Chapter 6 Review (Math 11)

Vocabulary

100

The _____ of 1/6 is 6

The reciprocal

200

In the equation, 3=5/2+x, the ________ is -2.

Non-permissible value

300

y=3+x y=x^2-5 are both examples of _____

Expression & Function

400

______ has a denominator and/ or numerator with polynomials.

Rational expression

500

We need to multiply each term by the _______ in all fractions with adding and/ or subtracting.

Least Common Denominator

Add/Subtract Rational Expression

100

What is the simplest form for 12x/6+18x/6

12x/6+18x/6 =(12x+18x)/6 =30x/6 =5x

200

What is the simplest form for 7x/4+9x/12

7x/4+9x/12 =21x/12+9x/12 =(21x+9x)/12 =30x/12 =5x/2

300

What is the simplest form for （4x/x^2-16）+（2x/x+8x+16）-（6/x-4）

（4x/x^2-16）+（2x/x+8x+16）-（6/x-4） =【4x/(x-4)(x+4)】+【2x/(x-4)^2】-(6/x-4) =[4x(x+4)+2x(x-4)-6(x+4)^2]/[(x-4)(x+4)^2] =[4x^2+16x+2x^2-8x-6x^2-48x-96]/[(x-4)(x+4)^2] =(-40x-96)/[(x-4)(x+4)^2] x≠4,-4

400

What is the simplest form for [(x^2+4x+4)/[(x-2)(x-1)]][(2x^2-2)/(x^2-4)]/[3/2(x^2-3x+2)]

[(x^2+4x+4)/[(x-2)(x-1)]][(2x^2-2)/(x^2-4)]/[3/2(x^2-3x+2)] =[(x+2)^2/(x-2)(x-1)] [2(x-1)(x+1)]/[(x+2)(x-2)] [2(x-1)(x-2)]/3 =[4(x+2)(x+1)(x-1)]/3(x-2) x≠2,-2,1

500

What is the simplest form for [(x-2)/(x+5)] +[(x^2-2x-3)/(x^2-x-6)][(x^2+2x)/(x^2-4x)]

[(x-2)/(x+5)] +[(x^2-2x-3)/(x^2-x-6)][(x^2+2x)/(x^2-4x)] =[(x-2)/(x+5)] +[(x+1)(x-3)/(x+2)(x-3)] [x(x+2)/x(x-4)] =[(x-2)(x+2)(x-3)] /[(x+2)(x-3)](x+5)] +[(x+1)(x-3)(x+5)] /[(x+2)(x-3)](x+5)] [x(x+2)/x(x-4)] =(x^3-3x^2-4x+12+x^3+3x^2-13x-15)/[(x+2)(x-3)](x+5)] [x(x+2)/x(x-4)] =(2x^3-17x-3)/[(x+2)(x-3)](x+5)] [x(x+2)/x(x-4)] =(2x^3-17x-3)/(x+5)(x-3)(x-4) x≠-5,3,4,-2,0

Multiply/ Divide Rational Expression

100

What is the simplest form for [(15x^2y^2)/m^3] [4m^2/5x^3y^3]

[(15x^2y^2)/m^3] [4m^2/5x^3y^3] =(3/m)(4/xy) m≠0,x≠0,y=0

200

What is the simplest form for [4(a-5)/(a-1)][3(a+6)/a-5]

[4(a-5)/(a-1)][3(a+6)/a-5] =12(a+6)/(a-1) a≠1,5

300

What is the simplest form for [(x^2-4)(x^2-4x)/(x^2+x-6)/(x^2+x-20)]

={(x+2)(x-2)/[x(x-4)]}/{[(x+3)(x-2)]/[(x+5)(x-4)]} ={(x+2)(x-2)/[x(x-4)]}{[(x+5)(x-4)][(x+3)(x-2)]} =(x+2)(x+5)/[x(x+3)] x≠-5,-3,0,-2,4

400

What is the simplest form for[ 2（x-4)/(x^2-16）][x+4/(x^2+8x+16)]/ [8x^2/(x^2-16)]

