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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. 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






2. 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






3. 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






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






5. 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






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






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






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






9. 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






10. 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






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






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






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






14. 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)






15. 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






16. 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






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






18. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






19. 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






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






21. 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






22. Probability= Favorable Outcomes/Total Possible Outcomes






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






24. Combine like terms






25. Factor out the perfect squares






26. 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






27. 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






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






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






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






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






32. 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






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






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






35. pr^2






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






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






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






39. 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.






40. 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






41. Add the exponents and keep the same base






42. To solve a proportion - cross multiply






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






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






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






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






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






48. 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






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






50. 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)