2nd Quarter Exam Math 8

8/10/2019 2nd Quarter Exam Math 8

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MATHEMATICS 8SECOND QUARTER EXAMINATION

NAME:_________________________ Date:________________ Score:_____________

I.

Multiple Choice: Identify the choice that best completes the statement or answers the question.(Each item is worth two points, show your solution for each item on the right side of this paper to get the

full points.)

______1. Simplify .

A. C.

B. D.

______2. Multiply.

A. C.

B. D.

______3. Multiply.

A. C.

B. D.

______4. Multiply.

A. C.B. D.

______5. Factor .A. C.

B. D.

______6. Factor the polynomial .

A.

B. Cannot be factoredC.

D.

______7. Simplify the rational expression . Identify any excluded values.

A. 3r; r 3 C. 3r; no excluded valuesB. 3r; r 3 or 0 D. ; r 3


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______8. Simplify the rational expression .

A. C.

B. D.

______9. Simplify the rational expression .

A. C.

B. D.

______10. Multiply. Simplify your answer.

A. C.

B. D.

______11. Multiply. Simplify your answer.

A. C.

B. D.

______12. Multiply. Simplify your answer. .

A. C.

B. D.

______13. Divide. Simplify your answer.

A. C.

B. D.

______14. Divide . Assume that all expressions are defined.

A. C.

B. D.


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______15. Add. Simplify your answer.

A. C.

B. D.

______16. Subtract. Simplify your answer.

A. C.

B. D.

______17. Add. Simplify your answer.

A. C.

B. D.

______18. Subtract and simplify. Find the excluded values.

A.;

B.; and

C.; , and

D.; and

______19. Add .

A. C.

B. D.

______20. Simplify . Assume that all expressions are defined.

A. C.

B. D.


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II. Arrange the steps in adding/subtracting rational expressions in order by writing the numbers 1 to 5, 1 beingthe first step to be done and 5 being the last, on the space provided.

_____ Add or subtract the numerators.

_____ Simplify, if possible.

_____ If necessary, find equivalent fractions that have the same denominator.

_____ Factor, if possible.

_____ Combine any like terms in the numerator.

III. Discussion.

1. The area of a rectangle is equal to square units. If the length of the rectangle is equal to units,how will you find the expression that represents its width? What is this expression?

2. The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of(4z3+ 8z2+ 4z) square meters.

A. List all possible expressions for the length and width of the wall. (Assume the factors are polynomials.)B. Give a value for z to find each possible length and width.

3. The formula for the difference in volumes between two square prisms of equal height is , where his

the height of the prisms, Sis the base length of the larger prism, and sis the base length of the smaller prism. Writethe formula for the difference in volumes between two square prisms in factored form. Then, use the factored formto find the difference in volumes with cm, cm, and cm.

Ss

h

h


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D QUARTER EXAM MATHEMATICS 8

wer Section

LTIPLE CHOICE

. ANS: B

=Rewrite without negative or zero

exponents.

=

Simplify each part of the expression.

.

= .

=

Feedback

A Any number to the zero power is equal to 1. A negative exponent in the numerator

becomes positive in the denominator.B Correct!C Any number to the zero power is equal to 1. A negative exponent in the numerator

becomes positive in the denominator.D A negative exponent in the denominator becomes positive in the numerator.

PTS: 1 DIF: Advanced REF: Page 396

OBJ: 7-1.4 Simplify Expressions with Zero and Negative ExponentsNAT: 12.5.3.d TOP: 7-1 Integer Exponents KEY: exponent | negative exponent | simplify

2. ANS: CUse FOIL.

Distribute nand5.

Distribute nand5 again.

Multiply.

Combine like-terms.

Feedback

A Distribute again, multiply and combine like-terms.B You did not multiply the outer terms.C Correct!

D You did not multiply the inner and outer terms.

PTS: 1 DIF: Basic REF: Page 448 OBJ: 7-8.3 Multiplying BinomialsNAT: 12.5.3.c TOP: 7-8 Multiplying Polynomials KEY: binomial | multiplication

. ANS: B

Distribute and .

Distribute and again.

Multiply.

Combine like terms.


