Federal Way Middle School Math Contest
Individual Test 2010
1. What is the sum of 1,285,974 and 3,452,768?
A. 4,738,742* B. 4,737,742 C. 4,727,742 D. 4,727,732 E. NOTA
2. What is the area of a triangle inscribed in a rectangle, if the area of the rectangle is 48𝑐𝑚2 .
A. 16𝑐𝑚2
B. 24𝑐𝑚2 *
C. 8𝑐𝑚2
D. 12𝑐𝑚2
E. NOTA
3. The average (mean) of 10 consecutive integers is 10.5. What is the largest integer in the set?
A. 13
B. 6
C. 15 *
D. 16
E. NOTA
4. How many distinct ways can you arrange the letters in “alfalfa”? (Switching the place of two
identical letters does NOT count as a different arrangement.)
A. 5040
B. 2520
C. 840
D. 210 *
E. NOTA
D. 9
E. NOTA*
5. What is the units digit of 72010.567?
A. 1
B. 3
C. 7
6. If A # B = A + B - (AB), what is 4 # 5?
A. -11 *
B. -7
C. 12
D. 29
E. NOTA
7. What is the other leg of a right triangle with hypotenuse of 41 and one leg of 40?
A. 60
B. 12
C. 9 *
D. 3281
E. NOTA
8. It takes Justin 3 hours to mow a lawn. It takes Paul 5 hours to mow the same lawn. How long,
in hours, will it take to mow the same lawn if they work together at the rates above?
A.
15
8
*
B.
8
15
C. 4
D. 3
E. NOTA
9. How many different ways can 3 people stand in a line?
A. 6 *
B. 9
C. 3
D. 4
E. NOTA
39
10. What is 273 reduced to lowest terms?
1
A. 4
1
1
B. 5
C. 6
1
D. 7 *
E.NOTA
11. What is the slope of a line that is perpendicular to the line 2x + 5y + 4 = 0?
5
A. 2 *
5
B. - 2
2
C. 5
2
D. - 5
E. NOTA
12. A car travels 8 miles east, 8 miles north then 2 miles west. How many miles is the car from
its original starting point?
A. 12
B. 14
C.10 *
D. 8
E. NOTA
13. How many cubic feet are in a cubic yard?
A. 27 *
B. 9
C. 3
D. 81
E. NOTA
14. If f(x) = x2 + 3x + 1, what is the value of f(4)?
A. 21
B. 4
C. 22
D. 25
E. NOTA *
15. A sheep is tied with a rope of length 4 feet to a corner of a square barn with a side length of 3
feet. What is the total area, in square feet, that the sheep could graze?
A. 12.5π *
B. 9π
C. 16π
D. 12π
E. NOTA
16. One video is 4 hours and 18 minutes. A second video is 2 hours and 43 minutes. How much
longer, in minutes, is the first video?
A. 35
B. 95 *
C. 85
D. 55
E. NOTA
17. If 2 zips equal 3 zaps and 9 zaps equal 5 zups. How many zups equal 18 zips?
A. 45
B. 30
C. 12
D. 15 *
E. NOTA
18. What is the mean of the mode, median, and range of the following set of numbers?
{10, 2, 6, 9, 8, 6, 7, 8,7 ,7 ,9}?
A. 7
B. 6
C. 8
79
D. 11
E. NOTA *
19. Express .125 as a fraction.
3
A. 8
2
B. 5
1
C. 6
1
D. 8 *
E. NOTA
20. What is
101!
99!
A. 10100 *
?
B. 101
C. 10,100,000
D. 10101
E. NOTA
21. How many different ways can change be made for one dollar using quarters, dimes and/or
nickels?
A. 27
B. 28
C. 29*
D. 30
E. NOTA
7 3
−
22. Simplify 84 42?
−
5 3
31
A. 32
15
B. 16*
C.
7
8
5
D. 6
E. NOTA
23. Express 245,000,000 in scientific notation.
A. 2.45 × 107
B. .245 × 1010
C. 245 × 108
D. 24.5 × 106
E. NOTA*
24. Solve for x: x2 + 6x + 8 = 0
A. 2,4
B. -2,4
C. 2,-4
D. -2,-4 *
E. NOTA
25. Metal A is 25% copper. Metal B is 50% copper. Using only those two metals, how many
grams of Metal A are needed to make 1500 grams of a metal with 45% copper?
A. 200
B. 300*
C. 1200
1
D. 1300
E. NOTA
D. 25% *
E. NOTA
1
26. What percent of 6 ÷ 2 is 6 × 2 ?
A. 20%
B. 10%
C. 50%
27. My secret positive number has two digits, is relatively prime to 330, is not prime, and the
sum of its digits is odd. What is it? (two numbers are relatively prime if they share no common
factors other than 1)
A. 49 *
B. 30
C. 35
D. 57
E. NOTA
28. How many integers n satisfy √8 < n < √111 ?
A. 6
B. 7
C. 8*
D. 9
E. NOTA
29. Josh decided to make a pyramid of oranges such that the bottom row was a square with a side
of 9, and each subsequent row was a square with one less orange in each side (9, 8 ,7 ,...,1). How
many oranges were used in the pyramid?
A. 240
B. 211
C. 365
D. 305
E. NOTA*
30. What day of the week is it 152 days after a Friday?
A. Tuesday
B. Wednesday*
1
C. Thursday
1
D. Friday
E. NOTA
1
31. If k = 3, find the value of 𝑘 + 2𝑘.
A. 9
1
B. 4 2 *
2
C. 3
D. ∅
E. NOTA
32. If all integers are written from 1 to 237, how many times is the digit 5 written?
A. 20
B. 25
C. 40
D. 44*
E. NOTA
33. A four-digit number 432x is a perfect cube (with x being the units digit). What is the smallest
possible value of x that is greater than one?
A. 1
B. 2
C. 3
D. 4
E. NOTA*
34. There are six red marbles and ten green marbles in a jar. What is the probability of drawing a
red marble followed by a green marble, without replacement?
1
A. 2
1
B. 4*
1
C. 3
3
D. 8
E. NOTA
35. The math team has 40 people and the swim team has 30. If there are 10 people on both
teams, how many students are in either math or swim team, but not both?
A. 30
B. 40
C. 50*
D. 55
E. NOTA
36. Joseph has one penny, one nickel, one dime and one quarter. How many different sums of
money can he have using one or more of his coins?
A. 9
B. 11
C. 13
D. 15 *
E. NOTA
D. 22
E. NOTA
37. What is the cube root of 1728?
A. 14
B. 12*
C. 24
38. What is the value of abc if ab = 4, bc = 2 and ac = 18 and a > 0?
A. 10
B. 14
C. 22
D. 24
E. NOTA * 12
39. What is the sum of all positive two-digit numbers that are divisible by 5?
A. 945 *
B. 1,045
C. 1,245
D. 1,345
E. NOTA
D. 4
E. NOTA
40. Solve for x: (24x+8)(42x+3) = 82x+6
A. 1
B. 2*
C. 3