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Operations with Integers
Evaluating and Simplifying Expressions
Solving Equations
Geometry (Area, Perimeter, etc.)
Functions
100
9 + -11
-2
100
-7x + 4x + 5
-3x + 5
100
3x + 1 = 16
3x = 15, so x = 5
100
What are the area AND perimeter of a rectangle whose length and width are 5 inches and 11 inches?
Area = 5in. * 11in. = 55 square inches; Perimeter = 2(5) + 2(11) = 10 + 22 = 32 inches.
100
What is the rule? (-1, 0) (0,2) (1, 4) (2, 6)
y = 2x + 2
200
-8 + 14 - 5
1
200
4x - 9 + 3x + 1
7x - 8
200
-4 + 2x = 12
2x = 16, so x = 8
200
What is the area of a triangle whose base and height are 10 yards and 15 yards?
Area = (10)(15)/2 = 150/2 = 75 yards
200
What are the next three terms in the sequence? 1, 3, 6, 10, ...
15, 21, 28
300
3(-6 - 5) + 5(2 + 3)
-33 + 25 = -8
300
7 - 3x - 7y + 11 + 5x + 4y
18 + 2x + -3y
300
-7 - 4x = 17
-4x = 24, so x = -6
300
What is the volume of a cube whose length, width, and height are 10, 20, and 30 feet?
10*20*30 = 6000 cubic feet
300
If f(x) = 30x + 40 and g(x) = 50x + 30, which function has the larger rate of change?
g(x) has a larger rate of change. (rate of change means slope... 50 > 30)
400
-3(3 - 9 + 2) + 4(8 - 7 + 2)
-3(-4) + 4(3) = 12+12 = 24
400
3 + 2(5x + 7) + 2(z - 8) + 5x - 2z
3 + 10x + 14 + 2z - 16 + 5x - 2z = 1 + 15x
400
3(x - 9) = 6
3x - 27 = 6, so 3x = 33, and x = 11
400
What are the area AND perimeter of a triangle with side lengths 3, 4, 5 cm, and whose base and height are 3 cm and 4 cm?
A = (3)(4)/2 = 12/2 = 6 square cm; P = 3+4+5=12cm
400
Planet Fitness charges $10 per month with an additional one-time fee of $30. Write a linear equation to represent the total cost for a membership there.
y = cost; x = # of months... y = 10x + 30
500
-5[3(2 - 5) + 3]
-5[3(-3) + 3] = -5[-9+3] = -5[-6] = 30
500
3 - (2x + z) + 3z - 7x + 1
4 - 2x - z + 3z - 7x = 4 - 9x + 2z
500
2x - 5 + 3x - 4 = -5x + 7x + 12
5x - 9 = 2x + 12, so 3x = 21, and x = 7
500
If one angle in a triangle measures 19 degrees and another measures 35 degrees, what is the measure of the third angle?
126 degrees (because 180 - 19 - 35 = 126)
500
If it is 86 degrees Fahrenheit, what is the temperature in Celsius? (Fahrenheit and Celsius temperatures can be related with the equation F = (9/5)C + 32.)
86 = (9/5)C + 32, so 54 = (9/5)C, and 54*(5/9) = 30 = C. So, 86 degrees Fahrenheit equals 30 degrees Celsius.