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






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






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






4. 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






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






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






7. 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






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






9. Volume of a Cylinder = pr^2h






10. 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






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






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






13. 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






14. 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






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






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






17. 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






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






19. pr^2






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






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






22. 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






23. Multiply the exponents






24. 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






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






26. 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






27. Part = Percent x Whole






28. 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






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






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






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






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






33. 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






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






35. 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






36. Probability= Favorable Outcomes/Total Possible Outcomes






37. Combine like terms






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. 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






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






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






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






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






44. 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






45. 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






46. 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






47. The whole # left over after division






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






49. Factor out the perfect squares






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