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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. 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






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






4. 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






5. 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)






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






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






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






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






10. Add the exponents and keep the same base






11. The whole # left over after division






12. 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






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






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






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






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






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






18. Volume of a Cylinder = pr^2h






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






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






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






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






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






25. 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






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






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






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






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






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






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






32. 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






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






34. 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






35. 2pr






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






38. 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






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






40. 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






41. 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






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






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






44. 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






45. Part = Percent x Whole






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






47. 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






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






49. Factor out the perfect squares






50. 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