Math 2 Part 1 BYU Course Flashcards

Questions and Answers

What is the coefficient in the monomial 4x²?

4 (correct)

x²

What is a polynomial?

A series of monomials.

What is a term in a polynomial?

Each item separated by an addition or subtraction sign.

What is the graph of a quadratic equation called?

A parabola. Signup and view all the answers

What does the term quadratic refer to?

A function or an equation whose graph is a parabola. Signup and view all the answers

What does the discriminant tell you about a quadratic equation?

Number of solutions Signup and view all the answers

What are the points where the graph crosses the x-axis called?

X-intercepts or roots. Signup and view all the answers

What happens if the quadratic term is negative?

The parabola opens down. Signup and view all the answers

The perimeter of any polygon is the sum of the length of its ______.

sides Signup and view all the answers

The formula for the perimeter of a rectangle can be written as P = ______.

2l + 2w Signup and view all the answers

The area of the polygon is the measure of the region ______ the polygon.

inside Signup and view all the answers

The formula for the area of a rectangle can be written as A = ______.

lw Signup and view all the answers

What is a linear equation?

An equation that represents a line. Signup and view all the answers

What is the Slope-intercept Formula?

y = mx + b Signup and view all the answers

The ______ is the vertical line on a coordinate plane.

y-axis Signup and view all the answers

What does it mean for lines to be parallel?

Run the same way and have the same slant, so they will not intersect. Signup and view all the answers

What is meant by vertical shift in graphing?

When the b value moves the line vertically, up and down from the usual position. Signup and view all the answers

What is a line to fit on a scatter plot?

A line drawn as close as possible to all the points on a scatter plot. Signup and view all the answers

How is standard form expressed?

Ax + By = C Signup and view all the answers

What is a scatter plot?

A collection of data points on a graph. Signup and view all the answers

What is a fitted line?

A straight line that goes through the center of data points. Signup and view all the answers

What is a prediction equation?

An equation suggested by the points of a scatter plot used to predict other points. Signup and view all the answers

Define correlation in statistics.

A relationship between two variables. Signup and view all the answers

What does causation imply?

When one variable causes the other variable. Signup and view all the answers

What does graphing linear functions involve?

Graph the boundary line, decide on its type, shade regions, and test points. Signup and view all the answers

What is a boundary in graphing?

Separates the coordinate plane into two regions. Signup and view all the answers

What do exponents tell us?

How many times the base is used as a factor. Signup and view all the answers

Define the base in an expression.

A number that is multiplied repeatedly. Signup and view all the answers

What is a power in mathematics?

The whole expression involving exponents. Signup and view all the answers

What is an exponential function?

A function that repeatedly multiplies an initial amount by the same positive number. Signup and view all the answers

What is scientific notation?

A method of writing very large or very small numbers using powers of 10. Signup and view all the answers

What does the equality property of exponential functions state?

When the bases are equal, we can set the exponents equal to each other. Signup and view all the answers

What shape is formed by joining three segments?

Triangle. Signup and view all the answers

What are the vertices of a triangle?

The points A, B, and C in triangle ABC. Signup and view all the answers

What term describes the segments of a triangle?

Sides. Signup and view all the answers

How can triangles be classified?

By the size of their angles. Signup and view all the answers

What is an equiangular triangle?

A triangle where all three angles have the same measure. Signup and view all the answers

How is an equilateral triangle defined?

A triangle that has three congruent sides. Signup and view all the answers

What is an isosceles triangle?

A triangle that has two congruent sides. Signup and view all the answers

Define a scalene triangle.

A triangle that has no congruent sides. Signup and view all the answers

Can a triangle be both right and obtuse?

No, it is impossible. Signup and view all the answers

What is the longest side of a right triangle called?

Hypotenuse. Signup and view all the answers

The longer sides of a triangle are opposite the angles with the largest measure.

True Signup and view all the answers

What does congruent mean in geometry?

Two figures are identical. Signup and view all the answers

What are CPCTC?

Corresponding Parts of Congruent Triangles are Congruent. Signup and view all the answers

What are the two special types of segments in a triangle?

Altitude of a triangle and median of a triangle. Signup and view all the answers

Define an angle bisector.

