Numbers
The square of an integer ends in 9. What can its last digit be?
3 or 7
What is the next term in the sequence:
1, 1, 2, 3, 5, 8, ___
13
A ladder reaches a 12-ft wall and its base is 5 ft away from the wall. What is the length of the ladder in ft?
13 ft
What is the slope of a perpendicular line to the line 2x+3y=1?
slope of a perpendicular line: 3/2
How many prime numbers are there between 1 and 20?
8
{2,3,5,7,11,13,17,19}
What is the next number in the sequence:
1, 3, 6, 10, 15, ___
21
What is the sum of the interior angles of a pentagon?
180*3=540
A school closes if the predicted snow fall exceeds 8 inches. The forecast model is given by S(t)=2t+1 inches after t hours. After how many hours will the school close? State the exact answer.
3.5 hours
Find three consecutive integers whose sum is 72.
23,24,25
What is the 50th term of the pattern:
1, 4, 9, 16, 25, …
502=2500
A rectangle’s sides are doubled. What happens to area?
The area is multiplied by 4
If
x+1/x=5
find
x^2+1/x^2
23
Smallest number that leaves remainder 1 when divided by 2, 3, 4, and 5.
61
A rumor triples daily. Initially, 4 people know the rumor. How many people know the rumor after 5 days?
4*3*3*3*3*3=972 people
A circle is inscribed in a square of side 10. What is the area of half the circle?
25/2*pi
Simplify completely:
(b^2-a^2)/(b-a)-(b^2-a^2)/(b+a)+(a^2-c^2)/(a+c)-(a^2-c^2)/(a-c)
2a-2c
22502 - 21502 =
(2250-2150)(2250+2150)=100*440=440,000
Without adding every term one-by-one, find
1+2+3+...+40
1+40=41, 2+39=41, 3+38=41, ... you do this 20 times = 41*20=820
A paper that is 0.1 mm thick is folded 42 times. What is the thickness (in mm) after folding?
0.1*242 = 439,804,651,110 mm = 439,804 km
(For context: the distance between the Earth and the Moon is 405,500 km)
There is a meme on social media where they claim to prove that math is "broken". The "proof" is as follows:
1. Let a = b
2. Multiply both sides by a:
3. Subtract b^2 from both sides:
4. Factor both sides:
5. Divide both sides by (a-b):
6. Since a = b, substitue b for a:
7. So 2b=b. Divide by b:
8. Subtract 1 from both sides:
What is the final result. Which step is invalid, and what rule is being broken?
0=1. Step 5 is invalid because when a = b, then a - b = 0, and division by zero is undefined. Everything after that step is meaningless.