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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. Multiply the exponents






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






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






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






5. 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.






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






7. 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






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






9. Part = Percent x Whole






10. 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






11. 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






12. 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






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






14. Combine like terms






15. 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






16. 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)






17. 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






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






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






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






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






22. 2pr






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






25. pr^2






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






27. Volume of a Cylinder = pr^2h






28. 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






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






30. 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






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






32. 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






33. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






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






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






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






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






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






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






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






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






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






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






44. 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






45. 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






46. 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






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






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






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






50. you can add/subtract when the part under the radical is the same