A line or ray that divides an angle into two congruent angles. Signup and view all the answers

What is a polygon?

Union of three or more coplanar segments where exactly two segments intersect at each endpoint. Signup and view all the answers

What do we call the segments of a polygon?

Sides. Signup and view all the answers

What are the two types of polygons?

Concave and Convex. Signup and view all the answers

What is a diagonal of a polygon?

A segment connecting any two nonconsecutive vertices of the polygon. Signup and view all the answers

How many diagonals can be drawn from each vertex of a hexagon?

Three. Signup and view all the answers

What is a convex polygon?

A polygon where all diagonals lie completely within the polygon. Signup and view all the answers

Define a concave polygon.

A polygon that has at least one diagonal that lies outside the polygon. Signup and view all the answers

How do you calculate the sum of the measures of the interior angles of a polygon?

Multiply the number of triangles by 180°. Signup and view all the answers

What is the sum of the measures of the exterior angles of any convex polygon?

360°. Signup and view all the answers

What does it mean for a polygon to be equilateral?

A polygon where all sides are congruent. Signup and view all the answers

What defines an equiangular polygon?

A polygon where all interior angles are congruent. Signup and view all the answers

How many sides would a regular polygon have if each interior angle measures 144°?

<ol start="10"> <li></li> </ol> Signup and view all the answers

What is a quadrilateral?

A polygon with four sides. Signup and view all the answers

What are consecutive sides in a quadrilateral?

Sides that share a common vertex. Signup and view all the answers

Define opposite sides in a quadrilateral.

Sides that do not intersect. Signup and view all the answers

What are parallelograms?

Quadrilaterals with two pairs of parallel opposite sides. Signup and view all the answers

What is a trapezoid?

A quadrilateral with one pair of parallel opposite sides. Signup and view all the answers

What defines a rectangle?

An equiangular quadrilateral. Signup and view all the answers

How do you determine if a parallelogram is a rectangle?

If its diagonals are congruent. Signup and view all the answers

What are the bases and legs of a trapezoid?

Bases are the parallel sides, and legs are the sides that are not parallel. Signup and view all the answers

What is the altitude of a trapezoid?

Any segment from one base to the other that is perpendicular to both bases. Signup and view all the answers

Define the median of a trapezoid.

The line segment that is parallel to the bases. Signup and view all the answers

What is an isosceles trapezoid?

A trapezoid with congruent legs. Signup and view all the answers

What is meant by translation in geometry?

The transformation of sliding a shape up, down, or sideways. Signup and view all the answers

What is a rotation in geometric transformation?

Turning a shape to change its orientation. Signup and view all the answers

What does reflection mean in geometry?

Flipping a shape over to face a different direction. Signup and view all the answers

What is a translation vector?

It indicates the length and direction of a transformation. Signup and view all the answers

What is a ratio?

The fraction of two measurements, expressed as a/b. Signup and view all the answers

What is the geometric mean?

A common type of proportion in geometry. Signup and view all the answers

What is a proportion?

An equation where two ratios are equal. Signup and view all the answers

What does cross multiplication refer to in algebra?

An algebraic method to change fractions into multiplication. Signup and view all the answers

What are similar polygons?

Polygons that have the same shape but not necessarily the same size. Signup and view all the answers

Define similarity transformation.

A transformation producing similar figures. Signup and view all the answers

What are rigid transformations?

Transformations that preserve the shape and size of figures. Signup and view all the answers

What are similar triangles?

Triangles with two angles congruent to two angles of another triangle. Signup and view all the answers

What is a radical expression?

An expression involving roots, such as the square root. Signup and view all the answers

What is a rational approximation?

An answer that is estimated rather than exact. Signup and view all the answers

Define rational numbers.

Any number that can be expressed as a fraction. Signup and view all the answers

What are irrational numbers?

Real numbers that cannot be expressed as fractions. Signup and view all the answers

State the Pythagorean theorem.

a² + b² = c² Signup and view all the answers

What does rationalizing the denominator involve?

Multiplying the numerator and denominator by the same radical expression. Signup and view all the answers

What is a monomial?

