Algebra 2 2nd Semester Review 2

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

____	1.	
a.	The solution set is .	c.	The solution set is .	
b.	
The solution set is .	d.	The solution set is .	

____	2.	
a.	The solution set is .	c.	The solution set is .	
b.	The solution set is .	d.	The solution set is .	

Write a quadratic equation with the given roots. Write the equation in the form , where a, b, and c are integers.

____	3.	–5 and 2
a.		c.		
b.		d.		

____	4.	 and 8
a.		c.		
b.		d.		

Solve the equation by factoring.

____	5.	
a.	{–4, }	c.	{–4, 7}	
b.	{, }	d.	{, 7}	

Simplify.

____	6.	
a.		c.		
b.		d.		

____	7.	
a.		c.		
b.		d.		

____	8.	
a.		c.		
b.		d.		

____	9.	 
a.		c.		
b.		d.		

____	10.	
a.		c.		
b.		d.		

____	11.	
a.		c.		
b.		d.		

Find the exact solution of the following quadratic equation by using the Quadratic Formula.

____	12.	
a.		c.		
b.		d.		

Find the value of the discriminant. Then describe the number and type of roots for the equation.

____	13.	
a.	The discriminant is 196. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.	
b.	The discriminant is –204. Because the discriminant is less than 0, the two roots are complex.	
c.	The discriminant is 204. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.	
d.	The discriminant is –188. Because the discriminant is less than 0, the two roots are complex.	

____	14.	
a.	The discriminant is –29.
Because the discriminant is less than 0, the two roots are complex.	
b.	The discriminant is 1.
Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.	
c.	The discriminant is –27.
Because the discriminant is less than 0, the two roots are complex.	
d.	The discriminant is 27.
Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.	

Write the following quadratic function in vertex form. Then, identify the axis of symmetry.

____	15.	
a.	The vertex form of the function is 
The equation of the axis of symmetry is .	
b.	The vertex form of the function is 
The equation of the axis of symmetry is .	
c.	The vertex form of the function is 
The equation of the axis of symmetry is .	
d.	The vertex form of the function is 
The equation of the axis of symmetry is .	

Solve the inequality algebraically.

____	16.	
a.	{x | < x  }	c.	{x | < x <  }	
b.	{x | < x <  }	d.	{x | < x <  }	

Simplify the given expression. Assume that no variable equals 0.

____	17.	
a.		c.		
b.		d.		

____	18.	
a.		c.		
b.		d.		

Simplify the expression using long division.

____	19.	
a.	quotient  and remainder 16	c.	quotient  and remainder –32	
b.	quotient  and remainder 0	d.	quotient  and remainder 32	

Simplify the expression using synthetic division.

____	20.	
a.	quotient  and remainder 1,152	
b.	quotient  and remainder 0	
c.	quotient  and remainder 1,536	
d.	quotient  and remainder 576	

____	21.	Find  and  for the function .
a.	51; 3,515	c.	–371; 1,525	
b.	61; 3,525	d.	113; 3,473	

____	22.	Use synthetic substitution to find  and g (–7) for the function .
a.	100, 2,216	c.	84, 11,896	
b.	76, 11,812	d.	36, –536	

Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials.

____	23.	; 
a.	()()	c.	()	
b.	()	d.	()()	

____	24.	; 
a.		c.	()()	
b.	2()	d.	()()	

____	25.	Find all of the zeros of the function .
a.	3, 6 – i, 6 + i	c.	3, 6 – i	
b.	6 – i, 6 + i	d.	–3, 6 – i, 6 + i	

____	26.	Find  and .

a.	
	c.	
	
b.	
	d.	

Find the inverse of the given relation.

____	27.	
a.		
b.		
c.		
d.		

Find the inverse of the given function.

____	28.	
a.		c.		
b.		d.		

____	29.	Determine whether each pair of functions are inverse functions.
1)                 2) 
a.	Only 1 is an inverse function.	
b.	Neither 1 nor 2 is an inverse function.	
c.	Both 1 and 2 are inverse functions.	
d.	Only 2 is an inverse function.	

Solve the given equation.

____	30.	
a.	n =  	c.	n =  	
b.	n = 	d.	n =  7	

____	31.	
a.	n = 	c.	n = 	
b.	n = –2	d.	n = 	

____	32.	
a.	2.24	c.	0.24	
b.	0.21	d.	0.19	

Evaluate the logarithmic expression.

____	33.	
a.		c.		
b.	32,768	d.		

____	34.	
a.	3	c.		
b.		d.	–3	

____	35.	Solve .
a.		c.	8	
b.		d.	16	

____	36.	Solve .
a.	18	c.	6	
b.	216	d.	729	

Solve the given equation. If necessary, round to four decimal places.

____	37.	
a.	26	c.	0.69	
b.	1.4444	d.	4	

____	38.	
a.	9	c.	130	
b.	1,329	d.	1,331	

____	39.	
a.	18.8519	c.	1.1870	
b.	0.2083	d.	3.0445	

____	40.	Evaluate the expression .
a.	e	c.		
b.		d.	2	

____	41.	Evaluate the expression .
a.		c.		
b.	14	d.	e	

Simplify the given expression.

____	42.	
a.		c.		
b.		d.		

____	43.	
a.		c.		
b.		d.		

____	44.	
a.		c.		
b.		d.		

Simplify the given expression.

