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






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






3. 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






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






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






6. The whole # left over after division






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






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






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






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






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






12. 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






13. 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






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. 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






16. 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






17. Subtract the smallest from the largest and add 1






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






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






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






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






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






23. 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)






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






25. 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






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






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






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






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






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






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






33. 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.






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






35. Probability= Favorable Outcomes/Total Possible Outcomes






36. 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






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






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






39. Multiply the exponents






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






41. Factor out the perfect squares






42. 2pr






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






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






45. To solve a proportion - cross multiply






46. Combine like terms






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






48. 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






49. 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






50. 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