Mathematics and Formula Sheet Review

A collection of vocabulary flashcards covering essential formulas and definitions from chapters 2 and 3 of the formula sheet transcript.

Stopping Distance Formula

$\text{Stopping distance} = v \times \text{reaction time in seconds} + \frac{v^2}{170}$ (where $v$ is speed of car)

BAC Formula (Male)

$$\text{BAC}_{\text{male}} = \frac{10N - 7.5H}{6.8M}$$

BAC Formula (Female)

$$\text{BAC}_{\text{female}} = \frac{10N - 7.5H}{5.5M}$$

Hours until BAC Zero Formula

$$\text{Hours until BAC zero} = \frac{\text{BAC}}{0.015}$$

Mean

The average of a set of numbers.

Median

The middle number in an ordered set of numbers.

Mode

The most frequent number in a dataset.

Range Formula

$$\text{Range} = \text{max} - \text{min}$$

Interquartile Range (IQR) Formula

$$\text{IQR} = Q_3 - Q_1$$

Lower Outlier Formula

$$\text{Lower outlier} = Q_1 - 1.5 \times \text{IQR}$$

Higher Outlier Formula

$$\text{Higher outlier} = Q_3 + 1.5 \times \text{IQR}$$

Liquid Medicine Dosage Formula

$$\text{Volume} = \frac{\text{Strength required}}{\text{Strength on bottle}} \times \text{volume of bottle}$$

Tablet Medicine Dosage Formula

$$\text{Number of tablets} = \frac{\text{Dose required}}{\text{dose of 1 tablet}}$$

Fried's Rule

$$\text{dose} = \frac{\text{age in months}}{150} \times \text{adult dose}$$

Young's Rule

$$\text{dose} = \frac{\text{years born}}{\text{years} + 12} \times \text{adult dose}$$

Clark's Rule

$$\text{dose} = \frac{\text{KG}}{70} \times \text{adult dose}$$

Original Amount (Discounted) Formula

$$\text{Original amount} = \frac{\text{discounted price}}{100\% - \text{discount}\%}$$

Original Amount (Increased) Formula

$$\text{Original amount} = \frac{\text{increased price}}{100\% + \text{increase}\%}$$

Percentage Change Formula

$$\text{Percentage change} = \frac{\text{change in value}}{\text{original value}} \times 100\%$$

Trapezoidal Rule Formula

$A = \frac{1}{2}h(d_f + d_l)$, where $h$ is distance between parallel ends, $d_f$ is length of first parallel side, and $d_l$ is length of last parallel side

Perimeter of Square Formula

$$P = 4 \times \text{side}$$

Perimeter of Rectangle Formula

$$P = 2 \times \text{length} + 2 \times \text{width}$$

Circumference of Circle Formula

$$C = 2\pi R$$

Sector Arc Length Formula

$$\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi R$$

Perimeter of Sector Formula

$$\text{Perimeter} = \frac{\theta}{360^\circ} \times 2\pi R + 2R$$

Area of Triangle Formula

$$A = \frac{1}{2} \times b \times h$$

Area of Square Formula

$$A = \text{Side}^2$$

Area of Rectangle Formula

$$A = \text{length} \times \text{width}$$

Area of Trapezium Formula

$$A = \frac{1}{2}(a + b)h$$

Area of Rhombus or Kite Formula

$$A = \frac{1}{2}xy$$

Area of Circle Formula

$$A = \pi R^2$$

Area of Sector Formula

$$A = \frac{\theta}{360^\circ} \times \pi R^2$$

Area of Annulus Formula

$$A = \pi R^2 - \pi r^2$$

Slope / Steepness Formula

$$\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}$$

Surface Area of Rectangular Prism Formula

$$\text{SA} = 2(lw + wh + lh)$$

Surface Area of Open Top Cylinder Formula

$$\text{SA} = \pi R^2 + 2\pi Rh$$

Surface Area of Closed Cylinder Formula

$$\text{SA} = 2\pi R^2 + 2\pi Rh$$

Surface Area of Open Pipe Cylinder Formula

$$\text{SA} = 2\pi Rh$$

Surface Area of Cone Formula

$\text{SA} = \pi R^2 + \pi R L$ (where $L$ is slant height)

Surface Area of Square-Based Pyramid Formula

$$\text{SA} = S^2 + 4\left(\frac{1}{2} \times \text{base} \times \text{slant}\right)$$

Surface Area of Sphere Formula

$$\text{SA} = 4\pi R^2$$

Surface Area of Open Hemisphere Formula

$$\text{SA} = 2\pi R^2$$

Surface Area of Closed Solid Hemisphere Formula

$$\text{SA} = 3\pi R^2$$

Volume of Cube Formula

$$V = \text{Side}^3$$

Volume of Cylinder Formula

$$V = \pi R^2 h$$

Volume of Sphere Formula

$$V = \frac{4}{3}\pi R^3$$

Volume of Cone Formula

$$V = \frac{1}{3}\pi R^2 h$$

Volume of Pyramid Formula

$$V = \frac{1}{3} A \times h$$