Equivalent Expressions
Equations
Inequalities
Circles
Miscellaneous
100
Simplify: 3x + 4y + 5x -12y
ANS: 8x - 8y OR 8x + -8y
3x+5x +4y -12y commutative property
8x - 8y combine like terms
100
How can you prove if a solution is correct for an equation?
ANSWER: substitution
For example: to prove that 5 is the solution to
4x + 5 = 25 ; 4(5)+5 = 20 +5 = 25; 25=25
100
What inequality symbol would you use to represent :
the cost of the trip will be at least $500
ANSWER: greater than or equal to
the answer can be that number or greater
100
If the diameter is 26 inches, what is the radius?
ANSWER: 13 inches
The radius of a circle is half the diameter.
Half of 26 is 13. (26/2)
100
What is 15 squared (152) ?
ANSWER: 225
152 = 15 x 15 = 225
200
Simplify: 7x2 + 12x - 18x2
ANSWER: -11x2 + 12x
7x2-18x2+12x commutative property
-11x2 + 12x combine like terms
200
Solve for y: 3x + 9 = 27
ANSWER: 6
3x+9 = 27 subtract 9 on each side of = sign
3x = 18 divide 3 on each side of the = sign
x = 6
check:3(6)+ 9 = 18+9 = 27
200
Graph this solution on a number line:
ANSWER: 
Closed circle because 2 is a solution
Shade to the right because that is where all the numbers that are greater than 2 are found
200
What is the exact circumference of this circle?
ANSWER: 14TT cm
C = 2TTr
C = 2TT(7)
C = 14TT cm
200
What is the factored form of 36x + 45y?
ANSWER: 9(4x + 5y)
>> determine the greatest common factor : 9
>> divide each term by GCF: 36x/9 and 45/9
>> write in factored form with the gcf on the outside of the parentheses. 9(4x+5y)
300
Simplify: 3(2x + 5)
ANSWER: 6x + 15
use the distributive property
multiply each term by 3
3(2x) = 6x 3(5) = 15
300
Solve for x: 2(x-5) = -40
ANSWER: -15
2(x-5) = -40 distributive property
2x - 10 = -40 add 10 on each side of = sign
2x =-30 divide 2 on each side of = sign
x = -15
check: 2(-15-5) = 2(-20)= -40
300
Write an inequality that represents this graph.
ANSWER: x < 5 OR 5>x
open circle means 5 is not a solution
shading to the left means less than <
300
What is the area of this circle? Use 3.14 for pi
ANSWER: 153.86 cm2
A = TTr2
A = 3.14(72) 72 = 7x7 = 49
A = 153.86 cm2
300
What is the area of this figure?
ANSWER: 80.64 cm2
A = length x width area of rectangle
A= 12.6 x 6.4
A = 80.64cm2
400
Simplify: 1/2(14x2 - 12x + 8)
ANSWER: 7x2 - 6x + 4
use the distributive property
multiply each term by 1/2
1/2(14x2) = 7x2 1/2(-12x) = -6x 1/2(8) = 4
400
Juan’s cell phone company charges $35 a month for phone service plus $0.50 for each text message, m. How many text messages does Juan send in a month if his bill was $52?
Write and solve an algebraic equation.
ANSWER: $35+0.50m = 52 m = 34
(200 points for equation, 200 points for solution)
35 + 0.50m = 52 subtract 35 each side of = sign
0.50m = 17 divide 0.50 each side of = sign
m = 34 messages
CHECK: 35+0.50(34) = 35 + 17 = 52
400
Solve: 4x - 7 > -47
ANSWER: x>-10 OR x is greater than -10
4x - 7 > -47 add 7 on each side of = sign
4x > -40 divide 4 on each side of = sign
x > -10
To prove the solution is greater than -10, pick a number that is greater than -10 to substitute
4(0)-7 = 0-7 = -7 -7>-47 TRUE
400
What is the area of this circle? Round to the nearest tenths place.
ANSWER: 254.5 in2
A = TTr2 need to 1st change diameter to radius
A = TT(92) radius is half the diameter (18/2=9)
A= 81TT press 81TT in your calculator
A = 254.4690049 now round to tenths place
A = 254.5 in2
400
What is the perimeter of a triangle with sides of (3x+4), (9x-5) and (7x+5)?
ANSWER: (19x + 4) units
perimeter is the sum of all sides of a shape
P = (3x+4) + (9x-5) + (7x+5)
P = 3x+9x+7x+4-5+5 commutative property
P = (19x + 4) units combine like terms
500
Simplify: -5x + 9(4x + 12)
ANSWER: 31x + 108
use the distributive property
9(4x)= 36x 9(12)= 108
then combine like terms
-5x + 36x + 108>>>> 31x + 108
500
You and three friends go to the town carnival. You have a coupon for $20 off that will save your group money! If the total bill to get into the carnival was $100, how much does one regular price ticket cost?
Write and solve an algebraic equation.
ANSWER: 4x -20 = 100, x = $30
(250 pts for equation, 250 points for solution)
4x-20 = 100 add 20 on each side of = sign
4x = 120 divide by 4 on each side of = sign
x = 30
CHECK: 4(30)-20 = 120-20 = 100
500
Keith has $500 in a savings account at the beginning of the summer. He wants to have more than $200 in the account by the end of the summer. He withdraws $25 each week, w, for expenses. What is the maximum number of weeks can he can withdraw money and still have more than $200 left in his account.
Write and solve an inequality.
ANSWER: $500-25w > 200 Max of 11 weeks
(250 points inequality, 250 points solution)
500 -25w>200 Subtract 500 on each side of = sign
-25w > -300 divide -25 on each side of = sign
CHECK: 500-25(11)= 225 left
500-25(12) = 200 (want more than 200)
w< 12 switch sign (negative coefficient)
500
Find the area of a circle with a circumference of 80TT.
ANSWER: 56.55 in
C = TTd A = TTr2
80TT =TTd A = TT(402)
80 = d A = 1600TT units2
40 = r
500
Find the area OR perimeter of the arc below. Use 3.14 for pi.
ANSWER: A = 100.48 cm2 C = 51.12 cm
A = 1/2(TTr2) C = 1/2(2TTr) + d
A = 1/2(3.14 x 82) C = 1/2 (2 x 3.14 x 8) + 16
A = 1/2(200.96) C = 1/2(50.24) + 16
A = 100.48 cm2 C = 25.12 + 26
C = 51.12 cm