Week 1 Quiz: Basics

SGPE Summer School

Rules for Exponents

Question 1: Simplify the following expression using the various rules for manipulating exponents:

x6

√x3

(A)√x4

(B) x3

(C)√x9

(D) x5.5

(E) None of the above

Question 2: Simplify the following expression using the various rules for manipulating exponents:

x3√x

(A) x32

(B) x7

(C)√x4

(D)√x7

(E) None of the above

Question 3: Simplify the following expression using the various rules for manipulating exponents:(x4

y8

)3

(A) x7

y11

(B) x12

y24

(C) (x4 − y8)3

(D) 3

√x4

y8

(E) None of the above

Question 4: Simplify the following expression using the various rules for manipulating exponents:

(x2y2x3y3)16

1

Question 5: Simplify the following expression using the various rules for manipulating exponents:

(x− 14y3

x12

) 13

Polynomials

Question 6: Expand the following expression:

(2x + 7)2

(A) 8x2 + 18x− 35

(B) 8x2 + 49

(C) 4x2 + 28x + 49

(D) 8x2 + 18x− 42

(E) None of the above

Question 7: Expand and regroup the following expression:

(4x + 3y)(5x2 − 2xy + 6y2)

(A) 20x3 + 7x2y + 18xy2 + 18y3

(B) 20x3 − 2xy + 18y3

(C) 9x3 + 8x2y + 6xy2 + 9y3

(D) 20x2 + 25xy + 18y2

(E) None of the above

Question 8: Expand and regroup the following expression:

(ax + b)2 + (cx− d)2

Factoring

Question 9: Simplify by factoring out the greatest common factor:

55x8y9 − 22x6y4 − 99x5y7

(A) 11(5x8y9 − 2x6y4 − 9x5y7)

(B) 11x4(x4y9 − 22x2y4 − 99xy7)

(C) 11x4y4(x4y5 − 22x2 − 99xy3)

(D) x5y4(55x4y5 − 22x− 99y3)

(E) None of the above

2

Question 10: Factor using integer coefficients:

x2 + 13x + 36

(A) (x + 6)(x + 7)

(B) (x + 12)(x + 1)

(C) (x + 9)(x + 4)

(D) (x + 5)(x + 8)

(E) None of the above

Question 11: Factor using integer coefficients:

x2 − 81

(A) (x + 9)2

(B) (x− 9)2

(C) (x + 9)(x− 9)

(D) (x + 81)(x− 1)

(E) None of the above

Question 12: Factor using integer coefficients:

7x2 − 39x− 18

(A) (x + 9)2

(B) (7x + 3)(x− 6)

(C) (x + 9)(x− 9)

(D) (x + 81)(x− 1)

(E) None of the above

Question 13: Factor the following polynomial:

16x2 − 49y2

(A) (x + 7)(16x + 7y2)

(B) (4x− 7y2)

(C) (4x− 7y)(4x− 7y)

(D) (4x− 7y)(4x + 7y)

(E) None of the above

Fractions

Question 14: Multiply the following rational expressions involving quotients of binomials and reduceto lowest terms.

x− 5

x + 8· x + 2

x− 9

(A) (x−5)(x+2)(x+8)(x−9)

3

(B) x2−3x−10x2−x−72

(C) (x−5)(x+3)(x+8)(x−9)

(D) x2+3x−10x2−x+72

(E) None of the above

Question 15: Divide the following expressions:

15ch4

5x2yz3÷ 3c4h

55y2z

(A) 55h3yc3x2z2

(B) 55h2y2

c4xz2

(C) 55h3yc3xz2

(D) 55h2yc3x2z2

(E) None of the above

Question 16: Add or subtract the following fractions:

12

x2 − 49+

7x

x + 7

(A) 12+7xx2+x−42

(B) 12(x+7)+7x3−49(x2−49)(x+7)

(C) 12(x+7)+7x(x2−49)x2−49

(D) 12+7x(x−7)x2+49

(E) None of the above

Question 17: Write the following expression in its simplest form:

x2 − 2x + 1

x + 3· x

2 + 5x + 6

x2 − 1

Radicals

Question 18: Simplify the following the radicals:√81x8y6

(A) 9x4y3

(B) 9√

x8y6

(C) −9x4y3

(D) 9x4y3and− 9x4y3

(E) None of the above

Question 19: Use the properties of radicals to solve for y:√3y = 6x4

4

(A) y = 12x10

(B) y = 36x8

(C) y = 12x8

(D) y = 24x4

(E) None of the above

Question 20: Simplify the following radical:

√169x6y8

5