TSI Math Test 156 Questions with Verified Answers,100% CORRECT

TSI Math Test 156 Questions with Verified Answers PEMDAS - CORRECT ANSWER (parenthesis, exponents, multiplication, division, addition, subtraction) work left to right Exponential Notation - CORRECT ANSWER Ex: 6^4, 2^3, 9^10, etc. Expanded Form - CORRECT ANSWER Ex: 7x7x7, 6x6, 2x2x2x2x2, etc. Standard Notation - CORRECT ANSWER Ex: 5^2= 25; 25 is the standard notation (the answer or solution) +x+ - CORRECT ANSWER =+ +x- - CORRECT ANSWER =- -x- - CORRECT ANSWER =+ Adding or Subtracting fractions - CORRECT ANSWER You need a common denominator Multiplying fractions - CORRECT ANSWER no special rule, just multiply Ex: 2/5 x 3/9= 6/45 Dividing fractions - CORRECT ANSWER flip 2nd fraction and multiply Ex: 2/5 divided by 3/9= 2/5 x 9/3 Solving Equations w/ fractions - CORRECT 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 - CORRECT 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 - CORRECT ANSWER Formula: interest= principal x rate x time (I= PxRxT) Point - CORRECT ANSWER -A point has no dimension -It is represented by a dot -A point is written using an upper-case letter Line - CORRECT 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 - CORRECT ANSWER Points that are on the same line Plane - CORRECT 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 - CORRECT ANSWER Points that lie in the same plane Line Segment - CORRECT ANSWER A line segment is named using both end points with a line above them Ray - CORRECT 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 - CORRECT ANSWER 2 lines that share exactly one point Parallel lines - CORRECT ANSWER 2 lines that are always the same distance apart and never touch Perpendicular lines - CORRECT ANSWER The relationship between 2 lines which meet at a right angle (90degrees). Perpendicular lines= 2 lines intersect at a right angle Right angle - CORRECT ANSWER 90 degrees Straight angle - CORRECT ANSWER 180 degrees Acute angle - CORRECT ANSWER between 0 degrees and 90 degrees Obtuse angle - CORRECT ANSWER between 90 degrees and 180 degrees Complementary angles - CORRECT ANSWER 2 angles that have the sum of 90 degrees Supplementary angles - CORRECT ANSWER 2 angles that have the sum of 180 degrees the sum of the angle measures in a triangle - CORRECT ANSWER 180 degrees Acute triangle - CORRECT ANSWER All angles are acute Right triangle - CORRECT ANSWER One angle is right Obtuse triangle - CORRECT ANSWER One angle is obtuse Scalene triangle - CORRECT ANSWER All sides have different lengths Isosceles triangle - CORRECT ANSWER At least 2 sides have the same length Equilateral triangle - CORRECT ANSWER All sides have the same length The sum of the lengths of a triangle - CORRECT ANSWER The sum of the lengths of any two sides of a triangle must be greater than the length of the third side Polygon - CORRECT ANSWER A polygon is a closed figure whose sides are line segments that do not cross Regular Polygon - CORRECT ANSWER A regular polygon is a polygon where all of the sides have equal lengths and all of the angles have equal measures Trapezoid - CORRECT ANSWER One pair of opposite sides are parallel Parallelogram - CORRECT ANSWER Both pairs of opposite sides parallel Rhombus - CORRECT ANSWER All sides congruent Rectangle - CORRECT ANSWER 4 right angles Square - CORRECT ANSWER All sides congruent and 4 right angles Circle - CORRECT ANSWER The set of all points in a plane that are a a given distance from a given pint, the center Radius - CORRECT ANSWER Any of the line segments from its center to its perimeter Diameter - CORRECT 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 - CORRECT ANSWER The angle that forms when two radii meet