Engalg1 Reviewer

ENGALG1 REVIEWER (Page 1 of 22)

QUESTION #1: The expression (a + b) = an + bn can be true if ________.

ANSWER: n = 1

QUESTION #2:Every real number has a multiplicative inverse except ________.

ANSWER: zero

QUESTION #3:The union of the set of natural numbers and their additive inverse is ________.

ANSWER: zero

QUESTION #4:If A = {w, s, 0} and B = {y, z, 0}, then A B is ________.

ANSWER: 0

QUESTION #5:By distributive law, (uv)(a + b) = ________.

ANSWER: uva + uvb

QUESTION #6:- 24 = ________.

ANSWER: -16

QUESTION #7:________ are set of numbers whose elements are natural numbers.

ANSWER: Whole numbers

QUESTION #8:(-2)3 = ________.

ANSWER: -8

QUESTION #9:(x + a)(x+ b) = ________.

ANSWER: x2 + (a+b)x + ab


QUESTION #10:(g3 + h3) = (g+h)(________)

ANSWER: g2 gh + h2

QUESTION #11:x + y(3 + z) = y(3 + z) + x by ________ property of real numbers.

ANSWER: commutative

QUESTION #12:(-8, 5] (2, 10) = ________.

ANSWER: (2, 5]

QUESTION #13:|-2 - |-12| | = ________.

ANSWER: 14

QUESTION #14:In scientific notation, 0.000005036 = ________.

ANSWER: 5.036 x 10-6

QUESTION #15:The factors of 2x2 + 1 + x4 are ________.

ANSWER: (x2 + 1)2

QUESTION #16:a2 + ________ + 81 = (a + 9)2

ANSWER: 16a

QUESTION #17:A ________ is a real number that can be expressed as a ratio of two integers.

ANSWER: fraction

QUESTION #18:The greatest common factor of the expression (1+x)-1/3(3 2x) + (1+x)-4/3(3 2x)-2

ANSWER: (1+x)-4/3(3 2x)-2


QUESTION #19:(an+1)2(bn1)2n

an+2(bn21)2

= ________.

ANSWER: anb-2n+2

QUESTION #20:________, a binomial, is a factor of 8x9 27.

ANSWER: 2x3 3

QUESTION #21:The expression [(2x2+my2z0)/(12xmy2+m)]-2 is equivalent to ________.

ANSWER: (36y2m)/(x4)

QUESTION #22:A/an ________ is any real number that cannot be expressed as a ratio of two integers.

ANSWER: irrational number

QUESTION #23:The type of factoring illustrated in (2x 3y)(2x + 3y) is ________.

ANSWER: common factoring

QUESTION #24:The factors of 2x2 + 3xy 2y2 are ________.

ANSWER: (2x y) and (x+2y)

QUESTION #25:12 [2 (5 9)] = ________.

ANSWER: 6

QUESTION #26:-2m(3n + 2n) + 5mn = ________.

ANSWER: -5mn

QUESTION #27:(s3r+1)(s2-5r) = ________.

ANSWER: s-2r+3


QUESTION #28:(7xy5)(-2xy2)4 = ________.

ANSWER: 112x5y13

QUESTION #29:[(-15y8)/(27y)]3 = ________.

ANSWER: (-125y21)/(729)

QUESTION #30:The ________ rule states that the sum or product of two numbers are not affected by

the order by which they are added or multiplied.

ANSWER: commutative

QUESTION #31:An algebraic expression whose terms are all non-negative integral powers of one or

more variables is called a ________.

ANSWER: polynomial

QUESTION #32:([22]n)m = ________.

ANSWER: 22mn

QUESTION #33:(2x + 3y z)2 = ________.

ANSWER: 4x2 + 9y2 + z2 + 12xy 6yz 4xz

QUESTION #34:(2x 3y)3 = ________.

ANSWER: 8x3 36x2y + 54xy2 27y3

QUESTION #35:(5x 2y2)2 = 25x2 + ________ + 4y4

ANSWER: -10xy2

QUESTION #36:x4 26x2 + 121 is factorable by adding and subtracting ________, a perfect square.

ANSWER: 4x2


QUESTION #37:The degree of the polynomial (3x5 2x2y2 2xy3 + 5y3) with respect to both x and y is

________.

ANSWER: 5

QUESTION #38:The additive inverse of a number a is ________.

