1 Chapter Test

Do you know HOW?

Evaluate each expression for x = 5 . x equals 5 .

1. 5 3 ( 3 x − 6 ) − ( 6 − 4 x ) 5 thirds , open 3 x minus 6 close minus open 6 minus 4 x close
2. 3 ( x 2 − 4 ) + 7 ( x − 2 ) 3 open , x squared , minus 4 close plus 7 open x minus 2 close
3. x − 2 x + 3 x − 4 x + 5 x x minus 2 x plus 3 x minus 4 x plus 5 x

Simplify each expression.

4. a 2 + a + a 2 eh squared , plus eh plus , eh squared
5. 2 x + 3 y − 5 x + 2 y 2 x plus 3 y minus 5 x plus 2 y
6. 5 ( a − 2 b ) − 3 ( a − 2 b ) 5 open eh minus 2 b close minus 3 open eh minus 2 b close
7. 3 [ 2 ( x − 3 ) + 2 ] + 5 ( x − 3 ) 3 left bracket 2 open x minus 3 close plus 2 right bracket plus 5 open x minus 3 close

Solve each equation.

8. 4 y − 6 = 2 y + 8 4 y minus 6 equals 2 y plus 8
9. 3 ( 2 z + 1 ) = 35 3 open 2 z plus 1 close equals 35
10. 5 ( 3 w − 2 ) − 7 = 23 5 open 3 w minus 2 close minus 7 equals 23
11. t − 2 ( 3 − 2 t ) = 2 t + 9 t minus 2 open 3 minus 2 t close equals 2 t plus 9
12. 5 ( s − 12 ) − 24 = 3 ( s + 2 ) 5 open s minus 12 close minus 24 equals 3 open s plus 2 close
13. The lateral surface area of a cylinder is given by the formula S = 2 π r h . s equals 2 pi r h .  Solve the equation for r.
14. Savings Briana and her sister Molly both want to buy the same model bicycle. Briana needs $73 more before she can afford the bike. Molly needs $65 more. If they combine their money, they will have just enough to buy one bicycle that they could share. What is the cost of the bicycle?
15. Musical There is only one freshman in the cast of a high school musical. There are 6 sophomores and 11 juniors. One third of the cast are seniors. How many seniors are in the musical?

Determine whether each equation is always, sometimes, or never true.

16. 2 x + 7 − x = 3 + x + 4 2 x plus 7 minus x equals 3 plus x plus 4
17. 5 a − 1 − 3 a = 2 a + 1 5 eh minus 1 minus 3 eh equals 2 eh plus 1

Solve each equation or inequality. Graph the solution.

18. 3 x + 17 ≥ 5 3 x plus 17 greater than or equal to 5
19. 25 − 2 x < 11 25 minus 2 x less than 11
20. 3 8 x < − 6  or  5 x > 2 3 eighths , x less than negative 6 , or , 5 x greater than 2
21. 2 < 10 − 4 d < 6 2 less than 10 minus 4 d less than 6
22. 4 − x = | 2 − 3 x | 4 minus x equals vertical line 2 minus 3 x vertical line
23. 5 | 3 w + 2 | − 3 > 7 5 vertical line 3 w plus 2 vertical line negative 3 greater than 7

Do you UNDERSTAND?

24. Writing Describe the relationships among these sets of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

25. Reasoning Justify each step by identifying the property used.

    t + 5 ( t + 1 ) = t + ( 5 t + 5 )   = ( t + 5 t ) + 5   = ( 1 t + 5 t ) + 5   = ( 1 + 5 ) t + 5   = ( 6 t + 5 ) table with 5 rows and 3 columns , row1 column 1 , t plus 5 . open , t plus 1 , close , column 2 equals , column 3 t plus . open , 5 t plus 5 , close , row2 column 1 , , column 2 equals , column 3 open , t plus 5 t , close . plus 5 , row3 column 1 , , column 2 equals , column 3 open . 1 t plus 5 t . close . plus 5 , row4 column 1 , , column 2 equals , column 3 open , 1 plus 5 , close . t plus 5 , row5 column 1 , , column 2 equals , column 3 open , 6 t plus 5 , close , end table

26. Reasoning The first four figures of a pattern are shown.

    
    Image Long Description

    Describe the tenth figure in the pattern.

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