Number Theory
What is the sum of the first 10 positive integers?
55
1+2+3+4+5+6+7+8+9+10 = 55
Solve for x: (x + 1)(x − 3) = 0
x = −1 or 3
What is the area of a triangle with sides 13, 14, and 15?
84
What is 20% of 15% of 250?
7.5
What is the 10th term of the arithmetic sequence: 5, 9, 13, … ?
41
What is the smallest positive integer n such that when 7n is divided by 10, the remainder is 1
3
If x + y = 7 and xy = 10, find x² + y².
29
A circle is inscribed in a square. What percent of the square’s area is not covered by the circle? (Round to nearest whole number)
21%
If 4 out of 10 marbles are red, what is the probability of picking two reds without replacement?
2/15
What is the 6th term in the Fibonacci sequence starting with 1, 1?
8
How many 3-digit numbers are divisible by both 4 and 9?
25
LCM(4,9)=36
Smallest 3-digit number: 100
Largest 3-digit number: 999
First 3-digit number divisible by 36
100/36=2.78=3; 3*36 =108
Last 3-digit number divisible by 36
999/36=27.75 = 27; 27*36=972
How many multiples of 36 are between 108 and 972
(972 -108)/36 + 1 =24+1=25
Solve for x: 3x² − 5x = 2
x = 2, x = −1/3
A regular hexagon has a perimeter of 72 cm. What is the area?
374.1 cm²
The ratio of boys to girls in a class is 3:4. If there are 28 students, how many are boys?
12
If the nth term of a sequence is 2n² + 3n, find the 5th term.
65
A number leaves a remainder of 2 when divided by 5, and 3 when divided by 7. What is the smallest such number?
17
The sum of the squares of three consecutive integers is 365. What are the integers?
10, 11, 12
The diagonals of a rhombus are 12 cm and 16 cm. What is the area?
96 cm²
A price is increased by 20% and then decreased by 20%. What is the net percent change?
4% decrease
A palindrome has the form abba. How many 4-digit palindromes of this form are there?
90
Find the sum of all positive integers less than 100 that are relatively prime to 100.
3040
If a, b, and c are in arithmetic progression, and a + b + c = 30 and abc = 440, what is b?
10
A right circular cone has radius 3 cm and height 4 cm. Find its volume.
12pi cm³
A bag contains 3 red, 2 blue, and 5 green marbles. What is the probability of drawing 1 red and 1 blue in that order, without replacement?
1/10
A bug crawls up 3 cm and slips down 2 cm every minute. How many minutes will it take to climb a 30 cm wall?
28 minutes