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Patterns
Order of Operations
Algebraic Expressions and Word Problems
Solving Equations
Miscellaneous
100
Find the next three terms in the pattern: 8, 15.5, 23, 30.5, ___, ___, ___ Describe the pattern.
38, 45.5, 53; First difference: +7.5
100
How do you solve fraction bars in Order of Operations?
Solve the numerator and denominator separately. Then divide at the end and simplify.
100
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
100
Simplify by combining like terms: (4y - 5) + (-3y +2)
y - 3
100
In a negative correlation, as x _____, y_____.
As x increases, y decreases. OR As x decreases, y increases.
200
The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant +4, what are the first five terms of the sequence? ___, ___, 26, 40, ___
10, 16, 26, 40, 58; First difference: +6, +10, +14, +18; Second difference: +4
200
Evaluate: 4[(3 + 2 * 3) - 5] + 7
23
200
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.
200
Solve the equation: 4n + 1 = 12 + 5n
n = -11
200
What is the difference between an expression and an equation?
Equation has an = sign. Usually you have to solve an equation and simplify an expression.
300
Find the equation for the pattern (x,y). (0,45), (1,43), (2,41), (3,39); y = ___x + ___
y = -2x + 45; Note: Pattern is -2
300
Insert inclusion symbols to make the equation true. 108 - 17 * 2 + 3 = 23
108 - 17 * (2 + 3) = 23
300
The Goldstein family lives in a farmhouse that has a 1000-gallon water tank. The family uses 80 gallons of wtaer 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
300
Solve the equation: 3(2r - 1) + 5 = 5(r + 1)
r = 3
300
Give an example of 3 situations representing a positive correlation, a negative correlation, and no correlation. Draw a simple graph for each.
Answers will vary.
400
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
400
Evaluate if a = 6 and b = -3: 3b^2 + (2a)^2 - |ab|
153
400
A rectangular rug has a length of 3x and a width of 5x+2. Write two expressions to represent the perimeter and area of the rug. Simplify both expressions.
Perimeter = 16x + 4; Area = 15x^2 + 6x
400
Solve the equation: 2(8y - 7) = 2(3 + 8y)
No solution
400
Make a table of values for the expression 3x - 2 (for x=1, 2, 3, 4, and 5). Then, draw a graph of the expression by plotting those values.
3x-2 = 1, 4, 7, 10, 13
500
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.
500
Evaluate the expression if a = -3, b = 5, and c = -4: [3a^3 + (b-c)] / |ab|
6
500
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".
0.85 (220 - a)
500
Solve the equation: (Answer in simplest form) 6 - (t/4) = 8 + (t/2)
t = -8/3
500
Create a word problem to represent this expression: 4(5x + 3)
Answers will vary.