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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. Add the exponents and keep the same base






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






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






4. 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






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






6. 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






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






8. 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






9. 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






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 find the reciprocal of a fraction switch the numerator and the denominator






12. To divide fractions - invert the second one and multiply






13. Combine like terms






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






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






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






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






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






19. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






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






21. 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






22. 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






23. 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






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






25. 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






26. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






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






28. Subtract the smallest from the largest and add 1






29. 2pr






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






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






32. The whole # left over after division






33. pr^2






34. Volume of a Cylinder = pr^2h






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






36. 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






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






38. 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)






39. 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






40. Probability= Favorable Outcomes/Total Possible Outcomes






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






42. Multiply the exponents






43. 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)






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






45. 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






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






47. 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.






48. 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






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






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