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






2. 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






3. Multiply the exponents






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






5. 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






6. 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






7. 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






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






9. 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)






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






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






12. To solve a proportion - cross multiply






13. 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






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






15. 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






16. 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.






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






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






19. 2pr






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






21. 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






22. 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






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






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






25. 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






26. 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






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






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






29. 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






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






31. 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






32. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






33. Combine like terms






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






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






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






37. 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






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






39. Subtract the smallest from the largest and add 1






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






41. Volume of a Cylinder = pr^2h






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






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






44. 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






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






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






47. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






50. 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