BODMAS Rule Quiz

<p>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.</p> Signup and view all the answers

<p>The ratio of a to b can be expressed as a:b or a/b.</p> Signup and view all the answers

<p>We write proportions to help us establish equivalent ratios and solve for unknown quantities.</p> Signup and view all the answers

<p>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: $\left(\frac{\text{value}}{\text{total value}}\right)\times 100%$.</p> Signup and view all the answers

<p>45% is equivalent to the decimal 0.45, or the fraction $\frac{45}{100}$.</p> Signup and view all the answers

<p>To calculate the value when it is 80% of the total value, you would multiply the total value by 0.80.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>The formula is $L = \int_{a}^{b} \sqrt{(x'(t)^2 + y'(t)^2)} dt$.</p> Signup and view all the answers

<p>Archimedes approximated the perimeter of a circle by surrounding it with regular polygons.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>The isoperimetric problem seeks to determine a figure with the largest area given a specific perimeter.</p> Signup and view all the answers

<p>The solution to the quadrilateral isoperimetric problem is the square.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>There is no direct relationship between the perimeter and area for ordinary shapes.</p> Signup and view all the answers

<p>Splitters and cleavers are lines that divide the perimeter of a triangle into equal lengths, intersecting at specific points.</p> Signup and view all the answers

<p>The perimeter of a regular polygon can be calculated using trigonometry by considering the angles and side lengths of the polygon.</p> Signup and view all the answers

<p>Perimeters are fundamental to determining the boundaries of geometric figures, with polygons being essential in approximating the perimeters of other shapes.</p> Signup and view all the answers

<p>The specific formula for calculating the perimeter of a rectangle is $P = 2l + 2w$, where $l$ is the length and $w$ is the width.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>L = \int_{a}^{b} \sqrt{(x'(t)^2 + y'(t)^2)} dt</p> Signup and view all the answers

<p>Archimedes approximated the perimeter of a circle by surrounding it with regular polygons</p> Signup and view all the answers

<p>The perimeter of a regular polygon can be calculated using trigonometry</p> Signup and view all the answers

<p>The perimeter of a rectangle is the sum of the lengths of its sides, with the specific formula 2 \times (length + width)</p> Signup and view all the answers

<p>Confusion between perimeter and area is common, but there is no direct relationship between the two for ordinary shapes</p> Signup and view all the answers

<p>The isoperimetric problem seeks to determine a figure with the largest area given a specific perimeter</p> Signup and view all the answers

<p>The solution to the quadrilateral isoperimetric problem is the square</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>Triangles have splitters and cleavers that divide the perimeter into equal lengths, intersecting at specific points</p> Signup and view all the answers

<p>The perimeter of a circle (circumference) can be calculated using the formulas P = \pi \cdot D or P = 2 \pi \cdot r</p> Signup and view all the answers

<p>The perimeter of a regular polygon is the sum of the lengths of its sides</p> Signup and view all the answers

<p>$P = 2\pi r$</p> Signup and view all the answers

<p>$P = n \times \text{side length}$</p> Signup and view all the answers

<p>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> Signup and view all the answers

<p>$P = \frac{n}{2} \cdot s \cdot \tan\left(\frac{\pi}{n}\right)$</p> Signup and view all the answers

<p>There is no direct relationship between the perimeter and area for ordinary shapes</p> Signup and view all the answers

<p>Square</p> Signup and view all the answers

<p>Regular polygons</p> Signup and view all the answers

<p>$P = 2 \pi \cdot r$</p> Signup and view all the answers

<p>$P = 2l + 2w$</p> Signup and view all the answers

<p>By using the law of cosines</p> Signup and view all the answers

<p>The figure with the largest area given a specific perimeter</p> Signup and view all the answers

<p>$L = \int_{a}^{b} \sqrt{x'(t)^2 + y'(t)^2} dt$</p> Signup and view all the answers

Signup and view all the answers