[ 2（x-4)/(x^2-16）][x+4/(x^2+8x+16)]/ [8x^2/x^2-16] =[ 2（x-4)/(x-4)(x+4）][x+4/(x+4)^2]/ [8x^2/(x+4)(x-4)] =2(x-4)/8x^2(x+4) =-2/8x^2 =-1/4x^2 x≠4,-4

500

What is the simplest form for [(2p^2+5p-3)/(2p-3)][(p^2-1)/(6p-3)][(2p-3)/(p^2+2p-3)]

={[(2p-1)(p+3)]/(2p-3)}{[(p+1)(p-1)]/[3(2p-1)]}{(2p-3)/[(p+3)(p-1)]} ={(p+3)(p+1)(p-1)/[3(2p-3)]}[(2p-3)/(p+3)(p-3)] =(p+1)/3 p≠3/2,1/2,-3,1,-1,-3

Solve Rational Equations

100

1/t + 2/t = 2

1 + 2 = 2t 3 = 2t t = 3/2

200

16/t + t/4 = 4

64 + t^2 = 16t t^2 -16t + 64 = 0 (t-6)^2 = 0 t = 6

300

4/(x-3) + 1/x = 4/(x^2-3x)

(4x+x-3)/x(x-3) = 4/(x^2-3x) 4x+x-3 = 7 5x = 7 x = 5/7

400

(2m+3)/ (m+4) + 1/2 = (m+2)/(m-2)

2(2m+3)(m-2) + (m+4)(m-2) = 2(m+2)(m+4) 2(2m^2-m-6) + m^2 + 2m - 8 = 2m^2 +12m + 8 3m^2 - 12m - 22 = 0 x= (6-√69)/3 x= (6+√69)/3

500

1/(x-4)+ 2x/(x-2) = 2/(x^2-6x+8)

x-2+2x(x-4)=2 x-2+2x^2-8x=2 2x^-7x-4=0 (2x+1)(x-4)=0 x=-1/2 x=4

Word Problems

100

Mike thinks 2/x is equivalent to x*0.5, Rebecca thinks it is 2* 1/x Who do you think is correct?

Rebecca is correct because 2 divided by x means 2 times 1/x, which is x*0.5

200

The flow of current can be represented by the following equation: F = c * [2/(x^2 )] a) What is F when c is 25 and x is 0.9? Keep to the whole number digit. b) What is c when F is 5 and x is 9?

a) first, we replace 25 into c and 0.9 into x. The equation becomes: F = 25 * (2/0.81) F = 62 (put the number into the calculator b) first, we replace F with 5 and x with 9. 9 = c * (2/81) c = 9 / (2/81) c = 365

300

A pharmaceutical company is researching the effect of a new kind of medicine on animals. Preliminary results show that the effect is given by the expression (600p)/(5+p) where p is the mass of the injection. a) explain whether NPV needs to be considered in this situation. b) What integral value for p gives the least effect.

a) The NPV is not needed because it doesn’t make sense to have a negative mass. b) p=0 because then there would be no more effect if no dose is taken.

400

Suppose you can run an average of 60m/min a) What is an expression for the time it would take to run a competition with 3 km? b) Write a sum of rational expressions to represent the time it would take you to run three competitions of 3km, 3.5km, and 4km. c) Simplify the sum in part b). What does the simplified expression tell you?

a) time = 3000m / (60m/1min) b) time = 3000/60 + 3500/60 + 4000/60 c) 175, it tells us the total time you take to run 3 competitions: 3km, 3.5km, and 4km.

500

a) A super printer prints 10 more sheets per minute than an ink-jet normal printer. If it takes the two printers a total of 17 min to print 340 pages, what is the printing rate of the super printer? b) A normal ink-jet printer prints 25 less sheets per minute than a super printer. If it takes the two printers a total of 14 min to finish their printing task. What is the printing rate of the super printer? Round to the nearest integer. c) Explain your logic behind your usage of rational equation.

a) Assume x is the printing rate of the slower normal printer: 17x + 17(x+10) = 340 34x+170 = 340 x=5 5+10=15 b) Assume x is the printing rate of the normal printer: 14/x + 14/(x+25) = 1 14(x+25) +14x = x(x+25) 28x + 350 = x^2 + 25x x^2 - 3x -350 = 0 x = 20 x = -17 - rejected c) We are assuming for question b that the total work load is 1, x/x.