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TSI Math test
PEMDAS -
โ๏ธ (parenthesis, exponents, multiplication, division, addition, subtraction) work left to right
Exponential Notation - โ๏ธ Ex: 6^4, 2^3, 9^10, etc.
Expanded Form - โ๏ธ Ex: 7x7x7, 6x6, 2x2x2x2x2, etc.
Standard Notation - โ๏ธ Ex: 5^2= 25; 25 is the standard notation (the answer or solution)
+x+ - โ๏ธ =+
+x- - โ๏ธ =-
-x- - โ๏ธ =+
Adding or Subtracting fractions - โ๏ธ You need a common denominator
Multiplying fractions - โ๏ธ no special rule, just multiply Ex: 2/5 x 3/9= 6/
Dividing fractions - โ๏ธ flip 2nd fraction and multiply Ex: 2/5 divided by 3/9= 2/5 x 9/
Solving Equations w/ fractions - โ๏ธ either multiply both sides of the equation by the reciprocal of the fraction, or multiply both sides of the equation by the denominator of the fraction
Percent Increase or Decrease problems - โ๏ธ Formula: amount of change/ original number. Ex: Find the percent decrease if the price changes from $60 to $39. 60-39= 21. amount of change= $21 original number= $60. $21/$60= 0.35. Convert to percents. 0.35= 35%
Interest - โ๏ธ Formula: interest= principal x rate x time (I= PxRxT)
Point - โ๏ธ -A point has no dimension -It is represented by a dot -A point is written using an upper-case letter
Line - โ๏ธ -A line has one dimension -Named using any two point on a line w a two sided arrow above them -It can also be named using a lower-case cursive letter
Collinear Points - โ๏ธ Points that are on the same line
Plane - โ๏ธ -A plane has two dimensions -It is represented by a shape that looks like a floor or a wall, but it extends w/o an end -Through any three points not on the same line there is exactly one plane -A plane is written using 3 non-collinear points or with upper-case cursive letter
Coplanar points - โ๏ธ Points that lie in the same plane
Line Segment - โ๏ธ A line segment is named using both end points with a line above them
Ray - โ๏ธ A ray is named using its endpoint first and then any other point on the ray pointing to the right above them
Intersecting lines - โ๏ธ 2 lines that share exactly one point
Parallel lines - โ๏ธ 2 lines that are always the same distance apart and never touch
Perpendicular lines - โ๏ธ The relationship between 2 lines which meet at a right angle (90degrees). Perpendicular lines= 2 lines intersect at a right angle
Right angle - โ๏ธ 90 degrees
Straight angle - โ๏ธ 180 degrees
Acute angle - โ๏ธ between 0 degrees and 90 degrees
Obtuse angle - โ๏ธ between 90 degrees and 180 degrees
Complementary angles - โ๏ธ 2 angles that have the sum of 90 degrees
Supplementary angles - โ๏ธ 2 angles that have the sum of 180 degrees
Diameter - โ๏ธ Any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The longest chord of the circle.
Central angle - โ๏ธ The angle that forms when two radii meet at the center of a circle
Chord - โ๏ธ A straight line segment whose endpoints both lie on the circle
All angle measures in a circle - โ๏ธ = 360 degrees
3-Dimensional figure - โ๏ธ A geometric shape whose vertices lie on more than one plane
Faces - โ๏ธ The flat surfaces of a 3-D figure
Edges - โ๏ธ The segments formed by intersecting faces
Vertices - โ๏ธ The points formed by intersecting edges
Net - โ๏ธ The shape formed by "unfolding" a 3-D figure, shows all the faces that make up the surface area
Surface Area of a Cube - โ๏ธ 6a^2 (a is the length of the side of the cube)
Surface Area of a Rectangular Prism - โ๏ธ 2ab+2bc+2ac (a, b, and c are the lengths of the 3 sides)
Surface Area of any Prism - โ๏ธ Surface Area = Lateral area + Area of two ends
(Lateral area) = (perimeter of shape b) * L
Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)
Surface Area of a Sphere - โ๏ธ 4pir^
Surface Area of a Cylinder - โ๏ธ
Congruent figures - โ๏ธ -Have the same size and shape -The corresponding angles are congruent
-The corresponding sides are congruent
Similar figures - โ๏ธ -Have the same shape but not necessarily the same size -The corresponding angles are congruent, but the corresponding sides are not necessarily congruent
