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






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






3. Factor out the perfect squares






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






5. 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






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






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






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






9. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






11. 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






12. 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






13. Combine like terms






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






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






16. 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.






17. 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






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






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






20. 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






21. 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






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






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






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






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






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






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






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






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






31. 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






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






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






34. Probability= Favorable Outcomes/Total Possible Outcomes






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






36. 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






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






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






39. The whole # left over after division






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






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






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






43. 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






44. 2pr






45. 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






46. Multiply the exponents






47. 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






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






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






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