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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. Subtract the smallest from the largest and add 1






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






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






4. 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






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






7. To solve a proportion - cross multiply






8. 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






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






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






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






13. 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






14. 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






15. Factor out the perfect squares






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






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






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






19. 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






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






21. 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






22. Add the exponents and keep the same base






23. 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






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






25. 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






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






27. Combine like terms






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






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






30. 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






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






32. 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






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






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






35. Probability= Favorable Outcomes/Total Possible Outcomes






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






37. Part = Percent x Whole






38. 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






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






40. 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






41. pr^2






42. 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






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






44. 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






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






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






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






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






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






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