
Maximum: 10
Range: 6
Median: 8
Mode: 10
Mean: 7.636
smallest value in the list
largest value in the list
difference between the max and min (10 – 4)
the middle value when values are listed least to greatest
the value that occurs most often
add the values; then divide by the number of values in the list
THE MATH BLACKBOARD
Emboldening students to reach their true math potential
through interactive, online tutoring and academic support
www.mathblackboard.com
[email protected]
218-310-1940
Posted 01/21:
A water pipe in Mike’s Machine Shop broke at 6:00 P.M. on Tuesday. The broken pipe leaked water at a rate of
2 quarts per hour. The pipe was not repaired until 8 A.M. on Thursday. How many gallons of water leaked from
the pipe?
A. 76 gallons
B. 38 gallons
C. 19 gallons There are 4 quarts in one gallon; so 2 quarts leaking per hour means ½ gallon leaked per hour.
The water was leaking for 38 hours; so the total number of gallons lost was 38 * ½ , which is 19.
D. 4 gallons
Posted 01/20:
On a coordinate grid, which of the following describes a path to get from (0,0) to (6,3) to (8,6)?
A. Right 3, up 6, right 3, up 2
B. Right 6, up 3, right 2, up 3 To move from (0, 0) to (6, 3), we move 6 right and 3 up. Then from that point
(6, 3) we need to move just 2 more right and 3 more up to get to (8, 6).
C. Right 6, up 8, right 2, up 3
D. Right 8, up 6, right 3, up 2
Posted 01/19:
About 1,300,000,000 people ride the New York Subway System each year. What is the value of the 3 in
1,300,000,000?
A. Three hundred thousand
B. Three million
C. Three hundred million
D. Three billion
Posted 01/16:
Multiple choice:
1. A National Park in Alaska has eighty thousand, nine-hundred twenty-three and eighty-six hundredths
acres of nonfederal land. Which shows this number in standard form?
A. 80,923.68
B. 80,923.86
C. 80,923.086
D. 80,923.806
2. Determine the numbers that best complete the pattern: 82, 73, ____, ____, 46, 37
A. 65, 56
B. 64, 55
C. 82, 91
D. 37, 64