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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. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






3. To solve a proportion - cross multiply






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






5. Multiply the exponents






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






7. 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






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






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






10. Combine equations in such a way that one of the variables cancel out






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






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






13. 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.






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






15. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






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






17. 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






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






19. 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






20. Add the exponents and keep the same base






21. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






22. 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






23. Subtract the smallest from the largest and add 1






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






25. 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






26. 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






27. The whole # left over after division






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






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






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






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






32. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






33. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






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






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






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






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






38. Sum=(Average) x (Number of Terms)






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






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






41. 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






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






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






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






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






46. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






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






48. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






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






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