1-1 Skills Practice - Weebly
[Pages:101]NAME ______________________________________________ DATE ____________ PERIOD _____
1-1 Skills Practice
Expressions and Formulas
Find the value of each expression.
1. 18 2 3 27
2. 9 6 2 1 13
3. (3 8)2(4) 3 97 5. 31 [9 10(3)] 7 7. (168 7)32 43 152
4. 5 3(2 12 2) 7 6. 6(7 4 5) 3 8. [3(5) 128 22]5 85
Lesson 1-1
Evaluate each expression if r 1, s 3, t 12, v 0, and w 12 .
9. 6r 2s 0
10. 2st 4rs 84
11. w(s r) 2
12. s 2r 16v 1
13. (4s)2 144
14. s2r wt 3
15. 2(3r w) 7
17. w[t (t r)] 225
19. 9r2 (s2 1)t 105
16. 35vs tt 4 18. rsv23 0 20. 7s 2v 2rw 22
21. TEMPERATURE The formula K C 273 gives the temperature in kelvins (K) for a given temperature in degrees Celsius. What is the temperature in kelvins when the temperature is 55 degrees Celsius? 328 K
22. TEMPERATURE The formula C 59 (F 32) gives the temperature in degrees Celsius
for a given temperature in degrees Fahrenheit. What is the temperature in degrees
Celsius when the temperature is 68 degrees Fahrenheit? 20C
? Glencoe/McGraw-Hill
3
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
1-2 Skills Practice
Properties of Real Numbers
Name the sets of numbers to which each number belongs.
1. 34 N, W, Z, Q, R
2. 525 Z, Q, R
3. 0.875 Q, R
5. 9 Z, Q, R
4. 132 N, W, Z, Q, R
6. 30 I, R
Lesson 1-2
Name the property illustrated by each equation.
7. 3 x x 3
Comm. ()
8. 3a 0 3a
Add. Iden.
9. 2(r w) 2r 2w
Distributive
11. 5y 51y 1
Mult. Inv.
10. 2r (3r 4r) (2r 3r) 4r
Assoc. ()
12. 15x(1) 15x
Mult. Iden.
13. 0.6[25(0.5)] [0.6(25)]0.5
Assoc. ()
14. (10b 12b) 7b (12b 10b) 7b
Comm. ()
Name the additive inverse and multiplicative inverse for each number.
15. 15 15, 115
16. 1.25 1.25, 0.8
17. 45 45 , 54
18. 334 334 , 145
Simplify each expression.
19. 3x 5 2x 3 5x 2 21. (3g 3h) 5g 10h 2g 13h 23. 3(m z) 5(2m z) 13m 8z 25. 6(2 v) 4(2v 1) 8 2v
? Glencoe/McGraw-Hill
20. x y z y x z 0
22. a2 a 4a 3a2 1 2a2 3a 1
24. 2x 3y (5x 3y 2z) 3x 2z
26. 13 (15d 3) 12 (8 10d) 10d 3
9
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
1-3 Skills Practice
Solving Equations
Write an algebraic expression to represent each verbal expression.
1. 4 times a number, increased by 7
4n 7
2. 8 less than 5 times a number
5n 8
3. 6 times the sum of a number and 5
4. the product of 3 and a number, divided by 9
6(n 5)
39n
5. 3 times the difference of 4 and a number 3(4 n)
6. the product of 11 and the square of a number 11n2
Write a verbal expression to represent each equation. 7?10. Sample answers
are given.
7. n 8 16
8. 8 3x 5
The difference of a number and 8 is 16.
The sum of 8 and 3 times a number is 5.
9. b2 3 b
Three added to the square of a number is the number.
10. 3y 2 2y
A number divided by 3 is the difference of 2 and twice the number.
Name the property illustrated by each statement.
11. If a 0.5b, and 0.5b 10, then a 10. 12. If d 1 f, then d f 1.
Transitive ()
Subtraction ()
13. If 7x 14, then 14 7x.
Symmetric ()
14. If (8 7)r 30, then 15r 30.
Substitution ()
Lesson 1-3
Solve each equation. Check your solution.