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Feedback

A Check the signs.B Correct!C Combine only like terms.D Combine only like terms.

PTS: 1 DIF: Average REF: Page 449 OBJ: 7-8.4 Multiplying PolynomialsNAT: 12.5.3.c TOP: 7-8 Multiplying Polynomials

4. ANS: A

= Use the rule for .

Use the FOIL method, and then combine like terms.

Simplify.

Feedback

A Correct!B The terms in the product should be squares.C First, use the FOIL method. Then, combine the like terms.D Use the FOIL method.

PTS: 1 DIF: Basic REF: Page 457OBJ: 7-9.3 Finding Products in the Form (a + b)(a b) NAT: 12.5.3.c

TOP: 7-9 Special Products of Binomials KEY: binomial | multiplication

5. ANS: DSince a= 2, the coefficients of the First terms must be factors of 2.Since c= 6, the Last terms must be factors of 6.Since b= , the Outer and Inner products must add up to .The sum of the products of the outer and inner terms should be .

It may be helpful to make a table to check all the factors of 2 and all the factors of 6. Then check the products of the outerand inner terms to see if the sum is .

Feedback

A You reversed the second terms in the parentheses.B When bis negative, the factors of care both negative. When bis positive, the factors of

care both positive.C The coefficient of thex-term in the second binomial cannot be 1. Check your answer.D Correct!

PTS: 1 DIF: Basic REF: Page 506

OBJ: 8-4.2 Factoring ax^2 + bx + c When c Is Positive NAT: 12.5.3.d

TOP: 8-4 Factoring ax^2 + bx + c6. ANS: A

Find the GCF. The GCF of , , and is

Write the terms as products using the GCF.

Use the Distributive Property to factor out the GCF.

Feedback

A Correct!B First, find the GCF. Then, use the Distributive Property to factor out the GCF.C First, find the GCF. Then, write the terms as products using the GCF.


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D First, find the GCF. Then, write the terms as products using the GCF.

PTS: 1 DIF: Average REF: Page 487 OBJ: 8-2.1 Factoring by Using the GCF

NAT: 12.1.5.b TOP: 8-2 Factoring by GCF

7. ANS: AFactor common factors out of the numerator and/or denominator. Divide out the common factors to simplify the

expression. Finally, use the original denominator to determine excluded factors.

Feedback

A Correct!B Determine excluded values from the original denominator.C Determine excluded values from the original denominator.D Divide out common factors.

PTS: 1 DIF: Basic REF: Page 643 OBJ: 10-3.2 Simplifying Rational Expressions

NAT: 12.5.3.c TOP: 10-3 Simplifying Rational Expressions

8. ANS: B

Factor the numerator and denominator.

Divide out the common factors.

Simplify.

Feedback

A Factor the denominator. Divide out common factors.B Correct!C Factor the denominator. Divide out common factors.D Factor the denominator. Divide out common factors.

PTS: 1 DIF: Basic REF: Page 643OBJ: 10-3.3 Simplifying Rational Expressions with Trinomials


9. ANS: B

=Factor.

=Identify the opposite binomials.

=Divide out the common factors, and simplify.

Feedback

A Factor the denominator also.B Correct!C Identify the opposite binomials. Then, divide out common factors and simplify.D Identify the opposite binomials. Then, divide out common factors and simplify.

PTS: 1 DIF: Average REF: Page 644OBJ: 10-3.4 Simplifying Rational Expressions Using Opposite Binomials


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0. ANS: C

Arrange the expressions so like terms are together: .

Multiply the numerators and denominators, remembering to add exponents when multiplying: .

Divide, remembering to subtract exponents: .

Since , this expression simplifies to

Feedback

A A variable raised to the 0 power simplifies to 1.B When dividing powers with the same base, subtract the exponents.C Correct!D Multiply, then simplify.

PTS: 1 DIF: Average REF: Page 652 OBJ: 10-4.1 Multiplying Rational Expressions

NAT: 12.5.3.c TOP: 10-4 Multiplying and Dividing Rational Expressions

. ANS: B

= Write the polynomial over 1.

= Factor the numerator and denominator.

= Divide out common factors.

= Multiply remaining factors.

