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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. 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






2. 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






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. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






5. Add the exponents and keep the same base






6. 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






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






8. 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






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






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






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






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






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






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






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






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






18. 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






19. Volume of a Cylinder = pr^2h






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






21. pr^2






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






23. Subtract the smallest from the largest and add 1






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






25. 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






26. To solve a proportion - cross multiply






27. 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






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






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






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






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






32. 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






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






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






35. Multiply the exponents






36. 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






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






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






39. 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






40. 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






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






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






44. 2pr






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






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






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






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






49. 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






50. 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