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






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






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






4. 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






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






6. The whole # left over after division






7. To solve a proportion - cross multiply






8. 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






9. 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






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






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






12. 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)






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






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






15. 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






16. 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






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






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






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






20. 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






21. 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






22. Multiply the exponents






23. 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






24. 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






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






26. 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






27. 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






28. 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






29. pr^2






30. Part = Percent x Whole






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






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






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






34. 2pr






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






36. 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






37. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






39. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






42. 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)






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






44. Combine like terms






45. Add the exponents and keep the same base






46. 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.






47. 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






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






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