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Integers
Powers and Exponents
Fractions
Surface Area
Equations
100
Solve 5 + 6 + 7 - 20
-2
100
Anything to the exponent of 0 equals 1
What is the Zero Exponent Law
100
When the numerator is larger than the denominator
What is an Improper Fraction
100
Calculate the surface area of a rectangular prism with length = 2 cm width = 1 cm height = 3 cm To earn the points, you must answer with the correct units
S.A. rectangular prism = 2(lw) + 2(lh) + 2(wh) = 2(2x1) + 2(2x3) + 2(1x3) = 4 + 12 + 6 = 22 cm^2
100
Solve 5x + 2 = 12
x = 2
200
Solve (-1)(-1)(-1)(-1)(-1)
-1
200
Simplify to a single power (a^3)(a^5)
a^8 Multiplying powers of the same base, we add the exponents (Product of Powers Rule)
200
When two or more fractions have the same value, but is represented by different numbers
What is Equivalent Fractions
200
Calculate the surface area of a cube with a side length of 5cm. Answer must include the correct units
All sides of a cube are equal Area of all faces are equal S.A. cube = 6(lxw) =6(5x5) =6(25) =150 cm^2
200
In the equation, 2x - 3 = 4 List all of the terms
Terms are numbers, variables, or the product of numbers and variables. Terms: 2x, -3, and 4
300
Solve [10 × (-3) ÷ 6] + 3^2 3^2 means 3 to the exponent of 2
[10 × (-3) ÷ 6] + 3^2 =[-30 ÷ 6] + 9 =-5 + 9 =4
300
Simplify to a single power (-6)^5 ÷ (-6)
(-6)^4 Dividing powers of the same base, we subtract the exponents (Quotient of Powers Rule)
300
Fractions that have different denominators
What is unlike fractions
300
The hidden areas where two objects meet
What is the overlap
300
Simplify this expression by combining like terms 4x + 2 - 3x + 5
You can re-arrange the terms to make it easier Remember, the signs move with the terms 4x + 2 - 3x + 5 = 4x - 3x + 2 + 5 = x + 7
400
Solve -2 + 30 ÷ 5(-2) + 32
-2 + 30 ÷ 5(-2) + 32 = -2 + 6(-2) + 32 = -2 -12 + 32 =-14 + 32 =18 BEDMAS
400
Express as a single power [(3^2)]^3 ÷ 3^5
= 3^6 ÷ 3^5 = 3 When a power is raised to another exponent, we multiply the exponents (Power Rule) When dividing powers of the same base, we subtract the exponents (Quotient of Powers Rule)
400
Order the following fractions in descending order: 4/3, 3/1, 3/4, 5/6
*change them to like fractions *find the LCM of the denominators *change each fraction to an equivalent fraction with the LCM as the denominator LCM of 3, 1, 4, and 6 is 12 4/3 = 16/12, 3/1 = 36/12, 3/4 = 9/12, 5/6 = 10/12 order is 3/1, 16/12, 5/6, 3/4
400
How do you calculate the Total Surface Area of a composite object? For example, How do you calculate the T.S.A. of a cube on top of a triangular prism?
T.S.A. = S.A. Object 1 + S.A. Object 2 - 2(area of the overlap) Or you can calculate the outer surfaces of the composite object and subtract the overlap once.
400
Solve 3x + 2 = -4x + 16
3x + 2 = -4x + 16 3x + 4x = 16 - 2 7x = 14 x = 2
500
Solve (-2 - 4) × 3 ÷ (-1) × 5
(-2 - 4) × 3 ÷ (-1) × 5 = (-6) × 3 ÷ (-1) × 5 *division and multiplication, whichever is first left to right = -18 ÷ (-1) × 5 = 18 × 5 =90
500
Solve -5^2 + (-4)^2 - (-3)^3
-5^2 + (-4)^2 - (-3)^3 =-25 + 16 - (-27) =18
500
Solve 2/3 + 3/5 - 1/15 To earn the points, you must change your answer to a mixed number, and simplify it to lowest terms.
Change to like fractions LCM = 15 2/3 becomes 10/15 3/5 becomes 9/15 1/15 stays the same 10/15 + 9/15 - 1/15 = 18/15 or 1 and 3/15 In lowest terms = 1 and 3/5
500
Calculate the T.S.A of a cube on a rectangular prism. The cube has side length of 2cm. The rectangular prism has length of 2 cm, height of 3 cm, and width of 4 cm
S.A. cube = 24 cm^2 S.A. rectangular prism = 52 cm^2 Overlapping area is the bottom of the cube = 4 cm^2 T.S.A. = 24 + 52 - 2(4) = 68 cm^2
500
Solve -6x - 3 = -10x - 5
-6x - 3 = -10x - 5 -6x + 10 x = -5 + 3 4x = -2 x = -1/2 or x = -0.5