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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. Multiply the exponents






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






3. 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






4. The whole # left over after division






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






6. 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






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






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






9. Probability= Favorable Outcomes/Total Possible Outcomes






10. Part = Percent x Whole






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






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






13. Factor out the perfect squares






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






15. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






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






17. 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






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






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






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






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






22. Subtract the smallest from the largest and add 1






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






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






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






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






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






28. 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.






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






30. 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






31. 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)






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






33. pr^2






34. 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






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






36. 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






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






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






39. 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






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






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






42. 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






43. 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






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






45. 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






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






47. 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






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






49. To solve a proportion - cross multiply






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