TSI Math test 2022 Questions and Answers

PEMDAS - ANSWER (parenthesis, exponents, multiplication, division, addition, subtraction) work left to right Exponential Notation - ANSWER Ex: 6^4, 2^3, 9^10, etc. Expanded Form - ANSWER Ex: 7x7x7, 6x6, 2x2x2x2x2, etc. Standard Notation - ANSWER Ex: 5^2= 25; 25 is the standard notation (the answer or solution) +x+ - ANSWER =+ +x- - ANSWER =- -x- - ANSWER =+ Adding or Subtracting fractions - ANSWER You need a common denominator Multiplying fractions - ANSWER no special rule, just multiply Ex: 2/5 x 3/9= 6/45 Dividing fractions - ANSWER flip 2nd fraction and multiply Ex: 2/5 divided by 3/9= 2/5 x 9/3 Solving Equations w/ fractions - ANSWER 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 - ANSWER 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 - ANSWER Formula: interest= principal x rate x time (I= PxRxT) Point - ANSWER -A point has no dimension -It is represented by a dot -A point is written using an upper-case letter Line - ANSWER -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 - ANSWER Points that are on the same line Plane - ANSWER -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 - ANSWER Points that lie in the same plane Line Segment - ANSWER A line segment is named using both end points with a line above them Ray - ANSWER A ray is named using its endpoint first and then any other point on the ray pointing to the right above them Intersecting lines - ANSWER 2 lines that share exactly one point Parallel lines - ANSWER 2 lines that are always the same distance apart and never touch Perpendicular lines - ANSWER The relationship between 2 lines which meet at a right angle (90degrees). Perpendicular lines= 2 lines intersect at a right angle Right angle - ANSWER 90 degrees Straight angle - ANSWER 180 degrees Acute angle - ANSWER between 0 degrees and 90 degrees Obtuse angle - ANSWER between 90 degrees and 180 degrees Complementary angles - ANSWER 2 angles that have the sum of 90 degrees Supplementary angles - ANSWER 2 angles that have the sum of 180 degrees the sum of the angle measures in a triangle - ANSWER 180 degrees Acute triangle - ANSWER All angles are acute Right triangle - ANSWER One angle is right Obtuse triangle - ANSWER One angle is obtuse Scalene triangle - ANSWER All sides have different lengths Isosceles triangle - ANSWER At least 2 sides have the same length Equilateral triangle - ANSWER All sides have the same length The sum of the lengths of a triangle - ANSWER The sum of the lengths of any two sides of a triangle must be greater than the length of the third side Polygon - ANSWER A polygon is a closed figure whose sides are line segments that do not cross Regular Polygon - ANSWER A regular polygon is a polygon where all of the sides have equal lengths and all of the angles have equal measures Trapezoid - ANSWER One pair of opposite sides are parallel Parallelogram - ANSWER Both pairs of opposite sides parallel Rhombus - ANSWER All sides congruent Rectangle - ANSWER 4 right angles Square - ANSWER All sides congruent and 4 right angles Circle - ANSWER The set of all points in a plane that are a a given distance from a given pint, the center Radius - ANSWER Any of the line segments from its center to its perimeter Diameter - ANSWER 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 - ANSWER The angle that forms when two radii meet at the center of a circle Chord - ANSWER A straight line segment whose endpoints both lie on the circle All angle measures in a circle - ANSWER = 360 degrees 3-Dimensional figure - ANSWER A geometric shape whose vertices lie on more than one plane Faces - ANSWER The flat surfaces of a 3-D figure Edges - ANSWER The segments formed by intersecting faces Vertices - ANSWER The points formed by intersecting edges Net - ANSWER The shape formed by "unfolding" a 3-D figure, shows all the faces that make up the surface area Surface Area of a Cube - ANSWER 6a^2 (a is the length of the side of the cube) Surface Area of a Rectangular Prism - ANSWER 2ab+2bc+2ac (a, b, and c are the lengths of the 3 sides) Surface Area of any Prism - ANSWER 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 - ANSWER 4pir^2 Surface Area of a Cylinder - ANSWER Congruent figures - ANSWER -Have the same size and shape -The corresponding angles are congruent -The corresponding sides are congruent Similar figures - ANSWER -Have the same shape but not necessarily the same size -The corresponding angles are congruent, but the corresponding sides are not necessarily congruent Symmetry - ANSWER A line of symmetry divides a figure into 2 parts, each of which is the mirror image of the other 1 foot= - ANSWER 12 inches 3 feet= - ANSWER 1 yard 5,280 feet= - ANSWER 1 mile 1,760 yards= - ANSWER 1 mile 1 centimeter= - ANSWER 10 millimeters 1 meter= - ANSWER 100 centimeters 1 kilometer= - ANSWER 1000 meters