Unit 2: Measurement & Geometry
What is the formula for finding the area of a rectangle?
Area=length×width
In a right-angled triangle, what is the ratio of the opposite side to the hypotenuse called?
Sine (sin)
Define a two-variable data set and provide an example
A set of paired data, e.g., heights and weights of individuals
Explain the concept of statistical bias and provide an example
Bias is a systematic error in one direction. Example: Surveying only a certain age group for opinions
State the exponent laws
Laws include product, quotient, power, and zero exponents or negative law
Calculate the volume of a cylinder with a radius of 5 cm and a height of 8 cm.
Volume=πr2h
Use the Sine Law to find the missing side in a triangle with angles A, B, and sides a, b, respectively.
sinA/ a = sinB/ b
Calculate the linear regression equation for a given set of data points
y=mx+b, where m is the slope and b is the y-intercept
Interpret statistical measures (mean, median, mode) in the context of a data set
Mean is the average, median is the middle value, and mode is the most frequent value
Represent exponential expressions using rational exponents
A m/n = n/ A^m
Given a composite figure made up of a triangle and a rectangle, find the total area
Find the area of each shape and add them
Solve a real-world application problem using Trigonometry, given angle measurements and side lengths
Application-specific, based on the provided scenario
Analyze a set of two-variable data and draw conclusions about the relationship between the variables
Discuss the trend, correlation, and any outliers in the data
Create an exponential model for a set of data points and explain its significance
y=ab^x, where a is the initial value and b is the growth factor
Solve an equation involving exponential expressions and rational exponents
Solve for the variable in the given exponential equation.
Determine the surface area of a cone with a radius of 6 meters and a slant height of 10 meters
Surface Area=πr2+π r slant height
Apply the Cosine Law to find the unknown side in a triangle
c^2=a^2 + b^2 - 2abcosC
Explain the concept of correlation in a scatter plot
Correlation measures the strength and direction of a linear relationship
Compare and contrast bar graphs and histograms, citing examples
Bar graphs show categorical data; histograms show the distribution of numerical data
Simplify a complex logarithmic expression
Apply logarithmic rules to simplify the expression
Solve for the missing side in a right-angled triangle using the Pythagorean theorem
c^2 = a^2 + b^2, where c is the hypotenuse
Evaluate the tangent of an angle in a right-angled triangle
tan0=opp/adj
Utilize the principles of surveying to design and interpret a statistical study
Discuss sampling methods, bias reduction, and interpretation of results
Analyze and critique statistical information presented in the media
Evaluate data sources, methods, and potential biases in media statistics
Apply the laws of logarithms to solve exponential equations
Use logarithmic properties to solve the given exponential equation