Miscellaneous Questions
Linear Equations in one and two variables
Linear Inequalities or misc question
Compound inequalities or misc question
Exponential Equations
Algebraic Expressions
Constraints and Literal equations
100
Convert 2-1 to an equivalent fraction
1/2
100
Solve to 1/2x + 3 = 1 ? Show your work algebraically
1/2x + 3 = 1
-3 -3
1/2 x =-2
2(1/2 x) = 2(-2)
x = -4
100
Solve for x showing work: -8x > 16 ?
-8x > 16
-8/-8 x > 16/-8
x < -2
100
What is the solution to x >0 and x > -2
x>0
100
How do you know if an equation is exponential and growth?
The exponent on a number base is a variable.
It will be growth if the base is >1.
100
Deconstruct 6x7 into terms.
x7 + x7 + x7 + x7 + x7 +x7
100
Solve for y: 2x + 3y = 12. Show work algebraically
2x + 3y = 12
-2x -2x
3y = -2x +12
3/3y = -2/3 x + 12/3
y = -2/3 x + 4
200
What is (2xz)0
1
200
Solve: 3x - 1 = -2. Show your work algebraically
3x - 1 = -2
+1 +1
3x = -1
3x/3 = -1/3
x = -1/3
200
Solve for x showing work : 3x - 2 < 0
3x - 2 < 0
+2 +2
3x < 2
3/3 x < 2/3
x < 2/3
200
What is the solution to x > 10 and x < 2
No solution. No numbers would make both equations true.
200
Make a quick sketch of an exponential growth graph.
200
Deconstruct 6x7 into factors
6*x*x*x*x*x*x*x or 2*3*x*x*x*x*x*x*x
200
Solve for b: A = (1/2)bh
A = (1/2)bh
2A = 2(1/2)bh
2A = bh
2A/h = bh/h
b = 2A/h
300
What is the first and last name of Sutter's Principal
Cristin Tahara
300
Find the y intercept of 2x + 3y = 12 (Hint, what do all y intercepts have in common?)
y intercept (0,y) Let x=0
2(0) + 3y = 12
3y = 12
3y/3 = 12/3
y = 4. The y intercept is 4
300
Solve showing work : 4x + 1 - 1 > -8
4x + 1 - 1 > -8
4x > -8
4/4 x > -8/4
x > -2
300
Describe in words all the solutions to x> 2 or x < -3 . Then give one example of one of the solutions.
Every number that is greater than 2 but not =2. In addition all the numbers that are less than -3 not including -3.
Answers varies: An example of a solution would be x=3 as 3>2. It doesn't matter that 3 is not less than -3. Only one of the inequalities need to work for an OR statement.
300
What is an asymptote?
It is a line that the graph approaches but doesn't interesect as the graph goes out to the far right (positive infinity) or goes out to the far left (negative infinity)
300
Simplify 6x2 + 3x - 10x2 - 7x -5
-4x2 -4x -5
300
Solve for b: a/b = c/d
a/b = c/d
(a/b)b = (c/d)b
a(d/c) = bc/d (d/c)
ad/c = b
b= ad/c
400
Convert 2-4 to an equivalent fraction
1/16
400
How do you know you have a linear equation in one variable?
The exponent on any variable base is 1.
400
What is the one rule you need to remember to do that will switch the inequality
Whenever you multiply or divide by a negative on both sides, you will need to switch the inequality symbol.
400
What is the difference between a compound inequality with an AND or an OR statement?
For the AND compound inequality the solution needs to work for both statements for the compound inequality to be true.
For the OR compound inequality the solution needs to work for ONLY one of the two statements for the compound inequality to be true.
400
How do you find the y intercept of the exponential equation?
Let x =0 for the x coordinate and sub it into the equation to find the y coordinate.
400
Find the difference of -4x2 -4x -5 and 5x2 -3x -10
-9x2 -x+5
400
Solve for L : P = 2(L + w)
P = 2(L + w)
P = 2L + 2w
-2w -2w
P-2w = 2L
(P-2w)/2 = 2L/2
(P-2w)/2 = L
500
Who is Mrs. Gee's favorite ex-King's player who didn't want to leave Sacramento but now plays for the Indiana Pacers?
Tyrese Haliburton
500
What is the slope and y intercept of the equation
y = 2/3x + 4
slope = m= 2/3
y intercept = 4
500
Solve the inequality showing work: -6(1+2x) > 18
-6 -12x > 18
+6 +6
-12x > 24
-12/-12 x > 24/-12
x < -2
500
Give a solution to -5 < x < 7
varies x = 0 since
-5 < 0 < 7 is a true statement
500
Give an example in the form y = a*bx so that it represents an exponential decay equation where a>0 and b>0.
Answers vary
y = 200* (.4)x
a must be a positive number, a = 200
b must be a positive number but less than 1 , b = .4
500
Subtract -4x2 -4x -5 from 5x2 -3x -10
9x2 +x -5
500
A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle train's average speed?
10 km/h
600
A pair of crocs is on sale for 27.00 after 13% is taken off. What are 3 different expressions expressing the cost for 5 of the crocs before taxes where x = original cost of 1 croc
1. 5(x -.13x)
2. 5(.87x)
3. 5(1x -.13x)
4. 5(1-.13)x
600
Colin wants to save for a Chanel purse for his wife. She wants just one more before she stops her investments in her purses. The one she likes is 5900. He has already saved 1300 and wants to put away 317 dollars each month. What is an equation that could be used to find out how long it would take him to save for the purse. Define the variable.
1300 + 317x = 5900 where x = number of months
600
Olivia was gifted 10,000 when she was born and the amount was put in her savings account. Her parents spend 125 dollars/month on necessities each month for Olivia. They want to keep at least 2500 in the bank at all times. What is the inequality that would represent how many months they can spend on Olivia while meeting the restriction. Define the variables.
let x = number of months
10000-125x < or = 2500
or 125x +2500 < or = 10000
600
A picture is reduced by 20% each time. If the length of the picture is 24 inches, what is the equation that you can generate to represent the length y of the picture after x scans
y = a(1-r)x
a=24
r=.2
y=24(.8)x
600
There are 5 pet hamsters in the Gee house. They tripe every 2 months. What is the equation that represents the growth of this population.
Let x = # of months and y= amount of hamsters at x months.
y =5(3x/2)
600
Given: 5x2 -3x -10
1. What are the terms?
2. What are the main factors of each (variable) term?
3. What are the coefficients of the terms?
4. What is the constant of the expression?
1. 5x2 , -3x, -10
2. 5 and x2 , -3 and x
3. 5 and -3
4. -10
600
Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.
4 hours