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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. The whole # left over after division






2. 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






3. 2pr






4. Subtract the smallest from the largest and add 1






5. 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






6. 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






7. 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






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






9. Add the exponents and keep the same base






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






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






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






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






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






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






16. 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






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






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






19. Combine like terms






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






21. Factor out the perfect squares






22. 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






23. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






26. To solve a proportion - cross multiply






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






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






29. 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






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






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






32. 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






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






34. 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






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






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






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






38. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






39. 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






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






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






42. 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






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






44. Multiply the exponents






45. Part = Percent x Whole






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






47. pr^2






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






49. 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






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