at the center of a circle Chord - CORRECT ANSWER A straight line segment whose endpoints both lie on the circle All angle measures in a circle - CORRECT ANSWER = 360 degrees 3-Dimensional figure - CORRECT ANSWER A geometric shape whose vertices lie on more than one plane Faces - CORRECT ANSWER The flat surfaces of a 3-D figure Edges - CORRECT ANSWER The segments formed by intersecting faces Vertices - CORRECT ANSWER The points formed by intersecting edges Net - CORRECT 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 - CORRECT ANSWER 6a^2 (a is the length of the side of the cube) Surface Area of a Rectangular Prism - CORRECT ANSWER 2ab+2bc+2ac (a, b, and c are the lengths of the 3 sides) Surface Area of any Prism - CORRECT 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 - CORRECT ANSWER 4pir^2 Surface Area of a Cylinder - CORRECT ANSWER Congruent figures - CORRECT ANSWER -Have the same size and shape -The corresponding angles are congruent -The corresponding sides are congruent Similar figures - CORRECT 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 - CORRECT ANSWER A line of symmetry divides a figure into 2 parts, each of which is the mirror image of the other 1 foot= - CORRECT ANSWER 12 inches 3 feet= - CORRECT ANSWER 1 yard 5,280 feet= - CORRECT ANSWER 1 mile 1,760 yards= - CORRECT ANSWER 1 mile 1 centimeter= - CORRECT ANSWER 10 millimeters 1 meter= - CORRECT ANSWER 100 centimeters 1 kilometer= - CORRECT ANSWER 1000 meters 16 ounces= - CORRECT ANSWER 1 pound 2000 lbs= - CORRECT ANSWER 1 ton 128 fl oz= - CORRECT ANSWER 1 gal 2 pt= - CORRECT ANSWER 1 qt 1 L= - CORRECT ANSWER 1000 mL 1 kg= - CORRECT ANSWER 1000 g 1,000 mg= - CORRECT ANSWER 1 g 1 L= - CORRECT ANSWER 2.1 pt 1000 mm= - CORRECT ANSWER 1 m 100 cm= - CORRECT ANSWER 1 m Circumference - CORRECT ANSWER Area of a Rectangle - CORRECT ANSWER Area of a Circle - CORRECT ANSWER Area of a Trapezoid - CORRECT ANSWER Area of a Square - CORRECT ANSWER S^2 Area of a Triangle - CORRECT ANSWER 1/2bh Area of a Parallelogram - CORRECT ANSWER Surface Area - CORRECT ANSWER The sum of the areas of all the faces of the figure Volume of a Prism - CORRECT ANSWER Volume of a Cube - CORRECT ANSWER Volume of a Cylinder - CORRECT ANSWER Volume of a Pyramid - CORRECT ANSWER Volume of a Sphere - CORRECT ANSWER Volume of a Cone - CORRECT ANSWER Transformations - CORRECT ANSWER Changing the position of a given figure Reflection - CORRECT ANSWER When a figure is flipped over to create a mirror image Translation - CORRECT ANSWER When a figure is turned to a new position Dilation - CORRECT ANSWER When the dimensions of a figure increase or decrease to create a new figure that is similar to the original figure Distance formula - CORRECT ANSWER Midpoint formula - CORRECT ANSWER Equation of a Circle - CORRECT ANSWER h and k are the x and y coordinates of the center of the circle Coin Word problems - CORRECT ANSWER total value= the number of coins X the value of each coin Intercept Method - CORRECT ANSWER 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 - CORRECT ANSWER The value of x when y is equal to 0 y-intercept - CORRECT ANSWER The value of y when x is equal to 0 Graphing Linear Equations - CORRECT ANSWER Make an x & y chart Graphing Linear Inequalities - CORRECT ANSWER 1) rearrange the equation so "y" is on the left and everything else is on the right 2) 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<) 3) 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 - CORRECT ANSWER 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 - CORRECT ANSWER flip the sign f(x)= - CORRECT ANSWER y Range - CORRECT ANSWER The y-values, set of outputs Difference of Two Squares - CORRECT ANSWER Factoring Quadratics - CORRECT ANSWER ask yourself what two numbers multiply to end number but add up to middle number Factors - CORRECT ANSWER 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 - CORRECT ANSWER Means divisible by without any remainder Common Factors - CORRECT ANSWER factors that 2 or more numbers have in common. 