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1. Identify the coefficients, variable terms (with exponents), and constants in the following expression.
2x3+5y2-3z+1
Coefficients: 2,5,3
Variable terms: x,y,z
Constants:1
2. Identify the coefficients, variable terms (with exponents), and constants in the following expression.
4z5-8x2-6
Coefficients: 4,8
Variable terms: z5,x2
Constants: -6
3. Combine like terms in the following expression. (Hint: You can color code the like terms.)
8x2+3x+9-x2+7x-2+y
Calculations:
8x2+3x+9-x2+7x-2+y=8x2-x2+7x+3x+y-2+9=7x2+10x+y+7
Answer: 7x2+10x+y+7
4. Distribute and combine like terms in the following expression.
3(6y2-9+7x-2x2-3x-6)
Calculations:
3(6y2-9+7x-2x2-3x-6)= 3(6y2-2x2+4x-15)= 18y2-6x2+12x-45
Answer: 18y2-6x2+12x-45
5. Write and simplify an expression that applies the distributive property. Include at least 3 different terms.
Calculations:
2(5y2-6+4y+4x2-6x+8+3x-y)= 2(5y2+4x2+3y-3x+2)= 10y2+8x2+6y-6x+4
Answer 10y2+8x2+6y-6x+4
6. Simplify the expression using the order of operations. (Note: * stands for multiplication)
(6*2-4) – 3(8-5) * 7
2
Calculations:
(6*2-4)2-38-5*7 = (12-4)2-33*7 = 4-63= -59
Answer: -59
7. Simplify the expression using the order of operations.
(3-5) * -| -22 - 52 * 4|
Calculations:
(3-5) * -| -22 - 52 * 4|=(-2) * -| -4 - 25 * 4|=(-2) * -| -4 - 100|=(-2) * -| -104|=(-2) * -(104)=208
Answer: 208
8. Translate the following statement.
The product of 3 more than a number and 3 less than the same number.
Calculations: a- number
3a>a>3
Answer: 3a>a>3
9. Translate and solve the following statement.
The quotient of 2x and 4 is the same as the product of 6 and 3.
Calculations:
2x4=6*3= 18x= 18*4/2= 18*2=36
Answer: 2x4=6*3; x=36
10. Write and translate your own statement using at least two different operations (i.e. - add, subtract, multiply, divide).
Calculations:
Product of 8x and 2 is the same as the quotient of 64 and 2.
8x*2= 642
16x= 32
x=2
Answer: 8x*2= 642; x=2
11. Simplify the expression. (Hint: Careful with the signs)
-6(-42-7)
Calculations:
-6(-42-7)= -6(-16-7)= -6(-23)=138
Answer: 138
12. Simplify the expression.
(-10)2 * -|23-7+12|
Calculations:
(-10)2 * -|23-7+12|= 100 * -|8-7+12|= 100 * -|20-7|=100 * -|13|=100 *( -13)=-1300
Answer: -1300
For problems 13-14, evaluate the expressions using the following values.
x= -3 y= 8 z= -12
13. 2y+3z
4x
Calculations:
2y+3z4x=2*8+3(-12)4(-3)=2*2+3(-3)-3=4-9-3=53
Answer: 53
14. 4x2-2z2
Calculations:
4x2-2z2 = 4(-3)2-2(-12)2 =4*9-2*144=36-288=-252
Answer: -252
For problems 15-16, evaluate the expressions using the following values.
a= -1 b= 11 c= -7
15. 14a + (7- 6b)
c
Calculations:
14ac+7- 6b=14(-1)-7+7- 6*1=2+1=3
Answer: 3
16. (a2+b2)(b2-c2)
Calculations:
(a2+b2)(b2-c2)= ((-1)2+12)(12-(-7)2)=(1+1)(1-49)=2(-48)=-96
Answer:-96
For problems 17-20, solve the equation. Check your answer by plugging it back into the equation.
17. 10x = 9x-15
Calculations:
10x = 9x-15
10x -9x=-15
x=-15
Check
10(-15) = 9(-15) -15
-150=-135-15
-150=-150
Answer: -15
18. 4x-9 = 7x+3
Calculations:
-9-3 = 7x-4x
3x=-12
x=-4
Check
4x-9 = 7x+3
4(-4)-9 = 7(-4)+3
-16-9=-28+3
-25=-25
Answer:-4
19. -3(8x-2x) = 72
Calculations:
-3(8x-2x) = 72
-3(6x)=72
x=72/(-18)
x=-4
Check
-3(8(-4)-2(-4)) = 72
-3(-32+8)=72
-3(-24)=72
72=72
Answer: -4
20. 9(4y-3)-12y = 4(27+5y)
Calculations:
9(4y-3)-12y = 4(27+5y)
36y-27-12y = 108+20y
24y-20y=108+27
4y=135
y=33.75
Check
9(4(33.75)-3)-12(33.75) = 4(27+5(33.75))
9(135-3)-405 = 108+675
1188-405=783
783=783
Answer: 33.75
