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






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






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






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






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






7. 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






8. Volume of a Cylinder = pr^2h






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






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. 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.






12. 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






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






14. 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)






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






16. pr^2






17. Probability= Favorable Outcomes/Total Possible Outcomes






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






19. 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






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






21. Combine equations in such a way that one of the variables cancel out






22. 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






23. 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






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






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






26. 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






27. 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






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






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






30. 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






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






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






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






34. 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






35. To solve a proportion - cross multiply






36. 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






37. 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)






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






39. 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






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






41. The whole # left over after division






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






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






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






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






46. 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






47. 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






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






49. Multiply the exponents






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