Math ICoursework # 2Sections:2.1 Evaluation of Algebraic Expressions2.2 Ratio and Proportions2.3 Law of Exponents2.4 Venn diagram and Set notation

2.1 Evaluation of Algebraic Expressions

PEMDAS Rule Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction from left to right1. 6 - {4 + [6 x (2 4) + (2 + 6 3)] - 8} = 6 - {4 + [6 x (-2) + (5)] - 8} = 6 - {4 + [-12 + 5] - 8} = 6 - {4 + (-7) - 8} = 6 - {-3 - 8} = 6 (-11) = 17

2. {[(4+2) x 3] 2} (2 + 5 x 3 3 1)= {[6 x 3] 2} (2+15 3 -1)= {[18] 2} (2 +5 -1)= (9) (7-1)= 9 6= 3

2.2 Ratio and Proportions

Ratio is another word for fraction, so in algebra fractions are often called as rational numbers

The ratio of a to b is written as a/b or a: b

1. The three sides of a triangle are in the ratio 2:3:4. The perimeter of the triangle is 63. Find the three sides.

P = a+b+c2x+3x+4x= 63 3x 2x 9x = 63 x = 7 Sides 4x4x= 4(7) = 283x= 3(7) = 212x= 2(7) = 14

2. If 200 ml of vinegar is mixed with 300 ml of water, what percentage of the mixture is vinegar?

200 ml vinegar300 ml + 200 ml = 500 ml (mixture)

So

Proportion is a statement that two ratios are equal

or a:b = c:d

Direct Proportion constant variable

1. There are 25 boys in a class of 38 students. Assuming that this is a typical class, now how many of the schools 7,500 students are boys?

2. In a bakery. Five loaves of bread are made in 1 hours. At this rate, how many loaves of bread can be made from 8:00 am to 5:00 pm?

Inverse Proportion - increase in one variable causes decrease in the other variable and vice versa

1. Two men can do a job in five hours. How many hours will it take three men to do the same job if all men work at the same rate?

2. An aircraft flying at an average speed of 770km/h takes 15 h to complete a journey. Find the time taken for the aircraft to complete the same journey if its average speed is 660 km/h?

3. Four pipes can fill a tank in 70 min. How long will it take to fill the tank if 7 pipes are used?

2.3 Law of Exponents

, if m > n then, , if n > m then,

)n =

1/n =

-n = n =

Examples

a. (2a-2b4)-3 = 2-3 (a-2)-3(b4)-3= (a6) (b-12)=

b. -2 = -2= -2= 2= =

c. = = =

d. -2= -2= -2= 2=

2.4 Venn diagram and set notation

Set NotationPronunciationMeaningVenn DiagramAnswer

A U B

"A union B"

Everything that is in either of the sets

{1, 2, 3}

A ^ Bor

"A intersect B"

Only the things that are in both of the sets

{2}

Acor~A

"A complement",or "not A"

Everything in the universe outside of A

{3, 4}

A B

"A minus B", or"A complement B"

Everything in A except for anythingin its overlap with B

{1}

~(A U B)

"not (A union B)"

Everything outside A and B

{4}

~(A ^ B)or~()

"not (A intersect B)"

Everything outside of the overlap of A andB

{1, 3, 4}

Examples:Illustrate the following Set notation

A B C1. (A-B) C

2. A (B-C)

A B C

x- 1 x 3x-1 A B x-1 C 3.

a. What is A B? This means A union B= x+1+x+3x-1=5x

b. U =?Take note that U stands for universal set, thus, all sets So, x + 1+x+3x-1+x-1= 6x 1

Applications of Venn diagram

1. In a class of 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry? Calculus Chemistry

27- x x 25 x

x+ 27 x + 25 x = 40-x +52 = 40-x = -12x= 12 students

2. Out of forty students, 14 are taking English composition and 29 are taking Chemistry. If 5 students are in both classes, how many are in either class? How many are in neither class? What is the probability that a randomly chosen from this group is taking only the chemistry class? English 14 Chemistry- 29 9 5 24 14 5 = 9 29 5 = 24Taking either class = 9+5+24 = 38 studentsTaking neither class = 40 38 = 2 studentsProbability of students in chemistry class only:24/40 = 0.6 x 100 = 60%

3. At the keep in shape club, 35 people swim, 24 play tennis, and 27 jog. Of these people, 12 swim and play tennis, 19 play tennis and jog, and 13 jog and swim. Nine people do all three activities. How many members are there altogether?

35 people swim 24 play tennis 1 16 12 13 9 19 14 27 jog= 1+12+16+13+9+19+14= 84 members