Permutations
What is the expanded form of nPr?
True or false: The order does not matter in Counting, because you are 'picking' objects.
True
5050
What is the Pythagorean Theorem?
a^2 + b^2 = c^2
What are two types of special-angled triangles?
30°-60°-90° and 45°-45°-90°
How many 4 digit numbers with no repeating digits exist such that the first digit is even and the other 3 digits are odd?
240
How many different ways are there to choose three students from a group of seven?
35
What is the full name of the mathematician Gauss?
Johann Carl Friedrich Gauss
You can only use the Pythagorean Theorem in which type of triangle?
Right-angled triangle
A triangle has the angles 30°-60°-90°. If the hypotenuse is 6, what is the length of the other two sides?
3 and 3√3
There are a hundred students in the school of Factorial Academy. How many ways are there to select three students to fill three distinct positions on the student council from this student body?
970,200
There are 5 different-colored marbles in a bag. Sarah will pick out 3 marbles without looking. How many different ways can she pick?
10
What is 16 + 18 + 20 + 22 + 24 + 26 + 28 +30?
184
Complete the Pythagorean Triple: 7 : ? : 25
24
A square with side length √2 is cut in half diagonally to form two equal triangles. What is the length of the hypotenuse of these two triangles?
2
There are six friends: P, Q, R, S, T and U. They want to sit in a row for a group picture. If P must sit next to Q, how many different ways can they arrange themselves?
240
There are 5 cats and 4 dogs in the animal shelter. How many ways are there to pick 2 cats and 1 dog to adopt?
40
When Yunji added up all the numbers from 1 to 9, she mistakenly left out a number. Her sum was 36. What number did she leave out? (Adapted from 2024 AMC 8 Problem 4)
9
A right triangle has legs of length 5cm and 12cm. What is the length of the hypotenuse?
13
An equilateral triangle with side length 5/2 is cut in half vertically to form two new congruent triangles. What is the length of height and base of these new triangles?
(5√3)/4 and 5/4
How many rearrangements of 'abcd' are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either 'ab' or 'ba'. (2015 AMC 10A Question #10)
2
How many different pairs of numbers can you choose from 1, 2, 3, ... 100 such that their sum is an even number?
2450
What is the value of 1 + 3 + 5 + ... + 2017 + 2019 - 2 - 4 - 6 - … - 2016 - 2018? (2018 AMC 8 Problem 5)
-1008
In Triangle ABC, the short leg (AC) is 9m and the hypotenuse (BC) is 15m. What is the length of the longer leg (AB)?
12
A triangle has sides 2√2, 2√6, and 2√8. Find the angles of this triangle.
30°-60°-90°