Answer all the questions below and press submit to see how many you got right.
Area : The amount of unit squares that is needed to cover a 2-dimensional shape.
Base area : In a prism or pyramid base area refers to the area of the base face of the pyramid or prism.
Base triangle : If the base face of a pyramid or prism is a triangle it is called base triangle.
Centimeter : A centimeter ($cm$) is $\frac{1}{100}$ of a meter.
Cubic centimeter : A cubic centimeter or $cm^3$ is a unit to measure volume. A cubic centimeter is the volume of a cube with edge length 1 centimeter and we have $1,000,000 cm^3=1 m^3.$
Height : In a triangle a height (or altitude) is the shortest line segment that connects a side to its opposing corner. A height of a triangle is perpendicular to the side is started at. The three heights of a triangle intersect in a point, the so called orthocenter of the triangle. In a parallelogram the height is the shortest distance between two opposing sides. In a pyramid the height is the shortest distance between the base area and the corner of the pyramid that is not part of the base area. In a prism the height is the shortest distance between the two base faces.
Product : A product is the result of a multiplication.
Square centimeter : Square centimeter or $cm^2$ is a unit of measurement for measuring area. 1 square centimeter is the area of a square with side length 1 $cm,$ so 10,000 $cm^2$ are one $m^2.$
Triangular prism : A triangular prism is a prism that has triangles as bases.
Volume : Volume refers to the size of a three-dimensional objects measured by how many unit cubes it would take to fill the shape.
What is volume in $cm^3$ of a triangular prism that is 2 cm high and has a base triangle that has an area of $1 cm^2?$
Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.
Infinity : Infinity or $\infty$ represents a number that is bigger than all numbers in $\mathbb{R}.$
Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$
Solution : A solution to an equation is a choice of variables that when substituted into the equation results in a true statement.
Zero : The number 0.
How many solutions $x,y$ are there that solve the two following equations at the same time: $$3x+2y=9,$$ $$6x+4y=20?$$
Fractional exponent : The definition of a power with a fractional exponent is $x^\frac{a}{b}:=\sqrt[b]{{x}^a}.$ For example $8^{\frac{2}{3}}=\sqrt[3]{{8}^2}=4.$
Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$
Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$
What is ${4}^{\frac{4}{2}}=\sqrt{4^{4}}=(\sqrt{4})^{4}?$