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






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






3. 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






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






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






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






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






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






9. 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






10. 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






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






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






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






14. 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






15. Probability= Favorable Outcomes/Total Possible Outcomes






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






17. 2pr






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






19. 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






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






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






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






23. 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






24. Combine like terms






25. Factor out the perfect squares






26. Part = Percent x Whole






27. 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






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






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






30. 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






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






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






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






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






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






36. 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






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






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






39. The whole # left over after division






40. pr^2






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






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






43. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






44. 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






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






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






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






48. 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






49. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






50. Add the exponents and keep the same base