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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. 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






2. 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






3. Part = Percent x Whole






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






5. 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






6. 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






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






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






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. pr^2






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






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






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






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






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






16. 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






17. 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






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






19. 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






20. 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






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






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






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






24. Add the exponents and keep the same base






25. 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






26. 2pr






27. 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






28. 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






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






30. 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






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






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






33. Combine like terms






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






35. 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






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






37. 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






38. Subtract the smallest from the largest and add 1






39. 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






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






42. 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






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






44. Multiply the exponents






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






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






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






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






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






50. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520