Algebra Unit 1-4 Quiz: Linear Systems & Quadratics

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Questions and Answers

What is the initial height of the bottle rocket at launch?

10 meters

20 meters

40 meters

0 meters (correct)

What price will generate the maximum revenue for the software company?

$36 (correct)

$28

$30

$32

At what price will the revenue be zero for the computer software company?

$50

$30

$40

$70 (correct)

What is the equation of the parabola representing the height of the bridge?

$y = -rac{1}{5}(x - 25)^2 + 20$ Signup and view all the answers

How long did it take the bottle rocket to reach a height of 40 m?

5 seconds Signup and view all the answers

What is the height of the cliff if a boat moves 110 m away and the angles of elevation change from 7 degrees to 4 degrees?

Approximately 8.68 m Signup and view all the answers

After 30 minutes of hiking, will Sam and Harry be able to communicate over their walkie-talkies?

No, they will be too far apart. Signup and view all the answers

If the clock hands of Big Ben are 7.7 m and 3.85 m long, what is the distance between the tips at 5 o'clock?

5.7 m Signup and view all the answers

What is the area of a triangular garden with side lengths of 3m, 5m, and 6m?

10.5 m² Signup and view all the answers

What is the new angle of elevation observed if the boat moves away from the cliff?

4 degrees Signup and view all the answers

What methods can be used to solve a system of linear equations?

Elimination and substitution Signup and view all the answers

Which of the following represents the correct form for writing the equation of a circle?

(x – h)^2 + (y – k)^2 = r Signup and view all the answers

What do the roots of a quadratic equation represent?

The x-intercepts of the graph Signup and view all the answers

Using the quadratic formula, what indicates that a quadratic equation has no real solutions?

The discriminant is negative Signup and view all the answers

What is the relationship between the angles and sides of similar triangles?

Their corresponding angles are equal, and their sides are proportional Signup and view all the answers

What does the term 'vertex form' mean in the context of quadratic functions?

An expression that highlights the vertex of a parabola Signup and view all the answers

Which law would you use to solve for an unknown side in a right triangle given two side lengths?

Pythagorean Theorem Signup and view all the answers

Which statement about the transformations of the quadratic function $y = a(x-h) + k$ is correct?

All of the above Signup and view all the answers

What is the equation of a circle with a diameter of 11 units?

$(x - 0)^2 + (y - 0)^2 = 121$ Signup and view all the answers

What is the slope of the line connecting points A(–4, 8) and B(5, –2)?

$2$ Signup and view all the answers

How many sides does a quadrilateral have?

4 Signup and view all the answers

Which classification best fits a triangle with vertices D(5, 6), E(2, -8), and F(-4, 10)?

Scalene Signup and view all the answers

What is the diameter of a circle with the equation $x^2 + y^2 = 200$?

20 Signup and view all the answers

What can be concluded about the point (3, 6) in relation to the circle defined by the equation $x^2 + y^2 = 200$?

Outside the circle Signup and view all the answers

Which equation represents the median from vertex F in triangle DEF?

$y = rac{2}{3}x + 1$ Signup and view all the answers

What is a necessary criterion to classify a polynomial as a difference of squares?

It must have two terms that are both perfect squares. Signup and view all the answers

Study Notes

Unit 1: Linear Systems

Solving systems using elimination or substitution
Word problems requiring "let statements" and equation creation
Determining the number of solutions to a system (0, 1, infinite)

Unit 2: Coordinate Geometry

Calculating the length of a line segment
Finding the midpoint of a line segment
Equations of circles
Equations of perpendicular bisectors, medians, and altitudes
Analyzing properties of triangles and quadrilaterals

Unit 3-4: Quadratics

Algebra of Quadratics

Expanding and simplifying polynomial expressions
Factoring polynomials (common, grouping, simple/complex trinomials, difference of squares, perfect squares)
Completing the square to convert to vertex form
Solving quadratic equations using the quadratic formula

Quadratic Functions

Determining key properties of quadratic functions (vertex, x-intercepts) using algebra
Graphing quadratic functions (at least 5 points) given different forms
Finding equations of quadratic functions given the vertex, x-intercepts, or a point
Determining the number of x-intercepts using the discriminant, domain and range.
Transformations of quadratic functions
Quadratic word problems (projectile motion, revenue, geometry)

Unit 5-6: Similar Triangles and Trigonometry

Creating similarity statements and proving similar triangles
Solving for unknown side lengths using proportionality statements
Using SOH CAH TOA, sine law, and cosine law
Solving for sides and angles using appropriate theorems
Solving problems with multiple triangles (e.g., two-triangle problems)
Angle of elevation and depression problems
Word problems (diagrams, bearings, clocks, two angles of elevation)

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Description

Test your knowledge on key algebra concepts including linear systems, coordinate geometry, and quadratic functions. Solve problems involving elimination and substitution, line segment calculations, polynomial expressions, and properties of quadratic equations. This quiz encompasses critical skills you'll need in algebra.