15. 4m 2 18 4
16. x 4 5x 2 21
17. 3t 2t 5 5
18. 3b 7 15 2b 252
19. 5x 3x 24 3
20. 4v 20 6 34 5
21. a 25a 3 5
22. 2.2n 0.8n 5 4n 5
Solve each equation or formula for the specified variable.
23. I prt, for p p rIt 25. A x 2 y , for y y 2A x
24. y 14 x 12, for x x 4y 48 26. A 2r2 2rh, for h h A 2 2rr2
? Glencoe/McGraw-Hill
15
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
1-4 Skills Practice
Solving Absolute Value Equations
Evaluate each expression if w 0.4, x 2, y 3, and z 10.
1. 5w 2
2. 9y 27
3. 9y z 17
4. 17z 170
5. 10z 31 131
6. 8x 3y 2y 5x 21
7. 25 5z 1 24
8. 44 2x y 45
9. 24w 3.2
10. 3 1 6w 1.6
11. 3x 2y 4 4
12. 6.4 w 1 7
Lesson 1-4
Solve each equation. Check your solutions.
13. y 3 2 {5, 1}
14. 5a 10 {2, 2}
15. 3k 6 2 43 , 83
16. 2g 6 0 {3}
17. 10 1 c {9, 11}
18. 2x x 9 {3, 3}
19. p 7 14
20. 23w 12 {2, 2}
21. 7x 3x 2 18 {4, 4}
23. 3n 2 12 12 , 56 25. 56a 2 15 56 , 16
22. 47 y 1 11 {4, 10} 24. 8d 4d 5 13 {2, 2} 26. k 10 9
? Glencoe/McGraw-Hill
21
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
1-5 Skills Practice
Solving Inequalities
Solve each inequality. Describe the solution set using set-builder or interval notation. Then, graph the solution set on a number line.
1. z4 2 {zz 8} or (, 8]
2. 3a 7 16 {aa 3} or (, 3]
987654321
3. 16 3q 4 {qq 4} or (4, )
4 3 2 10 1 2 3 4
4. 20 3s 7s {ss 2} or (, 2)
10 1 2 3 4 5 6 7
5. 3x 9 {xx 3} or [3, )
4 3 2 10 1 2 3 4
6. 4b 9 7 {bb 4} or (, 4]
4 3 2 10 1 2 3 4
7. 2z 9 5z {zz 3} or (3, )
2 10 1 2 3 4 5 6
8. 7f 9 3f 1 {ff 2} or (2, )
2 10 1 2 3 4 5 6
4 3 2 10 1 2 3 4
9. 3s 8 5s {ss 1} or [1, ) 10. 7t (t 4) 25 tt 27 or , 72
4 3 2 10 1 2 3 4
11. 0.7m 0.3m 2m 4 {mm 4} or (, 4]
2 10 1 2 3 4 5 6
4 3 2 10 1 2 3 4
12. 4(5x 7) 13 xx 34 or
4 3 2 10 1 2 3 4
, 34
13. 1.7y 0.78 5 {yy 3.4}
14. 4x 9 2x 1 {xx 5} or (5, )
or (3.4, )
2 10 1 2 3 4 5 6
10 1 2 3 4 5 6 7
Lesson 1-5
Define a variable and write an inequality for each problem. Then solve.
15. Nineteen more than a number is less than 42. n 19 42; n 23
16. The difference of three times a number and 16 is at least 8. 3n 16 8; n 8
17. One half of a number is more than 6 less than the same number. 21 n n 6; n 12
18. Five less than the product of 6 and a number is no more than twice that same number.
6n 5 2n; n 54
? Glencoe/McGraw-Hill
27
Glencoe Algebra 2
Lesson 1-6
NAME ______________________________________________ DATE ____________ PERIOD _____
1-6 Skills Practice
Solving Compound and Absolute Value Inequalities
Write an absolute value inequality for each of the following. Then graph the solution set on a number line.
