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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Combine equations in such a way that one of the variables cancel out






2. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






3. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






4. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






5. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






6. Combine like terms






7. Volume of a Cylinder = pr^2h






8. To divide fractions - invert the second one and multiply






9. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






10. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






11. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






12. (average of the x coordinates - average of the y coordinates)






13. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






14. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






15. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






16. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






17. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






18. Part = Percent x Whole






19. The median is the value that falls in the middle of the set - the mode is the value that appears most often






20. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






21. The whole # left over after division






22. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






23. To solve a proportion - cross multiply






24. A square is a rectangle with four equal sides; Area of Square = side*side






25. 1. Re-express them with common denominators 2. Convert them to decimals






26. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






27. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






28. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






29. Surface Area = 2lw + 2wh + 2lh






30. pr^2






31. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






32. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






33. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






34. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






35. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






36. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






37. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






38. Probability= Favorable Outcomes/Total Possible Outcomes






39. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






40. The smallest multiple (other than zero) that two or more numbers have in common.






41. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






42. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






43. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






44. Multiply the exponents






45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






46. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






47. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






48. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






49. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






50. Add the exponents and keep the same base