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






2. 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






3. Combine like terms






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






6. 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






7. Multiply the exponents






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






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






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






11. 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






12. 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






13. 2pr






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






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. 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)






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






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






19. 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






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






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






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






23. 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






24. 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






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






26. pr^2






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






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






29. Part = Percent x Whole






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






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






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






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






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






35. 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






36. 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






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






38. To solve a proportion - cross multiply






39. 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






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






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






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






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






44. 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






45. 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






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






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






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






49. 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






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