An expression that is a numeral, variable, or product of both. Signup and view all the answers

Study Notes

Linear Equations and Graphing

Linear Equation: Represents a straight line in a coordinate plane.
Slope-Intercept Formula: y = mx + b, where m is the slope and b is the y-intercept.
Y-Axis: Vertical line representing output values (y).
Parallel Lines: Run in the same direction without intersecting.
Vertical Shift: Changes the position of a line vertically by modifying the b value.
Fitted Line: Drawn close to scatter plot data points for trend analysis.
Standard Form: Written as Ax + By = C, a common way to express linear equations.
Scatter Plot: Displays data points on a graph for visual analysis of relationships.
Prediction Equation: Derived from scatter plot data to forecast additional points.
Correlation vs. Causation: Correlation indicates a relationship, while causation implies one variable influences another.

Graphing Linear Inequalities

Identify and graph the boundary line using slope-intercept form.
Use dotted lines for < and >; solid lines for ≤ and ≥.
Shade regions based on the inequality direction (above or below the line).
Test a point in the shaded region to confirm it's part of the solution.

Triangles

Triangle Types: Classifications include acute (all angles < 90°), obtuse (one angle > 90°), and right (one angle = 90°).
Equilateral Triangle: All sides and angles are congruent.
Isosceles Triangle: Two sides and angles are congruent.
Scalene Triangle: No congruent sides or angles.
Triangle Properties: Longer sides are opposite larger angles; no triangle can be both right and obtuse.

Triangle Segments

Hypotenuse: Longest side in a right triangle.
Altitude: Perpendicular segment from a vertex to the opposite side.
Median: Segment from a vertex to the midpoint of the opposite side.

Polygons

Polygon: Formed by three or more connected segments with non-intersecting sides.
Types of Polygons: Classified as convex or concave.
Diagonals: Segments connecting non-consecutive vertices.
Convex Polygon: All diagonals remain inside the polygon.
Concave Polygon: At least one diagonal extends outside.
Sum of Interior Angles: For an n-gon, equals (n - 2) × 180°.

Quadrilaterals

Quadrilateral: Four-sided polygon with angles summing to 360°.
Parallelograms: Quadrilaterals with two pairs of parallel sides.
Trapezoids: One pair of parallel sides.
Rectangle: Equiangular quadrilateral with congruent diagonals.
Isosceles Trapezoid: Has congruent legs and base angles.

Transformations

Translations: Movement of shapes up, down, left, or right.
Rotations: Turning shapes around a fixed point.
Reflections: Flipping shapes across a line.
Rigid Transformations: Preserve shape and size; includes translations, rotations, and reflections.

Ratios and Proportions

Ratio: Comparison of two measurements as a fraction.
Proportion: Equality of two ratios, commonly solved using cross multiplication.
Geometric Mean: Calculated for proportions, establishing a relationship between values.

Quadratic Functions

Quadratic Function: Represents a parabolic graph with a squared term.
Vertex: Highest or lowest point in a parabola, related to the direction it opens.
Discriminant: Determines the number of real solutions (b² - 4ac); zero for one solution, positive for two, and negative for none.

Exponential Functions

Exponential Growth/Decay: Models changing quantities, expressed in forms like y = a(1±r)ᵡ.
Scientific Notation: Represents large or small numbers using powers of 10.

Rational and Irrational Numbers

Rational Numbers: Numbers expressible as fractions.
Irrational Numbers: Non-repeating and non-terminating decimal representations.

Miscellaneous

Rationalizing the Denominator: Process to eliminate radicals from the denominator of fractions.
Monomial: A singular term in mathematics, including numbers and variables.
Polynomial: A sum of two or more monomials.### Perimeter of a Rectangle
Farmers calculate the perimeter of a pasture for fencing material.
The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where l is length and w is width.

Area of a Polygon

The area of a polygon measures the space inside it.
Example application: Area calculation determines the amount of carpet needed for a room.
Area is expressed in square units, representing how many squares fit in the region.
For rectangles, the area (A) can be calculated using the formula A = lw, where l is length and w is width.
Visualizing the rectangle as a partition of squares simplifies understanding of area.

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Test your knowledge with these flashcards covering key concepts from the Math 2 Part 1 BYU online course. This quiz includes definitions and formulas related to linear equations and the slope-intercept formula. Perfect for students wanting to reinforce their understanding of algebraic principles.