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






2. 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






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






4. 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






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






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






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






8. 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






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






10. The whole # left over after division






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






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






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






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






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






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






17. Combine like terms






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






19. 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






20. 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






21. Subtract the smallest from the largest and add 1






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






23. pr^2






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






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






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






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






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






29. 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






30. Factor out the perfect squares






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






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






33. 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






34. Add the exponents and keep the same base






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






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






37. 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






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






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






40. 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.






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






42. 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






43. 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






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






45. 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






46. Multiply the exponents






47. 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






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






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






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