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






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






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






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






5. Subtract the smallest from the largest and add 1






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






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






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






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






10. 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.






11. To solve a proportion - cross multiply






12. The whole # left over after division






13. 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






14. 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






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






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






17. 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






18. 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






19. 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






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






21. pr^2






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






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






24. 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






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






26. 2pr






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






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






30. Volume of a Cylinder = pr^2h






31. 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






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






33. 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






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






35. 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






36. 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






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






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






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






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






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






42. 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






43. Add the exponents and keep the same base






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






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






46. 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






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






48. Combine like terms






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






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