____	45.	 + 
a.		c.		
b.		d.		

____	46.	
a.		c.		
b.		d.		

____	47.	If y varies directly as x and  when , find y when .
a.	168	c.	–168	
b.	16,800	d.	–16,800	

____	48.	Suppose y varies jointly as x and z. Find y when x = 2 and z = 11, if y = 160 when x = 3 and z = 8. Round your answer to the nearest hundredth, if necessary.
a.	1,173.33	c.	13.33	
b.	146.67	d.	174.55	

____	49.	If y varies inversely as x and  when , find y when . Round your answer to the nearest hundredth, if necessary.
a.	–746.15	c.	50.44	
b.	746.15	d.	–50.44	

Find the midpoint of the line segment with endpoints at the given coordinates.

____	50.	
a.	(, )	c.	(–6, –1)	
b.	(, )	d.	(, –2)	

Find the distance between the pair of points with the given coordinates.

____	51.	 and 
a.	18	c.		
b.		d.		

Write the equation in the standard form for a parabola.

____	52.	
a.		c.		
b.		d.		

Write the equation for a circle that satisfies the given conditions.

____	53.	center , radius 9 units
a.		c.		
b.		d.		

Find the center and radius of a circle with the given equation and then graph the circle.

____	54.	
a.	The center of the circle is  and the radius is 11. The graph of the circle is as follows:
	c.	The center of the circle is  and the radius is 11. The graph of the circle is as follows:
	
b.	The center of the circle is  and the radius is 11. The graph of the circle is as follows:
	d.	The center of the circle is  and the radius is 121. The graph of the circle is as follows:

Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola. Then graph the hyperbola.

____	55.	 
a.	The coordinates of the vertices are 
(±13, 0).
The coordinates of the foci are (0,± ).
The equation of the asymptotes is .y = ±  x .	c.	The coordinates of the vertices are (±13, 0)
The coordinates of the foci are (± , 0).
The equation of the asymptotes is y = ±  x.	
b.	The coordinates of the vertices are (±13, 0).
The coordinates of the foci are (± , 0).
The equation of the asymptotes is .y = ±  x.	d.	The coordinates of the vertices are (0, ±13).
The coordinates of the foci are (0, ± ).
The equation of the asymptotes is .y = ±  x.	

Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

____	56.	
a.	The equation in standard form is . The graph of the equation is an ellipse.

.	c.	The equation in standard form is . The graph of the equation is a parabola.

b.	The equation in standard form is . The graph of the equation is a hyperbola.

	d.	The equation in standard form is . The graph of the equation is a circle.

____	57.	
a.	The equation in standard form is .
The graph of the equation is a circle.	c.	The equation in standard form is .
The graph of the equation is a parabola.	
b.	The equation in standard form is .
The graph of the equation is an ellipse.	d.	The equation in standard form is .
The graph of the equation is a hyperbola.	

Without writing the equation in standard form, state whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.

____	58.	
a.	parabola	c.	circle	
b.	ellipse	d.	hyperbola	

____	59.	  
a.	parabola	c.	hyperbola	
b.	circle	d.	ellipse	

Find the exact solution(s) of the system of equations algebraically.

____	60.	
a.		c.		
b.		d.		

Algebra 2 2nd Semester Review 2
Answer Section

MULTIPLE CHOICE

	1.	ANS:	B
The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because  at those points.

	Feedback	
A	What are the x-intercepts of the graph?	
B	Correct!	
C	Find the zeros of the function, not the vertex.	
D	The zeros of the function are the solutions of the related equation.	

PTS:	1	DIF:	Advanced	REF:	Lesson 5-2	
OBJ:	5-2.1 Solve quadratic equations by graphing.	NAT:	NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA:	A1.2.5	TOP:	Solve quadratic equations by graphing.	
KEY:	Quadratic Equations | Solve Quadratic Equations	MSC:	1998 Lesson 6-1

	2.	ANS:	A
The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because  at those points.

	Feedback	
A	Correct!	
B	The zeros of the function are the solutions of the related equation.	
C	What are the x-intercepts of the graph?	
D	Find the zeros of the function, not the vertex.	

PTS:	1	DIF:	Advanced	REF:	Lesson 5-2	
OBJ:	5-2.1 Solve quadratic equations by graphing.	NAT:	NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA:	A1.2.5	TOP:	Solve quadratic equations by graphing.	
KEY:	Quadratic Equations | Solve Quadratic Equations	MSC:	1998 Lesson 6-1

	3.	ANS:	D
A quadratic equation with roots p and q can be written as , which can be further simplified.

	Feedback	
A	Did you verify the answer by substituting the values?	
B	Did you calculate the coefficients correctly?	
C	Did you check the signs of the coefficients?	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 5-3	
OBJ:	5-3.1 Write quadratic equations in intercept form.	NAT:	NA 1 | NA 3 | NA 7 | NA 8 | NA 2
TOP:	Write quadratic equations in intercept form.		
KEY:	Quadratic Equations | Roots of Quadratic Equations	MSC:	1998 Lesson 6-2 | 1998 Lesson 6-5

	4.	ANS:	A
A quadratic equation with roots p and q can be written as , which can be further simplified.

	Feedback	
A	Correct!	
B	Did you check the signs of the coefficients?	
C	Did you calculate the coefficients correctly?	
D	Did you verify the answer by substituting the values?	

PTS:	1	DIF:	Average	REF:	Lesson 5-3	
OBJ:	5-3.1 Write quadratic equations in intercept form.	NAT:	NA 1 | NA 3 | NA 7 | NA 8 | NA 2
TOP:	Write quadratic equations in intercept form.		
KEY:	Quadratic Equations | Roots of Quadratic Equations	MSC:	1998 Lesson 6-2 | 1998 Lesson 6-5

	5.	ANS:	B
For any real numbers a and b, if , then either , , or both a and b are equal to zero.

	Feedback	
A	Did you use the Zero Product Property correctly?	
B	Correct!	
C	Did you factor the binomial correctly?	
D	Did you verify the answer by substituting the values?	

