ALEKS Basic Math Placement Test Review Exam with verified solutions 2024

how to find domain with a given equation -if a fraction, set denom. to zero, then solve -in equation, plug in 0 for x usually can be a + or - solution (-) + (-)= ... (-) x (-)= ... (-) divided by a (-)= ... (-) (+) (+) quotient division adding and subtracting fractions -make denoms the same -add/subtract numerators multiplying fractions just multiply numerators across and denoms across and simplify dividing fraction multiply by reciprocal (change second fraction to reciprocal) multiplying/dividing/adding mixed fractions turn them into regular fractions (multiplying # by denom, adding it to num, keeping denom the same) and continue subtracting mixed fractions first: make denoms the same set up as if you're subtracting two large numbers (on top and on bottom) how to solve problems like 5-2 (1/3) 1) make problem 5- (2 (1/3)) 2) separate : 5- 2- (1/3) to get: 3- (1/3) 3) rewrite whole #: 2+1- (1/3) 4) rewrite as: 2 + (3/3) - (1/3) to ed up with: 2 (2/3) inequality problem rule (, , etc like problems) When multiplying/dividing each side by a positive number, the inequality sign stays the same When multiplying/dividing each side by a negative number, we flip the inequality sign. area and circumference of circle A= pi x r^2 C= 2 x pi x r area and perimeter of a triangle A= (1/2)bh (unit squared) P= side+side+ side Volume and surface area of a rectangular prism V=lwh (unit to the 3rd power) SA= 2(wl + hl+ hw) distance formula d= rate x time percent to fraction percent as numerator and 100 as denominator, then simplify fraction to percent 1) do long division with denom as outside and numerator as inside 2) move decimal over 2 places to make it into a % do not forget decimal ORRRR make denom 100 (multiply num and denom of original fraction by whatever to get it to 100) how to find percent of change 1) change/ original amount 2) make fraction into a decimal 3) move decimal to make it a percent how to find new price given a percentage off 1) subtract the given percent by 100 2) make that number into a decimal 3) multiply decimal by amount to get new price ORRRR 1) change percent to a decimal 2) multiply decimal by dollar amount 3) subtract that amount from the old amount to see new amount simple interest I= Prt (p= principle/ beginning amount) change percent into decimal Compounded Interest use when problem says annually A= P (1+r)^t functions... can have only different inputs/x values Borrowing for 0 and 1.... 0 -- 10 1 -- 11 integers ...-3,-2,-1,0,1,2,3... whole numbers and their negative numbers graphing when given an x-int and y-int x- int turns into (x,0) y-int turns into (0,y) then graph those points two variable equations plug any number into x or y to solve for either one dividing of exponents subtract the exponents ex: a^5 / a^7 = 1/a^2 decimal to % % to decimal -decimal to %: move decimal over to left twice -% to decimal: move decimal over to right twice fraction word problems fraction x cost= amount one has how to multiply with decimals ex: 9 x 0.6 do (9 x 6) divided by 10 to get: 54 divided by 10 to get 5.4