1. all numbers greater than or equal to 2
or less than or equal to 2 n 2
2. all numbers less than 5 and greater
than 5 n 5
4 3 2 10 1 2 3 4
8 6 4 20 2 4 6 8
3. all numbers less than 1 or greater
than 1 n 1
4. all numbers between 6 and 6 n 6
4 3 2 10 1 2 3 4
8 6 4 20 2 4 6 8
Write an absolute value inequality for each graph.
5.
4 3 2 10 1 2 3 4
n 1
6.
4 3 2 10 1 2 3 4
7.
4 3 2 10 1 2 3 4
n 3
8.
4 3 2 10 1 2 3 4
n 4 n 2.5
Solve each inequality. Graph the solution set on a number line.
9. 2c 1 5 or c 0 {cc 2
4 3 2 10 1 2 3 4
or c 0}
10. 11 4y 3 1 {y2 y 1}
4 3 2 10 1 2 3 4
11. 10 5x 5 {x2 x 1}
4 3 2 10 1 2 3 4
12. 4a 8 or a 3 {aa 2
4 3 2 10 1 2 3 4
or a 3}
13. 8 3x 2 23 {x2 x 7}
012345678
14. w 4 10 or 2w 6 all real
4 3 2 10 1 2 3 4
numbers
15. t 3 {tt 3 or t 3}
16. 6x 12 {x2 x 2}
4 3 2 10 1 2 3 4
4 3 2 10 1 2 3 4
17. 7r 14 {rr 2 or r 2}
18. p 2 2
4 3 2 10 1 2 3 4
4 3 2 10 1 2 3 4
19. n 5 7 {n2 n 12}
20. h 1 5 {hh 6 or h 4}
4 2 0 2 4 6 8 10 12 ? Glencoe/McGraw-Hill
8 6 4 20 2 4 6 8
33
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
2-1 Skills Practice
Relations and Functions
Determine whether each relation is a function. Write yes or no.
1. D
R yes
2. D
R no
100
50
200
100
300
150
1 3
5
3. x y yes
12 24 36
4.
y
O
no
x
Lesson 2-1
Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function.
5. {(2, 3), (2, 4), (2, 1)}
y
6. {(2, 6), (6, 2)}
y
O
x
D {2}, R {3, 1, 4}; no
7. {(3, 4), (2, 4), (1, 1), (3, 1)}
y
O
x
D {2, 6}, R {2, 6}; yes
8. x 2
y
O
x
D {3, 2, 1, 3}, R {1, 4}; yes
O
x
D {2}, R all reals; no
Find each value if f (x) 2x 1 and g(x) 2 x2.
9. f(0) 1
10. f(12) 23
12. f(2) 5
13. g(1) 1
? Glencoe/McGraw-Hill
59
11. g(4) 14 14. f(d) 2d 1
Glencoe Algebra 2
NAME ______________________________________________ DATE ____________ PERIOD _____
2-2 Skills Practice
Linear Equations
State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
1. y 3x
yes
3. 2x y 10
yes
5. 3x y 15
No; x is in a denominator.
7. g(x) 8
yes
2. y 2 5x
yes
4. f (x) 4x2
No; the exponent of x is not 1.
6. 13 x y 8
yes
8. h(x) x 3
No; x is inside a square root.
Write each equation in standard form. Identify A, B, and C.
9. y x x y 0; 1, 1, 0
10. y 5x 1 5x y 1; 5, 1, 1
11. 2x 4 7y 2x 7y 4; 2, 7, 4
12. 3x 2y 2 3x 2y 2; 3, 2, 2
13. 5y 9 0 5y 9; 0, 5, 9
14. 6y 14 8x 4x 3y 7; 4, 3, 7
Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation.
15. y 3x 6 2, 6
y
16. y 2x 0, 0
y
O
x
O
x
Lesson 2-2
17. x y 5 5, 5
y
O
x
? Glencoe/McGraw-Hill
18. 2x 5y 10 5, 2
y
O
65
x Glencoe Algebra 2
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