INTERIM ASSESSMET REVIEW-QUARTER 2

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Mathematics

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10th Grade

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Hard

Maredy Melo

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16 Slides • 15 Questions

INTERIM ASSESSMET REVIEW-QUARTER 2

By Maredy Melo

Learning Target:

HSA-REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2 = q that has the same solutions. Derive the quadratic formula from this form.

Multiple Choice

Consider the equation below. 4t² - 28t = 6t² - 12t + 26 Which equation could be used when completing the square to solve for t?

A. (t + 4)² = 3

B. (t + 8)²= -13

t² + 8t + 4 = -13 + 4

t² + 8t + 64 = -13 + 64

Standards Description:

HSF-IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions.

Multiple Choice

2. What is the approximate rate of decay in the exponential function f(t) = (0.9)^1/5t ?

A. 0.02

B. 0.1

C. 0.41

D. 0.9

Standards Description:

HSN-CN.A.1 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Multiple Choice

4. Determine whether each equation has one real solution, two real solutions, or no real solutions. Select One Real Solution, Two Real Solutions, or No Real Solutions for each equation.

a,b,c

a,b,c,d

a,b

c,d

Standards Description: HSF-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Multiple Choice

modeled by the function h(t), where t is the number of minutes since the Ferris wheel started. The figure below is a graph of the function h(t).

Select all that apply. A. The function h(t) has a minimum at t = 0. B. The function h(t) has a relative ma5. The height, in meters, of a particular car on a Ferris wheel can be ximum at approximately t = 11. C. The function h(t) increases at a constant rate from minute 1 to minute 11. D. Riders get on the Ferris wheel approximately 3 meters off the ground. E. During a single revolution, the Ferris wheel car will pass its lowest point twice. F. It takes approximately 20 minutes for the Ferris wheel car to complete one revolution

a. B,D,F

b. A,B,C

c. C,D,F

d. D,C,F

Standards Description: HSA-REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)²= q that has the same solutions. Derive the quadratic formula from this form.

Fill in the Blanks

6. Melinda derives the quadratic formula from the following equation, and her first four steps are shown below. ax2 + bx + c = 0, where a ≠ 0 Melinda's steps:

Step 1: x² + a/x + c /a = 0

Step 2: x² + b /a x = - c/ a

Step 3: x² + b /a x + ( b/2a ) 2 = - c /a

Step 4: (x + b/ 2a ) 2 = - c/ a

Are Melinda's first four steps correct? • If her steps are correct, explain h

Type answer...

Standards Description:

HSN-CN.A.2 Use the relation i²= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Multiple Choice

7. Which of the following is equivalent to (3 - i)² ?

A. 6 - 2i

B. 8 - 6i

C. 9 - 5i

D. 10 - 6i

Standards Description:

HSF-IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Open Ended

8. The depth in feet, D, of a scuba diver can be modeled by the function D(x) = -x ² + 12x + 4, where x is the number of seconds spent diving. What is the number of seconds spent diving when the scuba diver reaches their maximum depth? Respond in the space provided.

Type response here

Standards Description:

HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

Multiple Choice

9. A function f(x) is defined to be f(x) = x² - 3x + 21. What are the solutions to the equation f(x) = 0?

A. x = 3 ± 5i $\sqrt[]{3}$

B. x = 3 ± 5 $\sqrt[]{3}$

C. x = 3 - 5i $\sqrt[]{3}$

D. There are no solutions.

Standards Description:

HSF-IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Open Ended

10. Graph the equation 2x - 6y = 15 on the coordinate plane below. Select two points on the coordinate plane. A line will be drawn through the points you selected.

Type response here

Standards Description:

HSN-CN.A.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Multiple Choice

11. Simplify. (-9 - 6i) - (4 + 4i)

A. -23i

B. -5 - 2i

C. -13 - 2i

D. -13 - 10i

Standards Description:

HSF-IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions.

Open Ended

Type response here

Standards Description:

HSA-REI.B.4.b Solve quadratic equations by inspection (e.g., for x ²= 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Multiple Choice

13. Consider the equation below. x ² - 36 = 0 Which of the following solution methods would not transform the equation in a way that would help in solving the equation?

A. factoring

B. taking square roots

C. completing the square

D. using the quadratic formula

Standards Description:

HSN-CN.A.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Multiple Choice

What is the product of (5 - 2i) and (7 + 8i)?

A. 19 + 26i

B. 35 - 16i

C. 35 + 10i

D. 51 + 26i

Standards Description:

HSF-IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Multiple Choice

16. The productivity, P, of a worker in a factory can be modeled by the function P(x) = -2x²+ 24x, where x is the number of hours worked. How many hours have been worked when productivity is at 0?

A. 6

B. 12

C. 24

D. 72

Standards Description:

HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

Open Ended

Solve the equation 0.5x2 - 8x + 34 = 0. Express your answer in the form of a ± bi.

Correct Answer: x = 8 ± 2i

Type response here

INTERIM ASSESSMET REVIEW-QUARTER 2

By Maredy Melo

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