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






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






3. 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






4. 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






5. The whole # left over after division






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






7. Factor out the perfect squares






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






9. pr^2






10. 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






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






12. Add the exponents and keep the same base






13. 2pr






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






15. A square is a rectangle with four equal sides; Area of Square = side*side






16. 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






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






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






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






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






21. 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






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






23. 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






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






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






26. 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






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






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






29. 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






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






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






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






33. 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






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






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






36. 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






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






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






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






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






41. Subtract the smallest from the largest and add 1






42. 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






43. 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






44. Volume of a Cylinder = pr^2h






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






46. 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






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






48. Part = Percent x Whole






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






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