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






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






3. Probability= Favorable Outcomes/Total Possible Outcomes






4. 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






5. Add the exponents and keep the same base






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






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






8. 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






9. 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






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






11. 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






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






13. 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






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






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






16. Multiply the exponents






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






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






19. 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






20. 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






21. 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






22. The whole # left over after division






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






24. 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






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






26. 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






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






28. To solve a proportion - cross multiply






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






30. 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






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






32. 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






33. 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






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






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






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. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






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






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






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






42. 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






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






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






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






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






47. pr^2






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






49. 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






50. 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