Patterns
Find the next three terms in the pattern: 8, 15.5, 23, 30.5, ___, ___, ___
Describe the pattern.
38, 45.5, 53
Add 7.5
How do you solve a fraction with an expression in both the numerator and denominator according to order of operations?
Solve the numerator and denominator separately. Then divide at the end and simplify.
To rent a car, it costs a user fee of $40 and then $0.20 per mile. Write an equation to represent how much it costs to rent a car.
C = 0.2m + 40
Simplify by combining like terms: (4y - 5) + (-3y +2)
y - 3
What property does the equation illustrate?
a(b+c)=ab+bc
Distributive Property
Find the next three terms in the pattern: 4,20,100, ___, ___, ___
Describe the pattern.
500, 2500, 12,500
Multiply by 5
Evaluate: 4[(3 + 2 * 3) - 5] + 7
23
The local ice skating rink costs $5 to rent skates and $3 per hour. Jean has $45. How many full hours can she skate? Write an equation to represent the situation and answer the question.
45 = 3h + 5; h = 13.33333; Jean can skate for 13 hours and she will have $1 left.
Solve the equation: 4n + 1 = 12 + 5n
n = -11
In addition, the additive identity is 0. In other words, a+0=a and 0+a=a.
What is the multiplicative identity?
1
a(1)=a and 1(a)=a
Find the equation for the pattern (x,y). (0,45), (1,43), (2,41), (3,39); y = ___x + ___
y = -2x + 45
Insert parentheses to make the equation true. 108 - 17 * 2 + 3 = 23
108 - 17 * (2 + 3) = 23
The Goldstein family lives in a farmhouse that has a 1000-gallon water tank. The family uses 80 gallons of water per day. Write an equation to represent how many days the family will have enough water.
g = number of gallons d = number of days
g = 1000 - 80d
Solve the equation: 3(2r - 1) + 5 = 5(r + 1)
r = 3
What is the definition of an irrational number? Give an example of an irrational number.
Irrational numbers cannot be written as a quotient of integers (ratio) and their decimal representations neither terminate or repeat.
Examples: pi, sqrt(2)
Find the equation for the pattern. Use the equation to find the 10th term in the pattern.
x=1, 2, 3, 4,...10;
y=25, 29, 33, 37,...?
y = 4x + 21; 10th term (or when x = 10): y = 61
Evaluate if a = 6 and b = -3
3b2 + (2a)2 - |ab|
153
A rectangular rug has a length of 3x and a width of 5x+2. Write two expressions. One to represent the perimeter and one area of the rug. Simplify both expressions.
Perimeter = 16x + 4
Area = 15x2 + 6x
Solve the equation: 2(8y - 7) = 2(3 + 8y)
No solution
Find a counterexample to the general statement to make the statement false:
There is no integer that has a reciprocal that is an integer.
-1
Long Reach High School's soccer team is purchasing shirts that cost $21 each. They also have to pay a $10 shipping fee. Make a table to represent how much it costs for 1 shirt, 2 shirts, and 3 shirts. Use the table to find a pattern and write an equation to represent the situation. How many shirts can they get if they have raised $325?
Equation: C = 21s + 10; They can buy 15 shirts.
Evaluate the expression if a = -3, b = 5, and c = -4: [3a3 + (b-c)] / |ac|
-6
Fitness experts say that while working out, the optimal heart rate is between 65% and 85% of your maximum heart rate in beats per minute (bpm). You can estimate your maximum heart rate by subtracting your age, in years, from 220. Write an expression to represent the UPPER limit of the optimal training zone for a person of age "a".
y=0.85 (220 - a)
Solve the equation: (Answer in simplest form) 6 - (t/4) = 8 + (t/2)
t = -8/3
Find a counterexample to the general statement to make the statement false:
The product of two irrational numbers is an irrational number.
Sqrt(2)*sqrt(2) = Sqrt(4) = 2