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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 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






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






3. 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.






4. 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






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






6. 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)






7. 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






8. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






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






11. 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






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






13. 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






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






15. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






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






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






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






19. 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






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






21. 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






22. pr^2






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






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






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






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






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






28. 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






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






30. 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






31. 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






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






33. 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






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






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






36. Subtract the smallest from the largest and add 1






37. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






40. 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






41. 2pr






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






43. 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






44. 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






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






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






47. Factor out the perfect squares






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






49. 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






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