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






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






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






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






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






6. 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






7. 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






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






9. Combine like terms






10. 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






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






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






13. 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






14. 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






15. 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






16. Volume of a Cylinder = pr^2h






17. Part = Percent x Whole






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






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






20. 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






21. 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.






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






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






24. To solve a proportion - cross multiply






25. 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)






26. 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






27. 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






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






29. 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






30. 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






31. Add the exponents and keep the same base






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






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






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






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






36. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






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






39. Probability= Favorable Outcomes/Total Possible Outcomes






40. Subtract the smallest from the largest and add 1






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






42. 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






43. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






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






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






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






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 whole # left over after division






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