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






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






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






4. 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






5. 2pr






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






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. 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






9. To solve a proportion - cross multiply






10. Probability= Favorable Outcomes/Total Possible Outcomes






11. 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






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






13. 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






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






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






16. 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.






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






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






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






20. 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






21. 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






22. 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






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






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






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






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






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






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






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






30. 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






31. Combine like terms






32. 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






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






34. 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






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






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






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






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






39. 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






40. 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






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






42. 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






43. Add the exponents and keep the same base






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






45. 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






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






47. 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






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






49. 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






50. 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