Algebra Exam Review - Quadratics and Triangles

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Questions and Answers

How many solutions do two equations have when intersecting (Check substitution/elimination)?

Infinite (correct)

One (correct)

Two (correct)

None (correct)

What is the formula for calculating the length of a line segment?

The distance formula: √((x₂ - x₁)² + (y₂ - y₁)²)

What is the process for solving a right bisector?

Find the midpoint of the line segment. 2. Find the negative reciprocal of the slope of the given line segment. 3. Use the midpoint and the negative reciprocal slope to create the equation of the right bisector.

The vertex of a quadratic equation in factored form is always the midpoint of the x-intercepts.

True Signup and view all the answers

Which of these methods are employed to factor quadratic equations?

Difference of squares Signup and view all the answers

What is the relationship between the vertex of a quadratic equation in vertex form and its graph?

The vertex represents the highest or lowest point of the parabola, depending on the leading coefficient Signup and view all the answers

Explain the process of completing the square to transform a standard form quadratic equation into vertex form.

Involves manipulating the equation by adding and subtracting a specific constant to create a perfect square trinomial. This results in an expression that can be factored into a squared term, simplifying the equation into vertex form. Signup and view all the answers

What does the phrase 'Picture Frame/Fence thinking' refer to in the context of quadratic equation solving?

A visual representation of the quadratic equation that helps visualise the relationship between the x-intercepts and the vertex. Signup and view all the answers

Describe how the cosine law can be used to solve problems involving triangle side lengths and angles.

The cosine law is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. By applying this law, you can determine unknown side lengths or angles given the lengths of two sides and the measure of the included angle. Signup and view all the answers

Explain what is meant by a double triangle question in trigonometry.

A double triangle question typically involves a scenario where multiple triangles share common sides or angles, requiring the application of trigonometric ratios using a combination of triangles to solve for the unknowns. Signup and view all the answers

What are the three primary trigonometric ratios, and how are they used in solving triangles?

The three primary trigonometric ratios are Sine (SOH), Cosine (CAH), and Tangent (TOA). They are used to relate the lengths of sides to the angles in a right-angled triangle, making it possible to solve for unknown sides or angles. Signup and view all the answers

The sine of a right angle is equal to 1.

True Signup and view all the answers

Study Notes

Detailed Exam Review - Multiple Choice (15 Marks)

Length of line segments
Solving right bisectors
Finding solutions for intersecting/overlapping circles.
Expanding and simplifying factored equations into standard form.
Identifying the vertex of a factored form equation.
Determining the vertex of an equation in vertex form.
Transforming equations based on descriptions..
Finding maximum/minimum points in quadratic equations
Solving right-angled triangles (using sine/cosine rules)
Solving non-right-angled triangles (using sine/cosine rules)

Full Solutions (45 Marks)

Expanding and simplifying factored equations into standard form.
Factoring standard equations into factored form.
Identifying common factors.
Factoring simple trinomials.
Completing the square method to find the vertex form of an equation.
Graphing vertex form equations.
Finding the solutions (zeros, roots, or x-intercepts).
Solving quadratic application questions involving movement (e.g., ball hitting the ground).
Applying cosine rule problems.
Trigonometric ratio problems (using SOHCAHTOA) for double triangle problems.

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Description

Prepare for your algebra exam with this comprehensive review quiz covering topics such as the length of line segments, solving right bisectors, and working with quadratic equations. Test your understanding of finding vertices, transforming equations, and applying sine and cosine rules for triangles. Get ready to tackle both multiple-choice and full solution questions for maximum success.