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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. 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.






2. 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






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






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






5. Volume of a Cylinder = pr^2h






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






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






8. 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






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






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






11. 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






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






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






14. Multiply the exponents






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






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






17. 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






18. Add the exponents and keep the same base






19. 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






20. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






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






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






23. 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






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






25. Factor out the perfect squares






26. Probability= Favorable Outcomes/Total Possible Outcomes






27. 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






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






29. Part = Percent x Whole






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






31. 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






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






33. 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)






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






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






36. 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






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






38. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






39. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






40. 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






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






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






43. Subtract the smallest from the largest and add 1






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






45. To solve a proportion - cross multiply






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






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






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






49. 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






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