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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 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






2. 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)






3. 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






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






5. 2pr






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






7. 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






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






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






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






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






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






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






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






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






16. 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






17. Add the exponents and keep the same base






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






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






21. Combine like terms






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






23. 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






24. 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






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






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






27. 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






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






29. 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






30. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






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






32. 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






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






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






35. Probability= Favorable Outcomes/Total Possible Outcomes






36. Multiply the exponents






37. 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






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






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






40. 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






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






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






43. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






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






46. 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






47. Subtract the smallest from the largest and add 1






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






49. 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






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