10 second calculations
Solve for x.
x99999999 = x
x = 0, ±1
099999999 = 0
199999999 = 1
(-1)99999999 = -1
Identify and correct the mistake.
a = b
a - b = 0
(a - b)(n) = 0
(a + b)(a - b) = b(a - b)
a + b = b
2 = 1
(a + b)(a - b) = b(a - b)
(a + b) (0) = b (0)
These zeros cannot be cancelled because dividing by zero is undefined.
Which number comes next?
6/11, -7/22, 8/44, ?
-9/88
Identify ALL of the following mathematicians:
A. related the sides of a right triangle
B. invented calculus and the 3 laws of motion
C. discovered the following sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, …
A. Pythagoras
B. Newton
C. Fibonacci
Last Christmas, my sister was 25% my age.
This Christmas, she is 33% my age.
How old will I be next Christmas?
Answer: 10 years
(Guess and check!!!)
Last Christmas:
8 years × 0.25 = 2 years
This Christmas:
9 years × 0.33 ≈ 3 years
∴ next year I will be 10 years old.
Solve for x.
4x2 - 8 = 37 - x2
4x2 - 8 = 37 - x2
5x2 - 8 = 37
5x2 = 45
x2 = 9
x = 3 or -3
You roll a die 50 times.
Rolling an even number doubles your money and rolling an odd number halves it.
You roll 21 odd numbers.
If you had $1 initially, how much money do you have after your risky game?
50 total rolls - 21 odd = 29 even rolls.
Initial $1 x 2even / 2odd
= $1 x 229 / 221
= $1 x 28
= $256
Let y = -4πi√5
Simplify in terms of i, x, and x'
47{ln[sec3(x)+[(d/dx)(e2π-logx√y)]-cos4y[(d2/dx2)4y√π]-72y2x+(4/√y)}0
Where x≠(π/2)±πn, and n∈ℤ
Answer: 47
Anything to the power of zero is one.
47{x∼y}0
47(1)
47
Arrange the following fractions in ascending order:
17/40, 1/2, 5/12, 7/17, 5/11
7/17, 5/12, 17/40, 5/11, 1/2
The volume of a sphere can be calculated with the following formula:
V=4πr3/3
If a Christmas ornament has a diameter of 10cm, what is its volume?
r = 10/2=5cm
V = 4πr3/3
V = 4π (5)3 /3
V = 500π/3cm3
≈ 523.6cm3
Solve:
1 + + - + - 1 - - + - 1 - - 1 - - - - - - - 0
Answer: 2
1++-+-1--+-1--1-------0
1 + 1 - 1 + 1
2 - 1 + 1
1 + 1
2
Evaluate the following:
2^(2^(2^(2)))
65536
What number am I?
I am a perfect cube.
My absolute value is between 1 and 6000 (inclusive).
I am not divisible by 4.
The sum of my digits is divisible by 2, but not 4.
None of my digits repeat.
729
Find the error:
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.333... + 0.666... = 0.999...
3/3 = 1
Therefore 0.999... = 1
While 2/3 = 0.666... is technically correct, we cannot simply add 0.333... to it as if were not repeating in this case. Since 2/3 actually rounds to 0.666...7, we must consider the very last digit of 0.666... to be a 7, resulting in 3/3 making up to be a perfect 1.
0.333... + 0.666...7 = 1
A 25m tall man stands next to a Christmas tree twice his height.
Another man stands next to the Christmas tree, and he is exactly 60% the tree’s height.
What is the difference in height between the 2 men?
Answer: 5m
Tree height: 2 × 25m = 50m
The second man's height:
60% = 0.6
0.6 × 50m = 30m
Difference in height:
30m - 25m = 5m
A cube's surface area is 24cm2.
What is its volume?
The volume is 8cm3.
A cube has 6 congruent faces, meaning each face is a square whose area is 24/6 or 4cm2.
Square root the area to find the side length, and since all side lengths are the same in a cube, the volume can be found with 2cm x 2cm x 2cm.
(Use exponents)
(28)(33)(5)
Name the first 12 digits of pi.
3.14159265358
(Also accept 3.14159265359)
If n% of y is x, then in terms of n, what percent of x is y?
y (n / 100) = x
(y) (n) = 100x
y = 100x / n
y = (x) (100/n)
100/n x 100% = 10 000/n %
Assuming the volume of an average snowflake is
3.16x10-18 km3 , how many cubic millimeters is an average snowflake? (1000mm = 1m, 1000m = 1km)
Answer: 3.16 mm3
*Reminder: Cubic measurements increase exponentially.
1km3 x 1000m/km x 1000m/km x 1000m/km
= 109m3
Multiple Choice: What is the square root of 790321?
A) 905
B) 889
C) 866
D) 907
Answer: C) 889
The unit digit of the square is completely dependent on the unit digit of the square root.
Look at the last digit of 790321. For an integer to have its square end in 1, the unit digit (last digit) must be either 1 or 9 (as 12=1, 92=81)
For example, the square root could not end in 7 because when you multiply it out, the square would end in 9 (as 72=49)
Hence the answer must be 889.
The square root of a negative number is undefined, and is denoted by a real number multiplied by √(-1) or i.
Therefore, i2 = -1 and √(-9) = 3i
Solve the following in terms of i:
[ √(-100) ] [ i3 + i - 1/2 ] - 42i8 + 13i7
(10i) [ i2i + i - 1/2 ] - 42i2i2i2i2 + 13i2i2i2i
10ii(-1) + 10ii - 10i (1/2) - 42(-1)4 + 13(-1)3i
-10(-1) + 10(-1) - 5i - 42 + (-13)i
10 - 10 - 5i - 42 - 13i
The answer is -18i - 42 or -6 ( 3i + 7)
CMXCVIII + CDXCI + MCCLXXIX
MMDCCLXXVIII
998 + 491 + 1289
=2778
The default base system is base 10. In other number systems, such as base 2 (binary) or base 8, counting resets and another digit is added when a certain number is reached (similar to how after 9, the digits reset to 0 and a 1 is added to create 10).
Ex. In binary, 2 is denoted by 10, 3 by 11, and 4 by 100.
In a certain number system, the number 31 is denoted by "43".
What base system is this? Assume the base of the system is a natural number. (1, 2, 3, ...)
Base 7
Since the new number outside base 10 is larger, the base system must be of a number less than 10.
If we replace 43 with 40 (subtract 3 temporarily), this must be the fourth multiple of the base as the unit digit has been newly replaced with zero. In base 10, the base is evident when we divide 40 by 4 and end up with 10, but we can solve for this value in an unknown base by comparing it to its base 10 counterpart, being 31-3=28.
28/4=7
Base 7.
Decipher the following phrases:
A) 13, 5, 18, 18, 25, 3, 8, 18, 9, 19, 20, 13, 1, 19
B) "NZGS RH ORUV"
A) "MERRY CHRISTMAS"
Key: Mathematical cipher
A=1, B=2, C=3, ... Z=26
B) "MATH IS LIFE"
Key: Atbash cipher
A=Z, B=Y, C=X, ... M=N