Symmetry - โ๏ธ A line of symmetry divides a figure into 2 parts, each of which is the mirror image of the other
1 foot= - โ๏ธ 12 inches
3 feet= - โ๏ธ 1 yard
5,280 feet= - โ๏ธ 1 mile
1,760 yards= - โ๏ธ 1 mile
1 centimeter= - โ๏ธ 10 millimeters
1 meter= - โ๏ธ 100 centimeters
1 kilometer= - โ๏ธ 1000 meters
16 ounces= - โ๏ธ 1 pound
2000 lbs= - โ๏ธ 1 ton
128 fl oz= - โ๏ธ 1 gal
2 pt= - โ๏ธ 1 qt
1 L= - โ๏ธ 1000 mL
1 kg= - โ๏ธ 1000 g
1,000 mg= - โ๏ธ 1 g
โ๏ธ Changing the position of a given figure
Reflection - โ๏ธ When a figure is flipped over to create a mirror image
Translation - โ๏ธ When a figure is turned to a new position
Dilation - โ๏ธ When the dimensions of a figure increase or decrease to create a new figure that is similar to the original figure
Distance formula - โ๏ธ
Midpoint formula - โ๏ธ
Equation of a Circle - โ๏ธ h and k are the x and y coordinates of the center of the circle
Coin Word problems - โ๏ธ total value= the number of coins X the value of each coin
Intercept Method - โ๏ธ Find the x & y intercepts, Ex: Graph x+2y=6. Substitute a 0 for y to find the x- intercept. x+2(0)=6 or x=6; X-int (6,0). Sub 0 for x to find the y-intercept, 0+2x=6 or x=3 (0,3)
x-intercept - โ๏ธ The value of x when y is equal to 0
y-intercept - โ๏ธ The value of y when x is equal to 0
Graphing Linear Equations - โ๏ธ Make an x & y chart
Graphing Linear Inequalities - โ๏ธ 1) rearrange the equation so "y" is on the left and everything else is on the right
- plot the "y=" line (make it a solid line for y< or equal to and y> or equal to) (make a dashed line for y> and y<)
- shade above the line for a "greater than" y> or y>or equal to shade below the line for a "less than" y< or y< or equal to
Domain - โ๏ธ The set of values of the independent variables (x) for which a function is defined. If there is a duplicate of x values in the domain then it is not a function.
Divide by a negative inequality - โ๏ธ flip the sign
f(x)= -
โ๏ธ y
Range - โ๏ธ The y-values, set of outputs
Difference of Two Squares - โ๏ธ
Factoring Quadratics - โ๏ธ ask yourself what two numbers multiply to end number but add up to middle number
Factors - โ๏ธ positive integers that can be divided evenly into the number Ex: the factors of 24= 24, 12, 8, 6, 4, 3, 2, 1
Divisible by - โ๏ธ Means divisible by without any remainder
Common Factors - โ๏ธ factors that 2 or more numbers have in common. 3 is a common factor of 12 & 18
Greatest Common Factor - โ๏ธ The largest common factor of two or more numbers. 6 is the GCF of 12 & 18
Multiples - โ๏ธ numbers that can be divided by that given number without a remainder. You can find the multiples of a number by multiplying it by 1, 2, 3, 4 and so on
Common Multiples - โ๏ธ any number that is a multiple of all given numbers. 48 & 96 are both common multiples of 8 & 12
Least Common Mulitple - โ๏ธ The smallest multiple of 2 or more numbers. 24 is the LCM of 8 & 12
Permutation - โ๏ธ order matters,
Combination - โ๏ธ order doesn't matter
Multiplying Expressions - โ๏ธ add the exponents. a^2 x a^5= a^
Dividing Expressions - โ๏ธ subtract exponents. r^5/ r^2= r^
Raised Exponents - โ๏ธ When a number raised to an exponent is raised to a 2nd exponent multiply the exponents. (n^3)^6= n^
Pythagorean theorem -
Axis of symmetry formula - โ๏ธ x= -b/2a
Area of a Right triangle - โ๏ธ 1/2 the product of its legs
Directly proportional - โ๏ธ if y=kx for some constant k
Inversely proportional - โ๏ธ if y=k/x for some constant k
is, was, has - โ๏ธ =
more than, older than, farther than, greater than, sum of - โ๏ธ +
less than, difference, younger than, fewer - โ๏ธ -
of - โ๏ธ x
for, per - โ๏ธ divide
Distance formula - โ๏ธ distance= rate x time
Absolute Value - โ๏ธ the number's distance from zero, disregard whether it is positive or negative
greater than - โ๏ธ >
less than - โ๏ธ <
Slope - โ๏ธ rise/run;
Slope intercept form - โ๏ธ y=mx+b m=slope b=y-intercept
