Basic Mathematics Practice
A collection of basic to intermediate mathematics problems covering arithmetic, algebra, geometry, number theory, and combinatorics suitable for high school practice.
Questions
What is the sum of the first 100 positive integers?
- 5050
- 5150
- 5250
- 5350
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is known as the Pythagorean theorem. If the hypotenuse of a right triangle is 10 and one of the other sides is 6, what is the length of the third side?
- 4
- 6
- 8
- 10
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. What is the smallest prime number?
- 1
- 2
- 3
- 5
A permutation is an arrangement of a set of elements in a specific order. How many permutations are there of the letters in the word "APPLE"?
- 60
- 120
- 240
- 360
A combination is a selection of items from a set where the order of the items does not matter. How many combinations are there of 3 letters from the set {A, B, C, D, E, F, G}?
- 21
- 35
- 56
- 70
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers. The first two numbers in the sequence are 0 and 1. What is the 10th number in the Fibonacci sequence?
- 34
- 55
- 89
- 144
A function is a relation that assigns to each element of a set a unique element of another set. If f(x) = x^2 + 2x + 1, what is the value of f(-1)?
- 0
- 2
- 4
- 6
A line is a one-dimensional geometric figure that extends infinitely in both directions. What is the equation of a line that passes through the points (2, 3) and (5, 7)?
- y = 2x + 1
- y = 2x - 1
- y = x + 3
- y = x - 3
A circle is a two-dimensional geometric figure that is defined by a fixed point (the center) and a fixed distance (the radius) from the center to any point on the circle. What is the area of a circle with radius 5?
- 25π
- 50π
- 75π
- 100π
A sphere is a three-dimensional geometric figure that is defined by a fixed point (the center) and a fixed distance (the radius) from the center to any point on the sphere. What is the volume of a sphere with radius 3?
- 36π
- 72π
- 108π
- 144π
A cube is a three-dimensional geometric figure that has six square faces. What is the volume of a cube with side length 4?
- 64
- 128
- 192
- 256
A pyramid is a three-dimensional geometric figure that has a polygonal base and triangular sides that meet at a common point (the apex). What is the volume of a pyramid with square base side length 6 and height 8?
- 96
- 192
- 288
- 384
A cone is a three-dimensional geometric figure that has a circular base and a single vertex. What is the volume of a cone with radius 5 and height 10?
- 50π
- 100π
- 150π
- 200π
A cylinder is a three-dimensional geometric figure that has two circular bases and a curved surface. What is the volume of a cylinder with radius 4 and height 6?
- 96π
- 192π
- 288π
- 384π
A sphere is a three-dimensional geometric figure that is defined by a fixed point (the center) and a fixed distance (the radius) from the center to any point on the sphere. What is the surface area of a sphere with radius 5?
- 100π
- 200π
- 300π
- 400π