PTS:	1	DIF:	Average	REF:	Lesson 5-3	
OBJ:	5-3.2 Solve quadratic equations by factoring.	NAT:	NA 1 | NA 3 | NA 7 | NA 8 | NA 2
STA:	A1.2.5	TOP:	Solve quadratic equations by factoring.	
KEY:	Quadratic Equations | Solve Quadratic Equations | Factoring	
MSC:	1998 Lesson 6-2 | 1998 Lesson 6-5

	6.	ANS:	C
Multiply the real numbers and imaginary numbers separately.

	Feedback	
A	Check your calculation.	
B	Check the sign.	
C	Correct!	
D	Multiply the imaginary numbers again.	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.2 Perform operations with pure imaginary numbers.	NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2
TOP:	Perform operations with pure imaginary numbers.

	7.	ANS:	A
Multiply the real numbers and imaginary numbers separately.

	Feedback	
A	Check your calculation.	
B	Check the sign.	
C	Correct!	
D	Compute again.	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.2 Perform operations with pure imaginary numbers.	NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2
TOP:	Perform operations with pure imaginary numbers.

	8.	ANS:	A
Combine the real and imaginary parts of the complex numbers to add them.

	Feedback	
A	Correct!	
B	Combine the real parts and then combine the imaginary parts.	
C	Add the real and imaginary parts of the two numbers separately.	
D	Did you combine the similar terms correctly?	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.3 Perform addition and subtraction operations with complex numbers.
NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2			
TOP:	Perform addition and subtraction operations with complex numbers.
KEY:	Complex Numbers | Add Complex Numbers | Subtract Complex Numbers
MSC:	1998 Lesson 5-9 | 1998 Lesson 5-10		

	9.	ANS:	B
Use the FOIL method to multiply the complex numbers and use the formula . Combine the real parts and then the imaginary parts of the two numbers.

	Feedback	
A	Did you combine the real parts?	
B	Correct!	
C	Use the value of i2.	
D	Did you use the FOIL method to find the product?	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.4 Perform multiplication operations with complex numbers.	
NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2			
TOP:	Perform multiplication operations with complex numbers.		
KEY:	Complex Numbers | Multiply Complex Numbers	MSC:	1998 Lesson 5-9 | 1998 Lesson 5-10

	10.	ANS:	D
Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression.

	Feedback	
A	Multiply the numerator with the conjugate of the denominator.	
B	Have you multiplied the constant in the numerator with its conjugate of the denominator?	
C	Did you multiply the conjugates correctly in the denominator?	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.5 Perform division operations with complex numbers.		
NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2			
TOP:	Perform division operations with complex numbers.	
KEY:	Complex Numbers | Divide Complex Numbers	MSC:	1998 Lesson 5-9 | 1998 Lesson 5-10

	11.	ANS:	A
Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression.

	Feedback	
A	Correct!	
B	Did you multiply the conjugates correctly in the denominator?	
C	Multiply the numerator also with the conjugate of the denominator.	
D	Did you combine the similar terms correctly?	

PTS:	1	DIF:	Average	REF:	Lesson 5-4	
OBJ:	5-4.5 Perform division operations with complex numbers.		
NAT:	NA 1 | NA 3 | NA 7 | NA 10 | NA 2			
TOP:	Perform division operations with complex numbers.	
KEY:	Complex Numbers | Divide Complex Numbers	MSC:	1998 Lesson 5-9 | 1998 Lesson 5-10

	12.	ANS:	D
The solution of a quadratic equation of the form , where , is obtained by using the formula .

	Feedback	
A	Did you substitute the values of a, b, and c correctly in the formula?	
B	Did you evaluate the discriminant correctly?	
C	Did you use the correct formula?	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 5-6	
OBJ:	5-6.1 Solve quadratic equations by using the Quadratic Formula.	
NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2	STA:	A1.2.5 | A1.2.9	
TOP:	Solve quadratic equations by using the Quadratic Formula.		
KEY:	Quadratic Equations | Solve Quadratic Equations | Quadratic Formula
MSC:	1998 Lesson 6-4	

	13.	ANS:	C
If  and  is a perfect square, then the roots are rational.
If  and  is not a perfect square, then the roots are real and irrational.

	Feedback	
A	Did you use the correct formula for the discriminant?	
B	Did you check the sign of the answer?	
C	Correct!	
D	Did you use the correct order of operations while evaluating the discriminant?	

PTS:	1	DIF:	Basic	REF:	Lesson 5-6	
OBJ:	5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.
NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2	STA:	A1.2.5 | A1.2.9	
TOP:	Use the discriminant to determine the number and types of roots of a quadratic equation.
KEY:	Quadratic Equations | Roots of Quadratic Equations | Discriminates
MSC:	1998 Lesson 6-4	

	14.	ANS:	C
If , then the roots are complex.

	Feedback	
A	Did you use the correct order of operations while evaluating the discriminant?	
B	Did you use the correct formula for the discriminant?	
C	Correct!	
D	Did you check the sign of the answer?	

PTS:	1	DIF:	Basic	REF:	Lesson 5-6	
OBJ:	5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.
NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2	STA:	A1.2.5 | A1.2.9	
TOP:	Use the discriminant to determine the number and types of roots of a quadratic equation.
KEY:	Quadratic Equations | Roots of Quadratic Equations | Discriminates
MSC:	1998 Lesson 6-4	

	15.	ANS:	A
The vertex form of a quadratic function is .
The equation of the axis of symmetry of a parabola is .

	Feedback	
A	Correct!	
B	Did you check the x-coordinate of the vertex?	
C	Did you identify the coordinates of the vertex correctly?	
D	Did you use the correct equation of the axis of symmetry of a parabola?	