3 is a common factor of 12 & 18 Greatest Common Factor - CORRECT ANSWER The largest common factor of two or more numbers. 6 is the GCF of 12 & 18 Multiples - CORRECT ANSWER 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 - CORRECT ANSWER any number that is a multiple of all given numbers. 48 & 96 are both common multiples of 8 & 12 Least Common Mulitple - CORRECT ANSWER The smallest multiple of 2 or more numbers. 24 is the LCM of 8 & 12 Permutation - CORRECT ANSWER order matters, Combination - CORRECT ANSWER order doesn't matter Multiplying Expressions - CORRECT ANSWER add the exponents. a^2 x a^5= a^7 Dividing Expressions - CORRECT ANSWER subtract exponents. r^5/ r^2= r^3 Raised Exponents - CORRECT ANSWER When a number raised to an exponent is raised to a 2nd exponent multiply the exponents. (n^3)^6= n^18 Pythagorean theorem - CORRECT ANSWER Probability - CORRECT ANSWER Number of ways is can happen/ total number of outcomes Mean - CORRECT ANSWER The sum of a list of values/ The number of values in a list Median - CORRECT ANSWER The middle value of a list when the numbers are in order. When the number of values in a list is an even number the median is the average of the two middle values. Mode - CORRECT ANSWER The value or values that appear the greatest number of times. It is possible to have multiple modes. Weighted Average - CORRECT ANSWER The average of two or more groups that do not all have the same number of members. 15 members of a class had an average SAT math score of 500. The remaining 10 members of the class had an average of 550. What is the average score of the entire class? - CORRECT ANSWER 1) multiply each individual average by its weighting factor weighting factor: the # of values that correspond to a particular average 2) (500 x 15) + (550 x 10) 3) then divide that by the # of students total (25) 4) the average score for the entire class is 520 Solutions - CORRECT ANSWER A value we can put in place of a variable (such as x) that makes the equation true. Also, where the equations "meet' or intersect. Same as x-intercepts and zeros and can also be called roots 1 solution - CORRECT ANSWER ex: x=5, x=23; intersecting lines no solutions - CORRECT ANSWER ex: 3=5, 8=2; parallel lines infinite solutions - CORRECT ANSWER ex: 13=13, 4=4; two equations on the same line Formula for Time - CORRECT ANSWER time= distance/ rate Formula for Rate - CORRECT ANSWER rate= distance/ time Quadratic formula - CORRECT ANSWER Standard format - CORRECT ANSWER y= ax^2+bx+c y= a(x-s1)(x-s2) Axis of symmetry formula - CORRECT ANSWER x= -b/2a Area of a Right triangle - CORRECT ANSWER 1/2 the product of its legs Directly proportional - CORRECT ANSWER if y=kx for some constant k Inversely proportional - CORRECT ANSWER if y=k/x for some constant k is, was, has - CORRECT ANSWER = more than, older than, farther than, greater than, sum of - CORRECT ANSWER + less than, difference, younger than, fewer - CORRECT ANSWER - of - CORRECT ANSWER x for, per - CORRECT ANSWER divide Distance formula - CORRECT ANSWER distance= rate x time Absolute Value - CORRECT ANSWER the number's distance from zero, disregard whether it is positive or negative greater than - CORRECT ANSWER > less than - CORRECT ANSWER < Slope - CORRECT ANSWER rise/run; Slope intercept form - CORRECT ANSWER y=mx+b m=slope b=y-intercept point slope formula - CORRECT ANSWER