ANSWER: -a

QUESTION #39:Factor out completely: 16xy5z 54x2y4z4 + 16x5y 54x2y4z3

ANSWER: (2x2y)(z+1)(2x-3yz)(4x2+6xyz+9y2z2)

QUESTION #40:Factor out completely: 3x2 7x 40 + 12y2 12xy + 14y

ANSWER: (3x-6y+8)(x-2y-5)

QUESTION #41:Factor out completely: 4uv + 4u2 + 6vw 12uw + v2 + 9w2

ANSWER: (v-2u+3w)2

QUESTION #42:Factor out completely: 12x5y2 (39x3y4 + 27xy6)

ANSWER: (3xy2)(x+y)(x-y)(2x-3y)(2x+3y)

QUESTION #43:Factor out completely: 4x4 + 3x2y2 + y4

ANSWER: (2x2-xy+y2)(2x2+xy+y2)

QUESTION #44:Factor out completely: 9x2 24xy + 16y2

ANSWER: (3x-4y)2

QUESTION #45:Factor out completely: 14(x+y)2 (x+y) 3

ANSWER: (2x+2y-1)(7x+7y+3)


QUESTION #46:Factor out completely: x4 y2 + 2yz z2

ANSWER: (x2+y-z)(x2-y+z)

QUESTION #47:Factor out completely: 81m4 + 4n4

ANSWER: (9n2+6mn+2n2)(9n2-6mn+2n2)

QUESTION #48:Factor out completely: x6n+2y 16x2y(x3n 4)

ANSWER: (x2y)(xn-2)2(x2n+2xn+4)2

QUESTION #49:Factor out completely: 5x(x + y + 5) + x2y + 6(y+5)

ANSWER: (x+2)(x+3)(y+5)

QUESTION #50:Factor out completely: m4n4 34m2n2p4 + p8

ANSWER: (m2n2+6mnp2+p4)(m2n2-6mnp2+p4)

QUESTION #51:Factor out completely: 2xn+6y2 2y(7xn+3y + 8xny)

ANSWER: (2xny2)(x+1)(x2-x+1)(x-2)(x2+2x+4)

QUESTION #52:Factor out completely: 24x2n+3 81x2ny6

ANSWER: (3x2n)(2x-3y2)(4x2+6xy2+9y4)

QUESTION #53:Factor out completely: 3(x2+9)4(2)(2x+3)2 + (x2+9)3(4)(2x)(2x+3)3

ANSWER: (2)(x2+9)3(2x+3)2(11x2+12x+27)

QUESTION #54:Factor out completely: x4 + 2x2y2 + 9y4

ANSWER: (x2+2xy+3y2)(x2-2xy+3y2)


QUESTION #55:Factor out completely: 12a2 + 12ab 8a 4b + 3b2 + 1

ANSWER: (6a+3b-1)(2a+b-1)

QUESTION #56:Factor out completely: 3(x + y)2 2(x y)2 5x2 + 5y2

ANSWER: (-2)(x-3y)(2x+y)

QUESTION #57:________ are real numbers which can be expressed as a ratio of two integers.

ANSWER: Rational numbers

QUESTION #58:4 = ________.

ANSWER: 2i

QUESTION #59:A/an ________ is one which has one or more than one fractions in its numerator

and/or denominator.

ANSWER: complex fraction

QUESTION #60:The conjugate of 1+2 is ________.

ANSWER: 12

QUESTION #61:

Simplify: 2x83x12

+ x2

ANSWER: 3x+46

QUESTION #62:

Simplify:

3m2n4m2n3

ANSWER: 12m2n5


QUESTION #63:Simplify: 27327 627

ANSWER: 233

QUESTION #64:

Simplify: 32

2 4

ANSWER: 6322 32

2

QUESTION #65:Simplify: (32x5 y0)

45

ANSWER: 16x4

QUESTION #66:Simplify: x

12 y

23 664x3 y2

ANSWER: 2xy

QUESTION #67:Simplify: 5 35

ANSWER: 63125

QUESTION #68:

Simplify: 7 yx3 z2ANSWER:

7 x4 y z5xz

QUESTION #69:Simplify: 4n x6n y2n

ANSWER: x xy


QUESTION #70:

Simplify: 1

3 x1

ANSWER: 3 x2+3 x+1

x1

QUESTION #71:Simplify: a2ba+2b

ANSWER: a24b

QUESTION #72:

Simplify: x3

(x2) x3

ANSWER: 1x+1

QUESTION #73:

Simplify: 3x2+ y2

x2 y2+ 2x

y x

ANSWER: x yx+ y

QUESTION #74:

Simplify: a1b1

ab

ANSWER: 1ab

QUESTION #75:

Simplify: 32

32 3 4

ANSWER: (1+ 32+34)


QUESTION #76:

Simplify:

y+1 1

1 1

11zy+z

ANSWER: 1

QUESTION #77:

