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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 whole # left over after division






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






3. 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






4. 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






5. 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






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






7. 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






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






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. pr^2






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






12. 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






13. 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)






14. Volume of a Cylinder = pr^2h






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






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






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






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






19. 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






20. 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






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






22. 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)






23. 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






24. 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






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






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






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






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






29. 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






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






31. 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






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






34. 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






35. 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.






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






37. 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






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






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






40. To solve a proportion - cross multiply






41. 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






42. Part = Percent x Whole






43. 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






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






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






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






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






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






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






50. Subtract the smallest from the largest and add 1