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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 that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






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






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






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






5. 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






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






7. 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






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






9. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






10. 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






11. 2pr






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






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






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






15. 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






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






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. To find the reciprocal of a fraction switch the numerator and the denominator






19. Combine like terms






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






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






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






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






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






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






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






27. Part = Percent x Whole






28. Factor out the perfect squares






29. 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






30. To solve a proportion - cross multiply






31. 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






32. 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






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






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






35. Probability= Favorable Outcomes/Total Possible Outcomes






36. 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






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






38. The whole # left over after division






39. 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






40. 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






41. 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)






42. Multiply the exponents






43. 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






44. Subtract the smallest from the largest and add 1






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






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






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






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






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






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