Algebra & Functions

AF 1.1 & AF 1.2

11/15/10

11/16/10

Expression Translation

On some problems, the CAHSEE will ask you to turn a sentence into an equation.

Expression Translation

When you see… “plus, increased by, recieves, more than, combined, together, total of, sum, added to

Replace with… Addition

Expression Translation

When you see… minus, decreased by, sells off, less, difference between/of, less than, fewer than

Replace with… Subtraction

Expression Translation

When you see… times, product of, multiplied by, of

Replace with… Multiplication

Expression Translation

When you see…divided by, goes into, out of, ratio

Replace with… Division

Expression Translation

When you see… is equal to, is the same as, gives

Replace with… Equals

Symbols for Inequalities

< “less than”

> “greater than”

< “less than or equal to”

> “greater than or equal to”

Example:

At a local bookstore, books that normally cost b dollars are on sale for 10 dollars off the normal price. How many dollars does it cost to buy 3 books on sale?

Example continued

Break up each section of the question:

“books that normally cost b dollars”(normal cost)= b

“are on sale for 10 dollars off the normal price”(normal cost)- ($10)= b-10(sale price)= b-10

“buy 3 books on sale”3 X (sale price)= 3 X (b-10)

Answer:

3(b-10)

Solving for x

When you have a variable in an equation, you must isolate the variable and solve.

Example: 5x-4=16

Solving for x with Inequalities

Follow the same rules of solving for x

Example:

2x+5 > 11

Answer=

AF 1.2Evaluate Algebraic Expressions

When given values of specific variables, simply plug them into the algebraic expression given.

Example:

If a=3 and b=9, then a(b-7)= ?

a(b-7)= 3(9-7)

Remember PEMDAS

P-arentheses

E-xponents

M-ultiplication

D-ivision

A-ddition

S-ubtraction

Example:

If n=2 and x= 1/2, then n(4-x)= ?

Independent PracticeAF 1.1

1. Translate "the sum of 8 and y"

2. Translate "4 less than x"

3. Translate "x multiplied by 13”

4. Translate "the quotient of x and 3"

5. Translate "the difference of 5 and y"

6. Translate "the ratio of 9 more than x to x"

7. Translate "nine less than the total of a number and two" into an algebraic expression

8. The length of a football field is 30 yards more than its width. Express the length of the field in terms of its width w.

9. Twenty gallons of crude oil were poured into two containers of different size. Express the amount of crude oil poured into the smaller container in terms of the amount g poured into the larger container.

10. 3-x <1

11. Write the inequality that represents “A number x, decreased by 13 is less than or equal to 39”

Independent Practice AF 1.2

If x=2 and y=4, then (xy)+6=

If x=3, then 3(2x-4)=

m + 5q ; where m = 1, and q = 5

(y−x)3 ;where x=1,and y= 3

q(p + 2) ; where p = 4, and q = 3

y + y − x ; where x = 6, and y = 5

z + y) / 6 ; where y = 6, and z = 6

h(j − h) ; where h = 3, and j = 6

x + y + y ; where x = 5, and y = 2

z^2 −y; where y=4,and z= 3

Exit Slip AF 1.1 & 1.2

Evaluate the following expressions:

1. (h + j) / 6 ; where h = 2, and j = 4

2. m − n + m ; where m = 5, and n = 1

Translate the following expressions:

3. the sum of a number and thirty-seven

4. A grocer has y cases of energy bars in stock. He sells 8 cases and then receives a new shipment containing 3z cases. Write an expression that represents the number of energy bars he now has.