Algebraic Patterns
Linear Equations/Linear Regression
Challenging Algebraic Word Problems
Solving Equations
Factoring
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
A car rental company charges $50 plus $.20 every mile driven. Write a linear equation that represents the cost of the rental, y, and the number of miles driven, x.
y=.20x+50
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
Factor using Greatest Common Factor (GCF):
-2x+10
2(-x+5) or -2(x-5)
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
Company A charges $2.20 for every pound of trash dumped plus a $75 registration fee.
Company B charges $1.75 for every pound of trash dumped plus a $90 registration fee.
Write an equation that represents the amount of money paid,y, and the pounds of trash, x for COMPANY B.
y=1.75x+90
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
Factor using Greatest Common Factor (GCF):
-3x^3-3x
-3x(x^2+1)
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
Below is a graph of points showing weight and height. What type of correlation does this "line of best fit" have?
Strong Positive correlation
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
Factor using Greatest Common Factor (GCF):
2x^3+10x^2+20x
2x(x^2+5x+10)
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
Below is a graph of a data table. What type of correlation does the "line of best fit" have?
Strong negative correlation
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
Factor the following quadratic:
x^2-5x+6
(x-2)(x-3)
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
The equation below represents the amount of money earned, y, for every hour worked,x, plus your daily allowance. How much money can you expect to make if you work 10 hours that day?
y=12x+20
y= 140 dollars
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
Factor the following quadratic:
HINT: Remember that the "a" term is bigger than 1.
2x^2+17x+30
(2x+5)(x+6)