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Math Challenge
Math Challenge
1. Hailey added the product of
9 and 12 to the product of 7
and 5. She then subtracted the
product of 4 and 6 from the
result. What was her final
answer?
Math Challenge
Answer: 119
Math Challenge
2. Set A = {B, R,E,A,K,S}
Set B = {R, A, I, S, E,D}
How many proper
subsets does A ∩ B
contain ?
Math Challenge
Answer:
15
Hint: Find the letters in common. Count them. Use this
number as the exponent of 2. Two to the 4th power results
in 16 subsets. Subtract one to get the number of proper
subsets.
Math Challenge
What is the area
of a rhombus with
diagonals of 10 cm
and 28 cm ?
3.
Math Challenge
Answer:
140
The area of a rhombus equals the product of the diagonals
divided by 2.
Math Challenge
4. Two numbers are
relatively prime if their
only common factor is one.
How many positive integers
less than 21 are relatively
prime to 21 ?
Math Challenge
Answer:
12
For the #15, eliminate all multiples of 3 and 7.
Math Challenge
5. What is the area of
a triangle with a
base of fourteen and
a height of ten?
√49
Math Challenge
Answer:
70
The area of a triangle is base times height divided by 2.
Math Challenge
6. On a 12-hour clock, what
is the measure of the acute
angle between the hour and
minute hand at 4:30?
Math Challenge
Answer:
45 degrees
A circle contains 360 degrees. There are 12 hours on the
face of the clock. Divide 360 by 12, so 30 degrees separate
each number on the clock. At 4:30, the minute hand points
to the 6, and the hour hand is exactly half-way between the
4 and the 5. So, 30+15 = 45.
Math Challenge
7. Subtract the cube of
five from the square of
17. The result is 6 less
than ____ .
Math Challenge
Answer:
170
Hint: Cube means “to the third power.” Square means “to
the second power.”
Math Challenge
What is the
units digit of 4
th
to the 97
power?
8.
Math Challenge
Answer:
4
Hint: Write the first four powers of 4, which are 4, 16, 64,
and 256. Notice that 4 and 6 repeat, so every odd power
would end in a 4 and every even power would end in a 6.
The units digit is another name for the one's place.
Math Challenge
9. If A#B = 14 x A + B - 2
then what is the
value of 8#17 ?
Math Challenge
Answer:
127
Hint: Substitute 8 for A and 17 for B.
Math Challenge
10.
What is the
least common
multiple of 16
and 18?
Math Challenge
Answer:
144
Hint: The least common multiple (LCM) is the first
multiple that occurs on both lists of multiples. List the
multiples of 16 and 18. The first multiple on both lists is
144.
Shortcut: The LCM = (the product of the numbers)
divided by the GCF
Math Challenge
How many
prime numbers are
between 1 and 80?
11.
Math Challenge
Answer:
22
There are 25 primes between 1 and 100. Fifteen of these
are between 1 and 50. Ten of these are between 51 and 100.
97, 89, and 83 are prime, so 25 – 3 = 22.
Math Challenge
What is the sum
of the perimeters of
4 triangles and 5
squares if all sides
measure 6 inches?
12.
Math Challenge
Answer:
192
The perimeter of a polygon is the sum of the lengths of its
sides.
Math Challenge
13. 67.5 hm = _____ dm
Math Challenge
Answer: 67,500
King Henry Doesn't Mind Drinking Chocolate Milk
Km, hm, dam, meter, dm, cm, mm
Math Challenge
14. What is the sum of the
factors of 120 ?
Math Challenge
Answer: 360
Hint: The prime factorization of
120 is 2³ x 3 x 5. To find the sum,
(2³+2²+2+2°)x(3+3°)x(5+5°), which
is 15x4x6 which equals 360. You
could also just write the 16 factors
and add them.
Math Challenge
15. What is product of the
units digit and the tens
digit of 54,702 ?
Math Challenge
Answer:
0
Math Challenge
16. What is the prime
factorization of 280 ?
Math Challenge
Answer: Two to the third
power times five to the first
power times seven to the
first power.
Make a factor tree for 280.
Math Challenge
17. What is the
perimeter of a square
with an area of 289
square inches ?
Math Challenge
Answer: 68
Hint: 289 is a perfect square. 17²=324, so each side of
the square is 17. The perimeter is 68.
Math Challenge
18. If f(M) = 4M + 12,
what is the value of
f(15) ?
Math Challenge
Answer: 72
Hint: Substitute 15 for the letter M. The expression 3M
means 3 times M. In algebra, when a number is directly
beside a letter, it indicates multiplication.
Math Challenge
19. If 12 men can make 60
widgets in 3 days, how
many men will need to
work at the same rate to
make 20 widgets in 6 days?
Math Challenge
Answer: 2
Hint: Multiply 12 x 3 = 36. It takes 36 man-days to
produce 60 widgets. Therefore, it only takes 12 man-days
to make 20 widgets. So, 6 days times 2 men would equal 12
man days. The answer is 2.
Math Challenge
20. Which of these is an
irrational number:
A: 6.7389
B: the square root of 144
C: 3/5
D: π
Math Challenge
Answer: D
An irrational number is not an integer and not a fraction.
An irrational number can be represented by a decimal
value that is never ending and never repeats a pattern.
A,B, and C are rational. Only D is irrational.
Math Challenge
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