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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. 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






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






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






4. 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






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






6. 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)






7. The whole # left over after division






8. 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






9. 2pr






10. 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






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






12. Volume of a Cylinder = pr^2h






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






14. 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.






15. 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






16. 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






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






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






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






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






21. 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






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






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






24. 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






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






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






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






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






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






30. 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






31. To solve a proportion - cross multiply






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






37. Subtract the smallest from the largest and add 1






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






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






40. Multiply the exponents






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






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






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






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






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






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






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






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






49. 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






50. Add the exponents and keep the same base