Simplify: 3x

2x2+3xy2y2+ y

x24y2 2x y

2x25xy+2y2

ANSWER: x27xy+ y2

(2x y)(x+2y)( x2y)= x

27xy+ y2

2x3 x2y8xy2+4y3

QUESTION #78:

Simplify: [ 1532 2(8)1

3

( 122)2

(4 82253 3540 )0 ]

34

ANSWER: 8

QUESTION #79:

Simplify: [(9x224x+162x33x2 )

( x27( x7)x2 ) ][ 9x2166x2x12 9x

3+63x216x112x3+343 ]

ANSWER: 13x+4


QUESTION #80:Simplify: 2(a+1)

12 (a1)

23+2(a+1) 12 (a1)

23

ANSWER: 26(a+1)3(a1)2[(a+1)+(a1) 3a1]

(a+1)(a1)

QUESTION #81:

Simplify: 2+632

ANSWER: 5236

QUESTION #82:

Simplify: 2y3x3 + y 18yx3 + x5 50y3x5 x2y 32y5x7ANSWER: 5y2xy

x2

QUESTION #83:

Simplify: y34 yz

632y2 z2816y4 z4

ANSWER: y 68y2 z2

QUESTION #84:

Simplify: aa( 2a3a )2a+1+a

a2

ANSWER: 2(a2)3(a1)

QUESTION #85:

Simplify:

2x+4y4x3 y xy3

9y2

3y2+3x (2x+ y )x2+2xy3x6xy12x4 y3+6x3 y4

ANSWER: 4x2(x+ y)x3


QUESTION #86:

Simplify:

x2 x

2 x1x+1

1 xx+3

ANSWER: -2

QUESTION #87:

Simplify: x

x13x1

x21 11x

+ 2x22x+1

ANSWER: x2x+4x21

QUESTION #88:

Simplify: ( x4+x2 y 2+ y4

2x25xy+ y2

x3+8y3

2x2+xy y2)( x24y2x3 x2 y+(x y )(xy+ y2))

ANSWER: (x+ y)(x22y+ y2)

(x y)( x22x+4)

QUESTION #89:

Simplify: ( 6 x2 yz )(15 x4 y2 z )5 xz2 yz

ANSWER: 5 x2 y z2

z

QUESTION #90:

Simplify: 12(a2 x2)

12 (2x )+a( 1a1( xa )2)

ANSWER: a2x2

a+x


QUESTION #91:The sets of replacements for x for which the statement makes sense (though not

necessarily true) is called ________ of the variable x.

ANSWER: domain

QUESTION #92:The set of elements in the domain which makes the equation true is known as the

________ of the equation.

ANSWER: solution set

QUESTION #93:If an equation is satisfied only by some elements in the domain of the variable, then the

equation is called an ________.

ANSWER: conditional equation

QUESTION #94:An equation is called ________ if the solution set of the equation is identical to the

domain.

ANSWER: identical

QUESTION #95:Equations with the same solution set are called ________.

ANSWER: equivalent equations

QUESTION #96:Equations in which constants are also represented by letters are called ________.

ANSWER: literal equations

QUESTION #97:A/an ________ may be introduced to an equation if squaring is done to both sides of

the equation.

ANSWER: extraneous root

QUESTION #98:The ________ is the set of all roots of a given conditional equation.

ANSWER: solution set


QUESTION #99:If p/q (in lowest terms) is a rational root of the polynomial equation a0xn + a1xn-1 + +

an-1x + an = 0, then q is a factor of ________.

ANSWER: a0

QUESTION #100:If a two digit number has x for its units digits and y for its tens digits, then the number

can be represented as ________.

ANSWER: 10y + x

QUESTION #101:Determine the value of the discriminant of 2x2 + 6x + 7.

ANSWER: -20

QUESTION #102:Determine the value of the discriminant if a = 2, b = 8 and c = 8

ANSWER: 0

QUESTION #103:Determine the value of k of x2 + 4xk + 1 = 0 so that the roots of the equation are equal.

ANSWER: 1/2

QUESTION #104:Determine the value of k of kx2 15x + 4 = 0 so that the sum of the roots of the

equation is 20.

ANSWER: 3/4

QUESTION #105:Determine the value of k of (3k+2)x2 + 2x + k = 0 so that the product of the roots of the

equation is -1.

ANSWER: -1/2

QUESTION #106:

Simplify: (2+3i)2

54i[Note: i is an imaginary number.]

ANSWER: 7341+4041

i


QUESTION #107:

Simplify: i8(45 i)+38 ii [Note: i is an imaginary number.]

