Jakarta International School 8 th Grade AG1 Practice Test - BLACK

Transcription

1 Jakarta International School 8 th Grade AG1 Practice Test - BLACK Polynomials and Quadratic Equations Name: Date: Grade: Standard Level Learning Goals - Green Understand and Operate with Polynomials Graph quadratic functions Solve and apply quadratic equations - Classify polynomials by degree and number of terms - Understand how to add and subtract polynomials - Multiply polynomials by using the distributive property or FOIL memory tool - Understand, recognize, and use Special Product Patterns to multiply polynomials - Understand how to graph parabolas using the 3 point method - Graph quadratic functions that have already been factored - Graph quadratic functions using the x-intercepts and midpoint method - Solve quadratic equations that have already been factored - Solve quadratic equations that have a leading coefficient of 1 - Solve quadratic equations with a leading coefficient that is not 1 - Solve quadratic equations that contain special product patterns - Problem solve with quadratic equations Additional Advanced Concepts - Blue Transforming expressions Using substitution to solve quadratic equations Applying the Quadratic Formula when factoring isn t possible Working with similar rectangles Additional Highly Advanced Concepts - Black Deriving the equation for a quadratic function given information about its graph Deriving special product patterns geometrically Pythagorean Theorem applications Radical Equations A B C D F - All learning goals are met within the standard - The learner independently completes open-ended tasks. - Assessment scores indicate a high level of understanding of skills and concepts. - The learner demonstrates a sophisticated understanding through high order application and performance - Most of the learning goals are met within the standard - The learner occasionally needs support to complete open-ended tasks. - Assessment scores indicate a good grasp of skills and concepts. - The learner demonstrates considerable understanding through application and performance - Some of the learning goals are met within the standard - The learner needs some support to complete open-ended tasks. - Assessment scores indicate satisfactory acquisition of skills and concepts. - The learner demonstrates some understanding through application and performance - Few of the learning goals are met within the standard - The learner needs ongoing support to begin and/or complete tasks. - Assessment scores indicate weak acquisition of skills and concepts. - The learner demonstrates limited understanding through application and performance. - None or almost none of the learning goals are met within the standard - The learner needs significant support to begin and/or complete tasks. - Rarely completes tasks even with support. - Assessment scores indicate minimal grasp of skills and concepts. - The learner does not demonstrate understanding through application and performance.

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3 Polynomials Vocabulary Write each polynomial in standard form. Then, identify each polynomial by degree AND terms. Variable Expression 2 2x 5x w 9 3w Standard Form Identified by Degree and Number of Terms Always, Never, or Sometimes Fill in the blanks of the sentences below with ALWAYS, NEVER, or SOMETIMES. *** If you answer SOMETIMES, include examples to prove you are correct *** 1. The quotient of a quadratic binomial and a linear monomial is a linear monomial. 2. The sum of a trinomial and a binomial is a monomial. 3. Find the values of a and b that result in the difference [(2 + 1) ( 3) + 5] [( + 4) 4 + 5] = a x b x b x ax x x 4. What non-zero integer must be placed in the square so that the simplified product of these two binomials is a binomial? ( 8x+ 4)( 4x+ )

4 Instructions: Appropriately complete each problem. Factor polynomials completely. Solve equations. When and where appropriate, show all possible solutions. Check solutions. 4 x (hint: write an equivalent expression for which you can take advantage of the difference of two squares pattern) x 4x + 4 = x 8y x 75x+ 7x 175

5 9. x+ 2 x+ 3 x+ 4 x+ 5 = x+ 1 x+ 2 x+ 3 x x x+ = What are the possible values of x + y such that x + y = 90 and xy = 27? Derive the difference of two cubes pattern using a geometric volume model. Show how the factored form of the expression can be seen geometrically.

6 13. What is the formula for factoring the difference of two terms raised to the same powers? Give three examples that support your formula (make sure your examples involve different powers). x n n a = 14. The arch of a stone bridge has the shape of a parabola that is 20 feet wide at the water line and rises to its highest point 8 feet above the water. Suppose the vertex of the parabola is at the origin of a coordinate system. A. Write an equation for the parabola. Illustrate this situation on a coordinate plane. B. If the water level rises to 18 feet below the highest point of the bridge, how wide is the parabola at the water line?

7 15. 2 = 1 huh? Work through the following proof that 2 = 1. Step 1: Let a and b be equal and non-zero a = b Step 2: Multiply both sides by a 2 a = ab Step 3: Subtract b squared a b = ab b Step 4: Factorize ( a+ b)( a b) = b( a b) Step 5: Divide by (a-b) a+ b= b Step 6: But a = b (from Step 1), so b+ b= b Step 7: Therefore 2b= b Step 8: Divide both sides by b 2= 1 Now, describe the error that makes this proof false. 16. Find all values of x satisfying the equation 3 x+ x 1 15 = 3x x 1 11

8 17. Let P(x,y) be a point on the graph of y = x + 5. Connect P with Q (7,0). Let a perpendicular from P to the x-axis intersect it in R. Restricting the abscissa of P to values between 0 and 7, both included, find the maximum area of a right triangle PRQ. 18. I have an interesting rectangle here. If I cut a square off it, the remaining rectangle is similar to the original one (same shape, different size). If the width of my rectangle is one meter, what is its length? Provide an exact answer.