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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 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






2. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






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






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






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






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






7. 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






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






9. 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)






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






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






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






13. Subtract the smallest from the largest and add 1






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






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






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






17. Part = Percent x Whole






18. 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






19. 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






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






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






22. 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






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






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






25. 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






26. Volume of a Cylinder = pr^2h






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






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






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






30. 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






31. 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






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






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






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






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






36. The whole # left over after division






37. 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






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






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






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






41. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






42. 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






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






44. 2pr






45. 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






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






47. 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






48. Probability= Favorable Outcomes/Total Possible Outcomes






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






50. 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