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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. 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.






2. The whole # left over after division






3. 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






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






5. Factor out the perfect squares






6. To solve a proportion - cross multiply






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






8. pr^2






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






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






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






12. 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






13. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






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






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






16. 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






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






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






19. Probability= Favorable Outcomes/Total Possible Outcomes






20. 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






21. 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






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






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






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






25. 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






26. 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






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






28. 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)






29. 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






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






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






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






33. 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






34. Multiply the exponents






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






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






38. Combine like terms






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






41. 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






42. 2pr






43. 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






44. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






45. 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






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






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






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






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