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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 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






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






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






4. 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






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






7. Factor out the perfect squares






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






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






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






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






12. 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






13. Multiply the exponents






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






15. The whole # left over after division






16. 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






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






18. 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






19. 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






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






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






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






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






24. Part = Percent x Whole






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






26. pr^2






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






28. 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






29. 2pr






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






31. Subtract the smallest from the largest and add 1






32. Probability= Favorable Outcomes/Total Possible Outcomes






33. 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






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






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






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






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






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






39. 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






40. 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






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






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






43. 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






44. 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






45. To solve a proportion - cross multiply






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






47. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






48. 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)






49. 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






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