Semester Review Math Vocabulary

Unit 1: Equations and Operations

• Algebraic Equation: An equation in which at least one variable is used.
• Inverse Operations: Opposite operations. Inverse operations undo each other.
• Isolate the Variable: To get the variable alone on one side of an equation or inequality in order to solve the equation or inequality.
• Inequality: A mathematical sentence that compares two or more expressions by using an inequality symbol.
      - Example: The inequality 4x - 5 > 11 states that the expression $4x - 5$ is greater than $11$.
• Solution of an Inequality: The set of values that can be substituted for a variable to make an inequality true.
      - Example: For the inequality x + 2 > 6, the solution is x > 4.

Unit 2: Order of Operations, Angles, and Geometric Principles

• Order of Operations: The order in which math operations should be performed to solve a problem. The standard order of operations is:
      1. Grouping symbols
      2. Exponents
      3. Multiplication and division (from left to right)
      4. Addition and subtraction (from left to right)
• Scale Drawing: A drawing that represents a real object. The scale factor gives the ratio of the lengths in the scale drawing to the lengths in the real object.
• Scale Factor: A factor that gives the ratio of a side length in a scale drawing to the matching side length in the real object.
• Acute Angle: An angle that measures less than $90^\circ$. An acute angle is smaller than a right angle.
• Angle: An object formed by two rays that share an endpoint. The endpoint is called the vertex.
• Vertex: The point where rays or line segments meet to form an angle. The plural of vertex is vertices.
• Obtuse Angle: An angle that measures greater than $90^\circ$ but less than $180^\circ$.
• Protractor: A tool used to measure angles; usually marked in degrees.
• Right Angle: An angle that measures $90^\circ$. Right angles are often marked with a small square symbol.
• Right Triangle: A triangle that contains a right angle.
• Cross-section: The figure that results when a plane is passed through a solid.
• Plane: A flat surface that extends forever in all directions. A plane has no thickness, so it has only two dimensions. A plane is like an infinitely large piece of drawing paper.

Unit 3: Three-Dimensional Figures, Geometry of Circles, and Angle Relationships

• Right Rectangular Prism: A three-dimensional solid consisting of two parallel and congruent rectangular bases and all the points in between them.
• Right Rectangular Pyramid: A three-dimensional solid consisting of a rectangular base, a vertex that is perpendicular to the base, and all the points in between them.
• Solid: An object that has three dimensions: length, width, and height. A solid may also be called a three-dimensional figure or a solid figure.
• Area: The size of a surface. Area is measured in square units.
      - Example: The area of a rectangle with length $l$ and width $w$ is given by the formula $A = l \times w$.
• Center: The point at the exact center of the circle. All points on a circle are the same distance from the center.
• Circle: A closed curve in one plane with all its points the same distance from the center.
• Circumference: The measure of the distance around the perimeter of a circle. Circumference is measured in linear units.
• Diameter: A line segment that passes through the center of a circle and has endpoints on the circle. The length of a diameter of a circle is equal to twice the length of a radius of the circle.
• Pi: The ratio of the circumference of any circle to its diameter. This number is represented by the Greek letter $\pi$. It is approximately equal to $3.14$.
• Radius: A line segment that goes from the center of a circle to any point on the circle. The length of a radius of a circle is equal to $\frac{1}{2}$ the length of a diameter of the circle.
• Adjacent Angles: Angles that share a vertex and one side. Adjacent angles are "next to" each other.
• Complementary Angles: Two angles whose measures add up to $90^\circ$. If two complementary angles are adjacent, they form a right angle.
• Congruent: Having the same size and shape. If two polygons are congruent, their corresponding sides and angles are also congruent. The symbol $\cong$ means "is congruent to."
• Linear Pair: A pair of adjacent angles whose measures add up to $180^\circ$. Linear pairs of angles are supplementary.
• Straight Angle: An angle that has a measure of $180^\circ$ and whose sides form a line.
• Supplementary Angles: Angles whose measures add up to $180^\circ$. If two supplementary angles are adjacent, they form a straight angle.
• Vertical Angles: A pair of opposite angles formed by intersecting lines. Vertical angles are congruent.
• Composite Figure: A figure made up of two or more simpler shapes.
• Parallelogram: A four-sided figure in which both pairs of opposite sides are parallel and equal.
• Trapezoid: A four-sided figure with exactly one pair of parallel sides.
• Lateral Surface Area: The sum of the areas of the faces on a solid figure, excluding bases.
• Net: A two-dimensional drawing that can be folded up to make a solid. The net shows all of the flattened surfaces of the solid.
• Prism: A three-dimensional solid consisting of two parallel congruent polygons and all the points between them.
• Triangular Prism: A three-dimensional solid whose bases are triangles and whose other surfaces are rectangles.
• Rectangular Prism: A three-dimensional solid consisting of two parallel congruent rectangles and all the points between them.
• Surface Area: The total area of the exterior surface of a solid figure.

