TSI Math test with complete solution
PEMDAS
(parenthesis, exponents, multiplication, division, addition, subtraction) work left to right
Exponential Notation
Ex: 6^4, 2^3, 9^10, etc.
Expanded Form
Ex: 7x7x7, 6x6, 2x2x2x2x2, etc.
Standard Notation
Ex: 5^2= 25; 25 is the standard notation (the answer or solution)
+x+
=+
+x-
=-
-x-
=+
Adding or Subtracting fractions
You need a common denominator
Multiplying fractions
no special rule, just multiply Ex: 2/5 x 3/9= 6/45
Dividing fractions
flip 2nd fraction and multiply Ex: 2/5 divided by 3/9= 2/5 x 9/3
Solving Equations w/ fractions
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
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
Formula: interest= principal x rate x time (I= PxRxT)
Point
-A point has no dimension
-It is represented by a dot
-A point is written using an upper-case letter
Line
-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
Points that are on the same line
Plane
-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
Points that lie in the same plane
Line Segment
A line segment is named using both end points with a line above them
Ray
A ray is named using its endpoint first and then any other point on the ray pointing to the
right above them
Intersecting lines
2 lines that share exactly one point
Parallel lines
2 lines that are always the same distance apart and never touch
Perpendicular lines
The relationship between 2 lines which meet at a right angle (90degrees). Perpendicular
lines= 2 lines intersect at a right angle
PEMDAS
(parenthesis, exponents, multiplication, division, addition, subtraction) work left to right
Exponential Notation
Ex: 6^4, 2^3, 9^10, etc.
Expanded Form
Ex: 7x7x7, 6x6, 2x2x2x2x2, etc.
Standard Notation
Ex: 5^2= 25; 25 is the standard notation (the answer or solution)
+x+
=+
+x-
=-
-x-
=+
Adding or Subtracting fractions
You need a common denominator
Multiplying fractions
no special rule, just multiply Ex: 2/5 x 3/9= 6/45
Dividing fractions
flip 2nd fraction and multiply Ex: 2/5 divided by 3/9= 2/5 x 9/3
Solving Equations w/ fractions
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
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
Formula: interest= principal x rate x time (I= PxRxT)
Point
-A point has no dimension
-It is represented by a dot
-A point is written using an upper-case letter
Line
-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
Points that are on the same line
Plane
-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
Points that lie in the same plane
Line Segment
A line segment is named using both end points with a line above them
Ray
A ray is named using its endpoint first and then any other point on the ray pointing to the
right above them
Intersecting lines
2 lines that share exactly one point
Parallel lines
2 lines that are always the same distance apart and never touch
Perpendicular lines
The relationship between 2 lines which meet at a right angle (90degrees). Perpendicular
lines= 2 lines intersect at a right angle
