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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 whole # left over after division






2. 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






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






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






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






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






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






8. 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






9. 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






10. 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






11. 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






12. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






14. Subtract the smallest from the largest and add 1






15. 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






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






17. To solve a proportion - cross multiply






18. 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.






19. Combine like terms






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






21. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






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






23. 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






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






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






26. 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






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






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






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






30. Probability= Favorable Outcomes/Total Possible Outcomes






31. 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






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






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






34. 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






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






36. Add the exponents and keep the same base






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






38. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






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






40. Factor out the perfect squares






41. 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






42. 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






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






44. 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






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






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






47. 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






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






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






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