FeedbackA Divide out common factors, and multiply the remaining factors.B Correct!C First, rewrite the polynomial as an expression over 1. Then, multiply and simplify.D Continue simplifying until the answer is in simplest form.

PTS: 1 DIF: Average REF: Page 653OBJ: 10-4.2 Multiplying a Rational Expression by a Polynomial


2. ANS: A

= Factor the numerator and denominator.

= Simplify.

= Multiply the remaining factors.

Feedback

A Correct!


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B Factor the numerator and denominator and divide out the common factors.C Factor the numerator and denominator and divide out the common factors.D Factor the numerator and denominator and divide out the common factors.

PTS: 1 DIF: Average REF: Page 653OBJ: 10-4.3 Multiplying Rational Expressions Containing Polynomials


3. ANS: A

=Write as multiplication by the reciprocal.

=Multiply the numerators and the denominators.

=Divide out common factors. Simplify.

Feedback

A Correct!B Divide out common factors, and simplify.C First, write as multiplication by the reciprocal. Then, multiply the numerators and the

denominators.D Write as multiplication by the reciprocal first.

PTS: 1 DIF: Basic REF: Page 654OBJ: 10-4.4 Dividing by Rational Expressions and Polynomials


4. ANS: A

Rewrite as multiplication by the reciprocal.

= Simplify by canceling common factors.

=

Feedback

A Correct!B To divide by a fraction, you multiply by its reciprocal.C To divide by a fraction, you multiply by its reciprocal.

D Multiply the first fraction by the reciprocal of the second fraction.

PTS: 1 DIF: Basic REF: Page 579 OBJ: 8-2.4 Dividing Rational Expressions

NAT: 12.5.3.c TOP: 8-2 Multiplying and Dividing Rational ExpressionsKEY: divide rational expressions | simplify

5. ANS: C

Combine like terms in the numerator.


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Factor. Divide out common factors.

Simplify.

Feedback

A Divide out only common factors.B

Factor the denominator and continue simplifying your answer.C Correct!D The denominators are the same, so keep the common denominator.

PTS: 1 DIF: Average REF: Page 659OBJ: 10-5.1 Adding Rational Expressions with Like Denominators

NAT: 12.5.3.c TOP: 10-5 Adding and Subtracting Rational Expressions

6. ANS: D

=

= Subtract the numerators.

= Combine like terms.

= Factor. Divide out common factors.

= Simplify.

Feedback

A Factor the numerator and the denominator. Then, divide out common factors.B Subtract, not add.C Subtract the numerator. Then, combine like terms.D Correct!

PTS: 1 DIF: Average REF: Page 660OBJ: 10-5.2 Subtracting Rational Expressions with Like Denominators

NAT: 12.5.3.c TOP: 10-5 Adding and Subtracting Rational Expressions

7. ANS: C

Identify the LCD, .

=

= Rewrite each fraction with a denominator of .

= Add.


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=and are not like terms, so they cannot be combined.

Factor and divide out common factors.

= Simplify.

Feedback

A To simplify the numerator, factor out 3y.

B First find a common denominator. Then add the numerators.C Correct!D To simplify the numerator, factor out 3y.

PTS: 1 DIF: Basic REF: Page 661

OBJ: 10-5.4 Adding and Subtracting with Unlike DenominatorsNAT: 12.5.3.c TOP: 10-5 Adding and Subtracting Rational Expressions

8. ANS: B

=

Factor the difference of squares.

=Write each expression using the LCD.

=Subtract the numerators.

=Distribute.

=Simplify.

Excluded values are values that make the denominator equal to 0. If or , then the denominator is 0.Therefore, and .

Feedback

A First, factor the difference of squares. Then, write each expression using the LCD,

subtract, and simplify.B Correct!C Excluded values are values that make the denominator equal to 0.D Check the step where you used the Distributive Property.

PTS: 1 DIF: Advanced NAT: 12.5.3.cTOP: 10-5 Adding and Subtracting Rational Expressions KEY: rational expression

9. ANS: D

Factor the denominators. The LCD is .

= Multiply by .

=

= Add the numerators.


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2nd Quarter Exam Math 8