PTS:	1	DIF:	Basic	REF:	Lesson 5-7	
OBJ:	5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.	
NAT:	NA 2 | NA 7 | NA 8 | NA 10 | NA 6			STA:	A2.3.3
TOP:	Analyze quadratic functions in the form y = a(x - h)^2 + k.		
KEY:	Quadratic Functions | Axis of Symmetry		MSC:	1998 Lesson 6-6

	16.	ANS:	C
First, write the related quadratic equation and factor it. Then, use the Zero Product Property and solve each equation. The solution is all real numbers when all test points satisfy the inequality. The solution is an empty set when none of the test points satisfy the inequality.

	Feedback	
A	Is it possible to have this solution?	
B	Did you write the related quadratic equation and factor it correctly?	
C	Correct!	
D	Did you test a value in the interval to see if it satisfies the original inequality?	

PTS:	1	DIF:	Advanced	REF:	Lesson 5-8	
OBJ:	5-8.2 Solve quadratic inequalities in one variable.	NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3
TOP:	Solve quadratic inequalities in one variable.		
KEY:	Quadratic Inequalities | Solve Quadratic Inequalities	MSC:	1998 Lesson 6-7

	17.	ANS:	B
Multiply the constants and then multiply the powers using the Power of a Product Property.

	Feedback	
A	Multiply the powers of the same variable using the Power of a Product Property.	
B	Correct!	
C	Multiply the constants.	
D	A simplified expression cannot contain negative exponents.	

PTS:	1	DIF:	Basic	REF:	Lesson 6-1	
OBJ:	6-1.1 Use properties of exponents to multiply monomials.		
NAT:	NA 1 | NA 7 | NA 8 | NA 10 | NA 2			STA:	A1.1.4
TOP:	Use properties of exponents to multiply monomials.	KEY:	Monomials | Multiply Monomials
MSC:	1998 Lesson 5-1	

	18.	ANS:	D
Simplify each base using the properties of powers. Then, write all the fractions in the simplest terms and ensure there are no negative exponents.

	Feedback	
A	Use the Power of a Power Property to all the terms in the monomial.	
B	There should be no negative exponents.	
C	Raise the numerator and the denominator to the fourth power before simplifying.	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 6-1	
OBJ:	6-1.2 Use properties of exponents to divide monomials.	NAT:	NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA:	A1.1.5	TOP:	 Use properties of exponents to divide monomials.
KEY:	Monomials | Divide Monomials	MSC:	1998 Lesson 5-1	

	19.	ANS:	B
Use the division algorithm. When dividing, you can add or subtract only similar terms.

	Feedback	
A	Did you consider both the terms of the divisor?	
B	Correct!	
C	Change the signs of the product terms only.	
D	Did you use the correct signs of the terms?	

PTS:	1	DIF:	Advanced	REF:	Lesson 6-2	
OBJ:	6-2.1 Divide polynomials using long division.	NAT:	NA 1 | NA 6 | NA 7 | NA 9 | NA 2
STA:	A1.1.5	TOP:	Divide polynomials using long division.	
KEY:	Polynomials | Divide Polynomials | Long Division	MSC:	1998 Lesson 5-3

	20.	ANS:	B
To use synthetic division, the divisor must be of the form .

	Feedback	
A	Multiply the first coefficient with the constant in the divisor and bring it below the second coefficient.	
B	Correct!	
C	Bring the first coefficient below itself in the third row.	
D	Add the product of the constant in the divisor to the coefficient above it.	

PTS:	1	DIF:	Advanced	REF:	Lesson 6-2	
OBJ:	6-2.2 Divide polynomials using synthetic division.	NAT:	NA 1 | NA 6 | NA 7 | NA 9 | NA 2
STA:	A1.1.5	TOP:	Divide polynomials using synthetic division.
KEY:	Polynomials | Divide Polynomials | Synthetic Division	MSC:	1998 Lesson 5-3

	21.	ANS:	B
Replace the values of p(x) with p(–3) and simplify.

	Feedback	
A	Add the value of the constant.	
B	Correct!	
C	The exponent value of the first term is 4, not 3.	
D	Did you substitute the correct values in the function?	

PTS:	1	DIF:	Average	REF:	Lesson 6-3	
OBJ:	6-3.1 Evaluate polynomial functions.			NAT:	NA 1 | NA 7 | NA 8 | NA 10 | NA 2
TOP:	Evaluate polynomial functions.	KEY:	Polynomial Functions	
MSC:	1998 Lesson 8-1	

	22.	ANS:	B
Use synthetic substitution to obtain the required answer.

	Feedback	
A	Did you calculate correctly?	
B	Correct!	
C	Did you substitute the correct values?	
D	The degree of the function is 4, not 3.	

PTS:	1	DIF:	Advanced	REF:	Lesson 6-6	
OBJ:	6-6.1 Evaluate functions using synthetic substitution.	NAT:	NA 1 | NA 3 | NA 9 | NA 10 | NA 2
TOP:	Evaluate functions using synthetic substitution.	
KEY:	Polynomial Functions | Synthetic Substitution	MSC:	1998 Lesson 8-2

	23.	ANS:	A
Use the Factor Theorem.

	Feedback	
A	Correct!	
B	You have to factor the depressed polynomial to its simplest form.	
C	Did you factor correctly?	
D	Did you verify the answer by multiplying the factors?	

