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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 reciprocal of a fraction switch the numerator and the denominator






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






3. 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.






4. 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






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






6. The whole # left over after division






7. Subtract the smallest from the largest and add 1






8. 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






9. 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






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






11. 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






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






13. 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






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






15. 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






16. 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






17. 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






18. 2pr






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






20. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






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






22. Multiply the exponents






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






24. 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






25. Probability= Favorable Outcomes/Total Possible Outcomes






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






27. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






28. 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






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






30. 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






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






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






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. 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






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






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






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






39. 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






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






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






42. 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






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






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






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






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






47. Factor out the perfect squares






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






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






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