Unit 4: Data Analysis and Statistics

• Inference: A conclusion drawn by using sample data to make predictions about a larger population.
• Mean: The sum of all of the values in a data set divided by the number of values. The mean is also called the average.
      - Example: To find the mean of $8, 9, 10, \text{ and } 20$, add $8 + 9 + 10 + 20 = 47$. Then divide by $4$: $\frac{47}{4} = 11.75$. The mean is $11.75$.
• Mean Absolute Deviation (MAD): The average distance between each data value and the mean.
      - Example: To find the mean absolute deviation for $6, 8, 12, \text{ and } 14$:
          - 1. Find the mean: $10$.
          - 2. Find the distance of each point from the mean: $4, 2, 2, \text{ and } 4$.
          - 3. Find the average of these distances: $\frac{12}{4} = 3$. The mean absolute deviation is $3$.
• Population: The entire group being considered.
• Random Sampling: The selection of a sample in which each item or individual has an equal chance of being selected.
• Representative Sample: A sample that represents the larger population and can provide accurate predictions about the entire population.
• Sample: A selection of items chosen from a larger population.
      - Example: Ralph might survey a sample of $10$ students to get an idea of the favorite types of music at his high school.
• Dot Plot: A chart that uses stacked dots to represent counts.
• Variation: The amount of spread in a data set.
• Measure of Center: A number that represents the middle or typical value in a set. The mean, median, and mode are all measures of center.
• Measure of Variability: A number that represents how much the values in a data set vary. The range, interquartile range, and mean absolute deviation are measures of variability.
• Median: The middle value in a data set. Half the values are below the median, and half are above the median.
      - Example: The numbers in the set ${2, 5, 6, 10, 12, 17, 25}$ are in order, so the median is $10$. There are three values below $10$ and three values above $10$.
• Range of a Data Set: The difference between the maximum value and the minimum value of a data set. Formula: $\text{Range} = \text{Maximum} - \text{Minimum}$.
      - Example: The range of the data set ${8, 9, 14, 16, 19, 20}$ is $12$, because the maximum is $20$ and the minimum is $8$.
• Spread: A measure describing how much the data in a data set are spread out or scattered.

Unit 5: Probability and Simulations

• Event: A set of outcomes.
      - Example: Rolling a number less than or equal to $4$ on a number cube.
• Outcome: The result of a random occurrence.
      - Example: The spinner landed on red; the number cube landed on $6$.
• Probability: A number from $0$ to $1$ that tells how likely an event is. An event that is impossible has a probability of $0$; an event that is certain to happen has a probability of $1$.
• Sample Space: The set of all possible outcomes.
      - Example: For a number cube, the sample space is the set ${1, 2, 3, 4, 5, 6}$.
• Empirical Probability: An estimated probability that is based on observations rather than theory. It equals the number of successful trials divided by the total number of trials. It is also called experimental probability.
      - Example: Sophie took $20$ shots in a basketball game and made $10$ of them. The empirical probability is $10 \div 20 = 0.5$.
• Frequency: The total number of observations for a category or interval.
      - Example: A survey of $10$ people found that $3$ of them spoke two languages. The frequency for speaking two languages is $3$.
• Probability Experiment: A single trial or group of trials.
• Relative Frequency: A frequency, usually expressed as a decimal or percent, that shows the proportion of data that falls into a category.
• Theoretical Probability: A probability based on theory, not on actual experiments.
      - Example: If a cube has faces numbered $1$ through $6$, the theoretical probability of rolling a $5$ is $\frac{1}{6}$.
• Trial: Any activity for which the outcome is uncertain.
• Compound Event: An event that is a combination of two or more separate events.
• Tree Diagram: A diagram that shows all the possible outcomes for an event as branches.
• Simulation: A model that imitates a real-world situation based on probabilities of individual events. A simulation can use a coin, number cube, spinner, or random number generator.
      - Example: Simulating a student randomly guessing answers to questions.