PTS:	1	DIF:	Advanced	REF:	Lesson 6-6	
OBJ:	6-6.2 Determine whether a binomial is a factor of a polynomial by using synthetic substitution.
NAT:	NA 1 | NA 3 | NA 9 | NA 10 | NA 2			STA:	A1.1.4
TOP:	Determine whether a binomial is a factor of a polynomial by using synthetic substitution.
KEY:	Polynomial Functions | Synthetic Substitution	MSC:	1998 Lesson 8-2

	24.	ANS:	C
Use the Factor Theorem.

	Feedback	
A	Is the square of the binomial equal to the depressed polynomial?	
B	Did you factor correctly?	
C	Correct!	
D	Did you verify the answer by multiplying the factors?	

PTS:	1	DIF:	Advanced	REF:	Lesson 6-6	
OBJ:	6-6.2 Determine whether a binomial is a factor of a polynomial by using synthetic substitution.
NAT:	NA 1 | NA 3 | NA 9 | NA 10 | NA 2			STA:	A1.1.4
TOP:	Determine whether a binomial is a factor of a polynomial by using synthetic substitution.
KEY:	Polynomial Functions | Synthetic Substitution	MSC:	1998 Lesson 8-2

	25.	ANS:	A
Use synthetic substitution to obtain the required answer.

	Feedback	
A	Correct!	
B	The function also has a positive real zero.	
C	Find all the possible imaginary zeros.	
D	There is no change in sign for the coefficients of f(–x).	

PTS:	1	DIF:	Average	REF:	Lesson 6-7	
OBJ:	6-7.2 Find the zeros of a polynomial function.	NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2
TOP:	Find the zeros of a polynomial function.		
KEY:	Polynomial Functions | Zeroes of Polynomial Functions	MSC:	1998 Lesson 8-4

	26.	ANS:	B
If f and g are functions such that the range of g is a subset of the domain of f, then the composite function  can be described as 

	Feedback	
A	Did you perform the composition correctly?	
B	Correct!	
C	Did you check the mathematical operators in the equation?	
D	Did you calculate correctly?	

PTS:	1	DIF:	Advanced	REF:	Lesson 7-1	
OBJ:	7-1.5 Find the composition of functions.		NAT:	NA 1 | NA 6 | NA 7 | NA 10 | NA 2
STA:	A2.2.5 | A2.2.6		TOP:	Find the composition of functions.
KEY:	Functions | Composition of Functions		MSC:	1998 Lesson 8-7

	27.	ANS:	C
The inverse relation is the set of ordered pairs obtained by reversing the coordinates of each original ordered pair.

	Feedback	
A	Write the inverse of all the ordered pairs in the relation.	
B	Did you write all the values with the correct sign?	
C	Correct!	
D	Did you check the sign of all the values?	

PTS:	1	DIF:	Basic	REF:	Lesson 7-2	OBJ:	7-2.1 Find the inverse of a relation.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A2.2.4 | A2.2.6	
TOP:	Find the inverse of a relation.	KEY:	Relations | Inverses of Relations
MSC:	1998 Lesson 8-8	

	28.	ANS:	B
The inverse function can be found by exchanging the domain and range of the function.

	Feedback	
A	The answer includes an incorrect negative sign.	
B	Correct!	
C	Did you calculate the correct value of the inverse of the function?	
D	You have interchanged the values.	

PTS:	1	DIF:	Average	REF:	Lesson 7-2	OBJ:	7-2.2 Find the inverse of a function.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A2.2.4 | A2.2.6	
TOP:	Find the inverse of a function.	KEY:	Functions | Inverses of Functions
MSC:	1998 Lesson 8-8	

	29.	ANS:	D
Two functions f and g are inverse functions if and only if both of their compositions are the identity function.

	Feedback	
A	Did you find both compositions in each pair?	
B	How will you determine whether a pair of functions are inverse functions?	
C	The composition of the first pair of functions is not an identity function.	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 7-2	
OBJ:	7-2.3 Determine whether two functions or relations are inverses.	
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A2.2.4 | A2.2.6	
TOP:	Determine whether two functions or relations are inverses.		
KEY:	Functions | Inverses of Functions	MSC:	1998 Lesson 8-8	

	30.	ANS:	A
Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation.

	Feedback	
A	Correct!	
B	Did you check the exponent of the base on the right side of the equation?	
C	Did you write the right side of the equation in the correct exponential form?	
D	Did you check the exponent of the base on the left side of the equation?	

PTS:	1	DIF:	Average	REF:	Lesson 8-2	OBJ:	8-2.1 Solve exponential equations.
NAT:	NA 1 | NA 3 | NA 4 | NA 10 | NA 2			STA:	A1.2.7
TOP:	Solve exponential equations.	KEY:	Solve Equations | Exponential Equations
MSC:	1998 Lesson 10-1	

	31.	ANS:	C
Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation.

	Feedback	
A	Did you check the exponent of the base on the right side of the equation?	
B	Check the exponent of the base on the left side of the equation.	
C	Correct!	
D	Did you solve the equation correctly?	

PTS:	1	DIF:	Average	REF:	Lesson 8-2	OBJ:	8-2.1 Solve exponential equations.
NAT:	NA 1 | NA 3 | NA 4 | NA 10 | NA 2			STA:	A1.2.7
TOP:	Solve exponential equations.	KEY:	Solve Equations | Exponential Equations
MSC:	1998 Lesson 10-1	

	32.	ANS:	C
Find the least common denominator and multiply both sides by it.

	Feedback	
A	Did you substitute the values correctly?	
B	Did you solve the equation correctly?	
C	Correct!	
D	Did you perform the correct arithmetic operation?	