ANSWER: 12 2i

QUESTION #108:

If R= 1

1R1+

1R2

, then R1 = ________.

ANSWER: R1=R R2R2R

QUESTION #109:

If TR=( P4 +2av 2 )(9+ba ) , then P = ________.

ANSWER: P=4[(TR)(9a+ba ) 2av2 ]QUESTION #110:

If yLr=ay

L2 P , then y = ________.

ANSWER: y= L22 PLrrLra

QUESTION #111:

Determine the solution set of the equation: 1

2x+5 4

2x1= 4x+4

4x2+8x5

ANSWER: S.S.: { }

QUESTION #112:Determine the solution set of the equation: 3x2 2x 6 = 0

ANSWER: S.S.:{ 1193

}


QUESTION #113:

Determine the solution set of the equation: 3(4x1x )2

4(4x1x)15=0ANSWER: S.S.: :{1, 13 ,

14,3

4}

QUESTION #114:Determine the solution set of the equation: x5 + 4x4 4x3 34x2 45x 18 = 0

ANSWER: S.S.: {-1,-1,-2,-3,3}

QUESTION #115:

Determine the solution set of the equation: 1x2x+1(3x+5) x2(2x3) x2

= 3x2 x

ANSWER: S.S.: {0}

QUESTION #116:Deterrmine the solution set of the equation: 6x2 = 4x 15

ANSWER: S.S.:{ 286 i6

}

QUESTION #117:Determine the solution set of the equation: 18x5 25x3 41x2 + 3x4 15x = 0

ANSWER: S.S.:{0, 53,1

2, 25 i

3}

QUESTION #118:Determine the solution set of the equation: 5bx2 + 2ax + 6 = 0

ANSWER: S.S.:{aa230b

5b}

QUESTION #119:Determine the solution set of the equation: (x2 2x)2 + 18(x2 + 2x) + 45 = 0

ANSWER: S.S.: {-1,-3,3,5}

QUESTION #120:Determine the solution set of the equation: x3+ x+5=2+2x2

ANSWER: S.S: {-1,7}


QUESTION #121:Determine the solution set of the equation: 3x4 17x3 + 37x2 33x + 10 = 0

ANSWER: S.S.: :{1, 23 ,22 i}

QUESTION #122:Ron and Hermione can paint a room for 6 hours. If both worked for 3 hours then

Hermione quits, Ron can complete the rest of the painting job in four more hours. How long will it take Ron and Hermione to finish the job alone.

ANSWER: Ron can finish the job alone in 8 hours while Hermione can finish the job alone in 24 hours.

QUESTION #123:A box with a square base and no top is to be made from a square piece of tin by cutting

out a 3-inch square from each corner and folding up the sides. If the box is to hold 48 in3, what size piece of tin should be used?

ANSWER: 10 inch by 10 inch

QUESTION #124:How many tons each of scrap iron and steel, which is 80% iron, must be fused to

produce 16 tons of 90% iron steel rods?

ANSWER: One needs 8 tons of scrap iron and 8 tons of steel.

QUESTION #125:Mr. Watson drives to office at 20 kph at half an hour earlier than Mr. Cole. Mr. Cole, a

neighbor who works at the same office building takes the same route at 50 kph. How long after Mr. Cole leaves will he overtake Mr. Watson and how far from home will they be?

ANSWER: Mr. Cole will overtake Mr. Watson at 20 minutes after he leaves home. By that time, they are 16.67 km far from home.

QUESTION #126:It took an airplane 7 hours to fly 4075 miles. During the first 3 hours of the flight, it had

good weather. It then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. Determine the rate on each part of the flight.

ANSWER: first part 625 mph, second part 550 mph


QUESTION #127:John, Pete and Lyn deliver advertising flyers in a small town. If each works alone, it

takes John 4 hours to deliver all the flyers, and it takes Lyn 1 hour longer than Pete. Working together, they can deliver all the flyers in 40% of the time it takes Pete working alone. How long does it take Pete to deliver all the flyers alone?

ANSWER: Pete can deliver advertising flyers alone for 3 hours.

QUESTION #128:The inverse function of y=3x2 is ________.

ANSWER: y=2+log3 x

QUESTION #129:The domain of y=log3 x1 is ________.

ANSWER: x > 1

QUESTION #130:The simplified form of e2 ln 3 is equal to ________.

ANSWER: 19

QUESTION #131:If expressed as a single algorithm, (2 + log3 x 2 log3 y) is equal to ________.

ANSWER: log39xy2

QUESTION #132:

Determine the solution set of the expression: 5

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