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






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






4. 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






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






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






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






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






9. 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






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






11. 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






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






13. 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)






14. 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






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 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






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






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






21. 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






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






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






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






25. 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






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






27. 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)






28. 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






29. 2pr






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






31. 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






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






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






34. 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






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






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. Probability= Favorable Outcomes/Total Possible Outcomes






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






39. 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






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






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






42. Combine like terms






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






44. Factor out the perfect squares






45. Part = Percent x Whole






46. 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






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






48. 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






49. The whole # left over after division






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