PTS:	1	DIF:	Advanced	REF:	Lesson 9-6	OBJ:	9-6.1 Solve rational equations.
NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6			STA:	A1.2.5
TOP:	Solve rational equations.	KEY:	Rational Equations | Solve Rational Equations
MSC:	1998 Lesson 9-5	

	33.	ANS:	D
Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression.

	Feedback	
A	Use the Property of Equality for Exponential Functions.	
B	Write the correct exponential form of the given expression.	
C	The exponential and logarithmic functions are inverses.	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 8-3	
OBJ:	8-3.1 Evaluate logarithmic expressions.		NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2
STA:	A1.2.7 | A2.5.3		TOP:	Evaluate logarithmic expressions.
KEY:	Logarithms | Evaluate Expressions | Logarithmic Expressions	
MSC:	1998 Lesson 10-2	

	34.	ANS:	D
Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression.

	Feedback	
A	Did you check the exponential form?	
B	Use the Property of Equality for Exponential Functions.	
C	The exponential and logarithmic functions are inverses.	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 8-3	
OBJ:	8-3.1 Evaluate logarithmic expressions.		NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2
STA:	A1.2.7 | A2.5.3		TOP:	Evaluate logarithmic expressions.
KEY:	Logarithms | Evaluate Expressions | Logarithmic Expressions	
MSC:	1998 Lesson 10-2	

	35.	ANS:	D
Use the definition of logarithms with base b to solve the logarithmic equation.

	Feedback	
A	Did you apply the definition of logarithm?	
B	Did you simplify correctly?	
C	What is the value on the right side of the equation?	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 8-4	OBJ:	8-4.1 Solve logarithmic equations.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Solve logarithmic equations.	KEY:	Solve Equations | Logarithmic Equations
MSC:	1998 Lesson 10-2	

	36.	ANS:	D
Use the definition of logarithms with base b.

	Feedback	
A	Did you use the definition of logarithm correctly?	
B	Did you calculate correctly?	
C	Did you consider the base of the logarithm on the left side of the equation?	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 8-4	OBJ:	8-4.1 Solve logarithmic equations.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Solve logarithmic equations.	KEY:	Solve Equations | Logarithmic Equations
MSC:	1998 Lesson 10-2	

	37.	ANS:	B
Use the Product Property and the definition of logarithm.

	Feedback	
A	Did you substitute the values correctly?	
B	Correct!	
C	Have you used the Quotient Property of Logarithms?	
D	Did you use the properties of logarithms?	

PTS:	1	DIF:	Average	REF:	Lesson 8-5	
OBJ:	8-5.2 Solve logarithmic equations using the properties of logarithms.
NAT:	NA 1 | NA 4 | NA 6 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Solve logarithmic equations.	KEY:	Solve Equations | Logarithmic Equations
MSC:	1998 Lesson 10-3	

	38.	ANS:	B
Use the Quotient Property and the Property of Equality for Logarithmic Functions.

	Feedback	
A	Did you apply the Product Property of Logarithms?	
B	Correct!	
C	Did you use the properties of logarithms?	
D	You have substituted incorrect values.	

PTS:	1	DIF:	Average	REF:	Lesson 8-5	
OBJ:	8-5.2 Solve logarithmic equations using the properties of logarithms.
NAT:	NA 1 | NA 4 | NA 6 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Solve logarithmic equations.	KEY:	Solve Equations | Logarithmic Equations
MSC:	1998 Lesson 10-3	

	39.	ANS:	C
Use the Property of Inequality for Logarithmic Functions and the Power Property of Logarithms to solve the equation.

	Feedback	
A	Take the logarithms of both the sides of the equation.	
B	Did you use the Quotient Property of Logarithms?	
C	Correct!	
D	Did you substitute the values of the equation according to the Power Property of Logarithms?	

PTS:	1	DIF:	Average	REF:	Lesson 8-6	
OBJ:	8-6.1 Solve exponential equations using common logarithms.	
NAT:	NA 1 | NA 4 | NA 6 | NA 9 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Solve exponential equations using common logarithms.	
KEY:	Solve Equations | Exponential Equations | Common Logarithms	
MSC:	1998 Lesson 10-4	

	40.	ANS:	D
Use the Inverse Property of Base e and Natural Logarithms to evaluate the expression.

	Feedback	
A	You have used an incorrect base value.	
B	Did you apply the Inverse Property of Base e and Natural Logarithms correctly?	
C	The exponential and logarithmic functions are inverses.	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 8-7	
OBJ:	8-7.1 Evaluate expressions involving the natural base and natural logarithms.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Evaluate expressions involving the natural base and natural logarithms.
KEY:	Evaluate Expressions | Natural Logarithms		MSC:	1998 Lesson 10-5

	41.	ANS:	B
Use the Inverse Property of Base e and Natural Logarithms to evaluate the expression.

	Feedback	
A	The exponential and logarithmic functions are inverses.	
B	Correct!	
C	Did you apply the Inverse Property of Base e and Natural Logarithms correctly?	
D	You have used an incorrect base value.	

PTS:	1	DIF:	Basic	REF:	Lesson 8-7	
OBJ:	8-7.1 Evaluate expressions involving the natural base and natural logarithms.
NAT:	NA 1 | NA 3 | NA 4 | NA 7 | NA 2	STA:	A1.2.7 | A2.5.3	
TOP:	Evaluate expressions involving the natural base and natural logarithms.
KEY:	Evaluate Expressions | Natural Logarithms		MSC:	1998 Lesson 10-5

	42.	ANS:	C
First, multiply the values and then divide the numerator and the denominator by the common factors.

	Feedback	
A	Divide the denominator by x, not x2.	
B	Divide the numerator also with y.	
C	Correct!	
D	Did you multiply accurately?	

