BODMAS Rule Quiz

Multiplication

Multiplication

Square Root

A ratio is a comparison of two quantities, while a proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

The ratio of a to b can be expressed as a:b or a/b.

We write proportions to help us establish equivalent ratios and solve for unknown quantities.

To calculate a percentage, you divide the value by the total value, and then multiply the result by 100. The formula used to calculate percentage is: $\left(\frac{\text{value}}{\text{total value}}\right)\times 100%$.

45% is equivalent to the decimal 0.45, or the fraction $\frac{45}{100}$.

To calculate the value when it is 80% of the total value, you would multiply the total value by 0.80.

The formula for calculating the perimeter of a shape is the distance around the shape. For more general shapes, the perimeter can be calculated using the integral $\int_0^L ds$, where $L$ is the length of the path and $ds$ is an infinitesimal line element. The calculated perimeter can be used to determine the length of fence required to surround a yard or garden, describe the distance a wheel/circle will roll in one revolution, or determine the amount of string wound around a spool.

The perimeter of a circle or an ellipse is called its circumference. The circumference has practical applications such as determining the length of fence required to surround a yard or garden, describing the distance a wheel/circle will roll in one revolution, or determining the amount of string wound around a spool.

The perimeter of more general shapes can be calculated using the integral $\int_0^L ds$, where $L$ is the length of the path and $ds$ is an infinitesimal line element. In order to practically calculate the perimeter, both $L$ and $ds$ must be replaced by algebraic forms.

The formula is $L = \int_{a}^{b} \sqrt{(x'(t)^2 + y'(t)^2)} dt$.

Archimedes approximated the perimeter of a circle by surrounding it with regular polygons.

The general formula for calculating the perimeter of a regular polygon with n sides is $P = n \cdot s$, where $s$ is the length of each side.

The two formulas for calculating the perimeter of a circle are $P = \pi \cdot D$ and $P = 2 \pi \cdot r$, where $D$ is the diameter and $r$ is the radius.

The isoperimetric problem seeks to determine a figure with the largest area given a specific perimeter.

The solution to the quadrilateral isoperimetric problem is the square.

In general, the regular polygon with n sides has the largest area and a given perimeter compared to any irregular polygon with the same number of sides.

There is no direct relationship between the perimeter and area for ordinary shapes.

Splitters and cleavers are lines that divide the perimeter of a triangle into equal lengths, intersecting at specific points.

The perimeter of a regular polygon can be calculated using trigonometry by considering the angles and side lengths of the polygon.

Perimeters are fundamental to determining the boundaries of geometric figures, with polygons being essential in approximating the perimeters of other shapes.

The specific formula for calculating the perimeter of a rectangle is $P = 2l + 2w$, where $l$ is the length and $w$ is the width.

The perimeter is the distance around a shape and can be calculated using the formula $P = \int_0^L ds$, where $L$ is the length of the path and $ds$ is an infinitesimal line element. The practical applications of perimeter include determining the length of fence required to surround a yard or garden, describing how far a wheel or circle will roll in one revolution, and determining the amount of string wound around a spool.

The perimeter of a circle or an ellipse is called its circumference and can be calculated using the formulas $C = 2\pi r$ for a circle, where $r$ is the radius, and $C = 2\pi \sqrt{(\frac{a^2 + b^2},{2})}$ for an ellipse, where $a$ and $b$ are the semi-major and semi-minor axes respectively.

The perimeter of more general shapes can be calculated as any path with the formula $P = \int_0^L ds$, where $L$ is the length of the path and $ds$ is an infinitesimal line element. In order to practically calculate it, both $L$ and $ds$ must be replaced by algebraic forms.

L = \int_{a}^{b} \sqrt{(x'(t)^2 + y'(t)^2)} dt

Archimedes approximated the perimeter of a circle by surrounding it with regular polygons

The perimeter of a regular polygon can be calculated using trigonometry

The perimeter of a rectangle is the sum of the lengths of its sides, with the specific formula 2 \times (length + width)

Confusion between perimeter and area is common, but there is no direct relationship between the two for ordinary shapes

The isoperimetric problem seeks to determine a figure with the largest area given a specific perimeter

The solution to the quadrilateral isoperimetric problem is the square

The perimeter of a circle (circumference) is proportional to its diameter and radius, with the formula P = \pi \cdot D or P = 2 \pi \cdot r

In general, the regular polygon with n sides has the largest area and a given perimeter compared to any irregular polygon with the same number of sides

Triangles have splitters and cleavers that divide the perimeter into equal lengths, intersecting at specific points

The perimeter of a circle (circumference) can be calculated using the formulas P = \pi \cdot D or P = 2 \pi \cdot r

The perimeter of a regular polygon is the sum of the lengths of its sides

$P = 2\pi r$

$P = n \times \text{side length}$

It can be calculated using the formula $P = \int_0^L ds$, where $L$ is the length of the path and $ds$ is an infinitesimal line element; $L$ and $ds$ must be replaced by algebraic forms.

$P = \frac{n}{2} \cdot s \cdot \tan\left(\frac{\pi}{n}\right)$

There is no direct relationship between the perimeter and area for ordinary shapes

Square

Regular polygons

$P = 2 \pi \cdot r$

$P = 2l + 2w$

By using the law of cosines

The figure with the largest area given a specific perimeter

$L = \int_{a}^{b} \sqrt{x'(t)^2 + y'(t)^2} dt$