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1-1 Expressions and Formulas
Questions:
Find the value of each expression. (Note: Use Order of Operations, PEMDAS)1. 8(3+6) 2. 10-8/2 3. 14(2)-5 4. [9+3(5-7)] /3 5. [6-12-8^2] 6. 17(2+26)/4=119 Answer: 72 Answer: 6 Answer:23 Answer:1 Answer:-2 Do yourself!
Evaluate each expression if x=4, y=2, and z=6
10. z-x+y 11. x+(y-1)^2 12. x+[3(y+z)-y]Answer:0 Answer:-23 Answer: 18
Evaluate each expression.
13. √9 14. √16 15. √100 16. √169 17. - √4 18. -√25 19. √4/9 20. √36/49Answer:3 =4 =10 =13 = -2 = -5 =2/3 =6/7
1-2 Properties of Real Numbers
Information:
real numbers :all the numbers that you use in everyday use.real number= rational and irrational numbers.
What are rational and irrational numbers?rational numbers: integers like 1,2,3,4,5, etc. They can also be fractions and decimals that repeat and does not go on forever. irrational numbers: decimals that don't repeat and goes on forever. Example: √110, π
Classifying Numbers natural (N) whole(W) integers(Z) rational(Q) real (R) Irrational (I)
Questions:
Name the sets of numbers to which each number belongs.1. -4 Z, Q, R 2. 45 N, W, Z, Q, R 3. 6.233333333... Q,R
Name the property illustrated by each equation.7. 2/3 x 3/2=1 8. (a+4)+2= a+ (4+2) 9. 4x+0=4xAnswer: Multiplication Property Answer: Associative Property Answer: Addition Identity
Identify the addition inverse and multiplication inverse for each number.10. -8 11. 1/3 12. 1.5 Answer:8, -1/8 Answer: -1/3, 3 Answer: -1.5, 2/3
Simplify each expression.13. 3x+4y-5x 14. 9p-2n+4p+2n 15. 3(5c+4d) + 6(d-2c)Answer: -2x+4y Answer:13p Answer: 3c+18d
1-3 Solving Equations
Information:
Open Sentence: A mathematical sentence containing one or more variables.
Equation: a mathematical sentence stating that two mathematical expressions are equal.
Write an algebraic expression to represent each verbal expression. BOLD=Answer
4. five increased by four times a number. 5+4n 5. twice a number decreased by the cube of the same number. 2n-n^3
Write a verbal expression to represent each statement. BOLD=Answer6. 9n-3= 6 9 times a number decreased by 3 is 6 7. 5+3x^2=2x 5 plus 3 times the square of a number is twice that number.
Name the property illustrated by each statement. BOLD=Answer
8. (3x+2) -5= (3x+2)-5 9. IF 4c =15, then 4c+2= 15+2Reflexive Property Addition Property (=)
Solve each equation. Check your solution.
10. y+14=-7 11. 7+3x=49 12. -4 (b+7) = -12 13. 7q+q-3q= -24 14. 1.8a-5= -2.3 y=-21 x=14 b= -4 q= -4.8 a=1.5
1-4 Solving Absolute Value
Questions:
absolute value: a number is distance from 0 on a number line. Since distance is positive the absolute value is positive.
Information:
empty set: For example |x|= -5 is not a true statement which means it has no solution. The solution set for this type of equation.
Questions:
Evaluate each expression if a= -4 and b= 1.55. |a+12| 8 6. |-6b| 9 7. - |a+21| -17
Solve each equation. Check your solutions.
8. |x+4|=17 9. |b+15|=3 x=13 x= -12, -18[ -21,13]
Evaluate each equation if a= 5, b=6, and c= 2.8.17.|-3a| 15 18. |4b| 24 19. |a+5| 0 20. |2-b| 4 22. |4a+7| 1328. |a-b| -- |10c-a| DO YOURSELF
1-5 Solving Inequalities
Information:
Trichotomy Property: property of order
Addition Inequalities
In Words: For any real numbers, a,b,c, if a>b, then a+c>b+c
Addition Inequality Words: For any real numbers a,b,c. If a>b, then a+c>b+c. If a Example: 3
Subtraction Inequality Words: For any real numbers a,b,c. If a>b, then a-c> b+c. If a Example:2>7 ; 2-8>7-8
Multiplication Inequality Words: For any real numbers a,b,c. C is positive if a then ac>bc. If ben acb then ac>bc -2
Division Inequality Words: For any real numbers a,b,c. C is positive if abc. If bve if ab, then ac>bc. Example: -2
set-builder notation: The solution set of an inequality. For example {x|x>9}Interval notation: the solution set of an inequality being described x≥ -2 (+,-2)
Questions:
Solve each inequality. Describe the solution set using set builder notation or interval notation.
1-1;1-2
1-3, 1-4
1-5, 1-6
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