PTS:	1	DIF:	Average	REF:	Lesson 9-1	
OBJ:	9-1.1 Simplify rational expressions with multiplication.	NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA:	A1.1.4	TOP:	Simplify rational expressions with multiplication.
KEY:	Rational Expressions | Multiply Rational Expressions	MSC:	1998 Lesson 9-1

	43.	ANS:	C
To divide two rational expressions, multiply by the reciprocal of the divisor.

	Feedback	
A	Did you perform all the mathematical actions?	
B	Did you divide correctly?	
C	Correct!	
D	To simplify the values, divide the denominator by b3, not by b4.	

PTS:	1	DIF:	Average	REF:	Lesson 9-1	
OBJ:	9-1.2 Simplify rational expressions with division.	NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA:	A1.1.4	TOP:	Simplify rational expressions with division.	
KEY:	Rational Expressions | Divide Rational Expressions	MSC:	1998 Lesson 9-1

	44.	ANS:	B
To divide two rational expressions, multiply the first expression by the reciprocal of the divisor.

	Feedback	
A	Did you simplify correctly?	
B	Correct!	
C	Did you factor properly?	
D	Did you divide accurately?	

PTS:	1	DIF:	Advanced	REF:	Lesson 9-1	
OBJ:	9-1.2 Simplify rational expressions with division.	NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA:	A1.1.4	TOP:	Simplify rational expressions with division.	
KEY:	Rational Expressions | Divide Rational Expressions	MSC:	1998 Lesson 9-1

	45.	ANS:	C
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator and add the numerators.

	Feedback	
A	Did you calculate the numerator correctly?	
B	Add the numerators and simplify.	
C	Correct!	
D	Find the common denominator and then add the numerators.	

PTS:	1	DIF:	Average	REF:	Lesson 9-2	OBJ:	9-2.2 Add rational expressions.
NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6			STA:	A1.1.4
TOP:	Add rational expressions.	KEY:	Rational Expressions | Add Rational Expressions
MSC:	1998 Lesson 9-4	

	46.	ANS:	C
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator and subtract the numerators.

	Feedback	
A	Find the common denominator and then subtract the numerators.	
B	Did you simplify properly?	
C	Correct!	
D	Did you find the correct LCD?	

PTS:	1	DIF:	Average	REF:	Lesson 9-2	OBJ:	9-2.3 Subtract rational expressions.
NAT:	NA 2 | NA 8 | NA 9 | NA 10 | NA 6			STA:	A1.1.4
TOP:	Subtract rational expressions.	KEY:	Rational Expressions | Subtract Rational Expressions
MSC:	1998 Lesson 9-4	

	47.	ANS:	C
Use direct proportion to relate the values.

	Feedback	
A	Did you use the negative sign?	
B	Did you substitute the values correctly?	
C	Correct!	
D	Did you use the correct equation for direct variation?	

PTS:	1	DIF:	Basic	REF:	Lesson 9-5	
OBJ:	9-5.1 Recognize and solve direct variation problems.	NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP:	Recognize and solve direct variation problems.	KEY:	Direct Variation
MSC:	1998 Lesson 9-2	

	48.	ANS:	B
Use one set of proportions to find the other set of corresponding values in the equation .

	Feedback	
A	Did you substitute the values of all the variables?	
B	Correct!	
C	Have you used all the values of the variables?	
D	Did you use the correct equation for joint variation?	

PTS:	1	DIF:	Advanced	REF:	Lesson 9-5	
OBJ:	9-5.2 Recognize and solve joint variation problems.	NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP:	Recognize and solve joint variation problems.	KEY:	Joint Variation
MSC:	1998 Lesson 9-2	

	49.	ANS:	D
Use inverse proportion to relate values in the following equation.

	Feedback	
A	Did you substitute the values correctly?	
B	Did you use the correct equation for inverse variation?	
C	Did you forget to include the negative sign in the answer?	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 9-5	
OBJ:	9-5.3 Recognize and solve inverse variation problems.	NAT:	NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP:	Recognize and solve inverse variation problems.	KEY:	Inverse Variation
MSC:	1998 Lesson 9-2	

	50.	ANS:	A
The coordinates of the midpoint are the means of the coordinates of the endpoints.

	Feedback	
A	Correct!	
B	Did you take the mean of the coordinates according to their integral values?	
C	Did you consider the mean value of the coordinates of the endpoints?	
D	Did you take the mean of the x-coordinates and the y-coordinates of the end points?	

PTS:	1	DIF:	Average	REF:	Lesson 10-1	
OBJ:	10-1.1 Find a midpoint of a segment on the coordinate plane.	
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	A1.2.9
TOP:	Find the midpoint of a segment on the coordinate plane.	
KEY:	Midpoint Formula | Distance Formula | Midpoint of a Segment	
MSC:	1998 Lesson 7-1	

	51.	ANS:	C
The distance  between two points with coordinates  and  is given by the formula .

	Feedback	
A	Subtract the y-coordinates of the two points before squaring them.	
B	Take the squares of the difference of the coordinates before adding them.	
C	Correct!	
D	Subtract the x-coordinates of the two points before squaring them.	

PTS:	1	DIF:	Average	REF:	Lesson 10-1	
OBJ:	10-1.2 Find the distance between two points on the coordinate plane.
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	A1.2.9
TOP:	Find the distance between two points on the coordinate plane.	
KEY:	Distance Formula | Distance Between Two Points	MSC:	1998 Lesson 7-1

	52.	ANS:	A
Factor the x terms and complete the square on the right side. The number that is added to complete the square must be multiplied by the factor.

	Feedback	
A	Correct!	
B	Did you calculate all the values correctly?	
C	Did you subtract the number on the right side of the equation?	
D	Complete the square on the right side of the equation.	

