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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. Domain: all possible values of x for a function range: all possible outputs of a function






3. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






4. 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






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






6. To find the reciprocal of a fraction switch the numerator and the denominator






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






8. To multiply fractions - multiply the numerators and multiply the denominators






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






10. Combine like terms






11. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






12. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






13. Volume of a Cylinder = pr^2h






14. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






15. Change in y/ change in x rise/run






16. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






17. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






19. 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






20. you can add/subtract when the part under the radical is the same






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






22. Part = Percent x Whole






23. 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






24. Factor out the perfect squares






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






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






27. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






28. 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






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






30. 2pr






31. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






32. The largest factor that two or more numbers have in common.






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






34. Multiply the exponents






35. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






36. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






37. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






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






39. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






40. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






41. For all right triangles: a^2+b^2=c^2






42. 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






43. 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






44. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






45. Probability= Favorable Outcomes/Total Possible Outcomes






46. 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






47. 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






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






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