# Grade 8 Tennessee Middle/Junior High School Mathematics Contest

16. Hypotheses:

Some gidgets are widgets.

Given the above hypotheses, which is a valid conclusion?

a. Some widgets are not gadgets.
e. No valid conclusion can be reached from these hypotheses.

17. What is the ratio of the volume of a cube to its surface area if the length of a side is s?

18. A function is defined as f (x) = 3x + 4. The inverse of a function “undoes” the function.
Which of the fol lowing statements is true?
a. is the inverse of f(x).
b. There is no function that is the inverse of f(x).
c. is the inverse of f(x).
d. is the inverse of f(x).
e. is the inverse of f(x).

19. The mean high temperature in Nashville for the first twenty-one days of February was 46
degrees. What must the mean high temperature for the days from February 22 to February
28 be in order to raise the mean temperature for the entire month to 50 degrees?

a. 54°
b. 56°
c. 58°
d. 60°
e. 62°

20. The length of a rectangle is increased by 20% and its width is increased by 50%. What is
the percent increase in its area?

a. 10%
b. 30%
c. 70%
d. 80%
e. 100%

21. Pat has a collection of stickers for numbering pages in a scrapbook. Each sticker has 1 digit
on it (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Pat has twenty- two stickers that have "2" on them. Pat
has plenty of the rest of the digits. If Pat starts at 1, how many pages can he number?

a. 22
b. 99
c. 112
d. 119
e. 199

22. In my pocket, I have only dimes and quarters. I have twice as many dimes as quarters and I
have at least one quarter . If the number of dimes and quarters is reversed, by what percent
will the value of the money in my pocket increase?

c. 50%
d. 150%
e. 100%

23. In modular arithmetic , the statement 15 ≡ 3 mod 4 means that 15 and 3 both have the same
remainder when they are divided by 4. These would all be true statements in modular
arithmetic:

12 ≡ 7 mod 5
7 ≡ 13 mod 2
14 ≡ 42 mod 7

Consider the following statement where, a, b, c, d, and m are whole numbers {0, 1, 2, 3, ...}.

A: If a ≡ b (mod m) and c≡ d (mod m), then (a + b) ≡ (c + d) (mod m)
B: If a ≡ b (mod m) and c≡ d (mod m), then ( a · b) ≡ ( c · d ) (mod m)
C: If a ≡ b (mod m), then ( ac ) ≡ ( bc ) (mod m)

Which of the following is true?

a. Only Statement A is true for all whole numbers a, b, c, d, and m.
b. Only Statement B is true for all whole numbers a, b, c, d, and m.
c. Only Statement C is true for all whole numbers a, b, c, and m.
d. All three statements are true.
e. None of the statements is true for all whole numbers a, b, c, d, and m.

24. Which of the following pairs of algebraic expressions are equivalent ?

a. (x + 2)2 x2 and 2(x + 2) + 2x
b. (x + 3)2 and  x2 + 9
c. 2(xy) and 2x · 2y
d. and x + 3
e. 0x0 and 00

25. A nickel, a dime, and a penny are tossed. What is the probability that they do not all land
the same way—they are not all either heads nor are they all tails?

a.
b. 20%
c. 50%
d. 25%
e. 75%

26. The graph below shows the distribution for 100 rolls of two dice.

 100 Rolls of Two Dice

Sum of Two Dice

Which statement is true about the distribution of the sums of the two dice?

a. The standard deviation is 0.
b. The mean is 9.09.
c. The median is 6.
d. The mean is 6.64
e. The median is 6.5

27. When 1093 - 93 is ex pressed as a single whole number, what is the sum of its digits?

a. 10
b. 93
c. 819
d. 826
e. 833

28. A calculator displays 5.1698788285E+58 when 2542 is entered. Which statement is true?

a. The answer displayed is not exact.
b. The answer to 2542 would have 58 zeros at the end, if the calculator had a big enough
display.
c. The answer to 2542 would have 48 zeros at the end, if the calculator had a big enough
display.
d. The answer to 2542 would have 47 zeros at the end, if the calculator had a big enough
display.
e. The answer to 2542 would have 49 zeros at the end, if the calculator had a big enough
display.

29. A student sketched a graph of a situation as shown below:

TIME

Which situation would fit the above sketch?

a. A runner ran up a hill at a constant speed. The runner slowed down halfway up the
hill and then sped back up again.
b. A runner ran down a hill at a constant speed. The runner stopped to drink some
water. Then the runner started running at a constant speed again.
c. A runner started at the top of a hill. As he ran down, he gained speed. When he got
to a level part, he maintained his speed at a constant rate. Then the runner started
speeding up again.
d. A runner started a race at a constant speed. Then the runner gained speed during the
middle of the race. Finally the runner ended at a constant speed that was faster than
her beginning speed.
e. A runner started a race running very slowly and gradually accelerated at a constant
rate throughout the race.

30. A triangle has vertices A (3, 7), B (0, -1), and C (6, 2). The coordinates of each point are
multiplied by 6 to produce three new points. The new points are the vertices of a second
triangle. Which statement is true?

a. The new triangle is not necessarily similar to the original triangle.
b. The area of the new triangle is 36 times the area of the original triangle.
c. The perimeter of the new triangle is 36 times the area of the original triangle.
d. The area of the new triangle is 6 times the area of the original triangle.
e. The new triangle is congruent to the original triangle.

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