PTS:	1	DIF:	Advanced	REF:	Lesson 10-2	
OBJ:	10-2.1 Write equations of parabolas in standard form.	NAT:	NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA:	G1.7.2 | G1.7.4		TOP:	Write equations of parabolas in standard form.
KEY:	Parabolas | Equations of Parabolas	MSC:	1998 Lesson 7-2	

	53.	ANS:	D
If  are the coordinates of a point on a circle,  is the center, and r is the radius, then the equation of this circle is .

	Feedback	
A	Take the square of the radius on the right side of the equation.	
B	Did you subtract the y-coordinate of the center from y?	
C	Did you subtract the x-coordinate of the center from x?	
D	Correct!	

PTS:	1	DIF:	Average	REF:	Lesson 10-3	OBJ:	10-3.1 Write equations of circles.
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	G1.7.1
TOP:	Write equations of circles.	KEY:	Circles | Equations of Circles
MSC:	1998 Lesson 7-3	

	54.	ANS:	C
If  is the equation of a circle in standard form, then  is the center of the circle and r is the radius.

	Feedback	
A	How do you determine the coordinates of the center?	
B	The y-coordinate of the center of the circle is incorrect.	
C	Correct!	
D	Did you calculate the radius correctly?	

PTS:	1	DIF:	Advanced	REF:	Lesson 10-3	OBJ:	10-3.2 Graph circles.
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	G1.7.2
TOP:	Graph circles.			KEY:	Circles | Graph Circles
MSC:	1998 Lesson 7-3	

	55.	ANS:	B
For a hyperbola with the equation , the coordinates of the vertices are  and the coordinates of the foci are , where . The equation of the asymptotes is .

	Feedback	
A	Did you use the correct coordinates of the foci?	
B	Correct!	
C	Did you use the correct equations of the asymptotes?	
D	The coordinates of the foci and vertices are incorrect.	

PTS:	1	DIF:	Advanced	REF:	Lesson 10-5	OBJ:	10-5.2 Graph hyperbolas.
NAT:	NA 2 | NA 6 | NA 8 | NA 10 | NA 3			STA:	G1.7.2 | G1.7.3
TOP:	Graph hyperbolas.		KEY:	Hyperbolas | Graph Hyperbolas
MSC:	1998 Lesson 7-5	

	56.	ANS:	A
Write the equation of the given conic section in standard form and compare it to the standard form of a parabola, circle, ellipse, or hyperbola to state its type.

	Feedback	
A	Correct!	
B	Did you use the correct signs in the equation?	
C	Did you write the standard form of the equation correctly?	
D	The coefficient of the y2 term in the equation is incorrect.	

PTS:	1	DIF:	Advanced	REF:	Lesson 10-6	
OBJ:	10-6.1 Write equations of conic sections in standard form.		
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	G1.7.2 | G1.7.3
TOP:	Write equations of conic sections in standard form.	
KEY:	Conic Sections | Equations of Conic Sections | Standard Form	
MSC:	1998 Lesson 7-6	

	57.	ANS:	D
Write the equation of the given conic section in standard form and compare it to the standard form of a parabola, circle, ellipse, or hyperbola.

	Feedback	
A	Did you use the correct coefficient of the y2 term in the equation?	
B	Did you use the correct sign between the squared terms in the standard form?	
C	This is not the standard form of the given equation.	
D	Correct!	

PTS:	1	DIF:	Advanced	REF:	Lesson 10-6	
OBJ:	10-6.1 Write equations of conic sections in standard form.		
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			STA:	G1.7.2 | G1.7.3
TOP:	Write equations of conic sections in standard form.	
KEY:	Conic Sections | Equations of Conic Sections | Standard Form	
MSC:	1998 Lesson 7-6	

	58.	ANS:	C
You can determine the type of conic section represented by the equation , where , by checking the relationship between A and C.

	Feedback	
A	The coefficients of neither x2 nor y2  is zero.	
B	The coefficients of x2  and y2  are equal.	
C	Correct!	
D	The coefficients of x2  and y2  are equal and have the same signs.	

PTS:	1	DIF:	Basic	REF:	Lesson 10-6	
OBJ:	10-6.2 Identify conic sections from their equations.	NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA:	G1.7.2 | G1.7.3		TOP:	Identify conic sections from their equations.
KEY:	Conic Sections | Equations of Conic Sections | Identify Conic Sections
MSC:	1998 Lesson 7-6	

	59.	ANS:	D
You can determine the type of conic section represented by the equation , where , by checking the relationship between A and C.

	Feedback	
A	The coefficients of x2  and y2  are both non zero.	
B	The coefficients of x2  and y2  are not equal.	
C	The coefficients of x2  and y2  have the same signs.	
D	Correct!	

PTS:	1	DIF:	Basic	REF:	Lesson 10-6	
OBJ:	10-6.2 Identify conic sections from their equations.	NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA:	G1.7.2 | G1.7.3		TOP:	Identify conic sections from their equations.
KEY:	Conic Sections | Equations of Conic Sections | Identify Conic Sections
MSC:	1998 Lesson 7-6	

	60.	ANS:	A
Use the substitution or elimination method to solve the system.

	Feedback	
A	Correct!	
B	Did you solve the values correctly?	
C	Take the square root of each side after solving the system.	
D	The square root of a number will have both positive and negative signs.	

PTS:	1	DIF:	Average	REF:	Lesson 10-7	
OBJ:	10-7.1 Solve systems of quadratic equations algebraically.		
NAT:	NA 2 | NA 6 | NA 9 | NA 10 | NA 3			
TOP:	Solve systems of quadratic equations algebraically.	KEY:	Systems of Quadratic Equations
MSC:	1998 Lesson 7-7