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






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






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






4. 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






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






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






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






8. 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






9. Factor out the perfect squares






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






11. Subtract the smallest from the largest and add 1






12. 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






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






14. The whole # left over after division






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






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






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






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






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






20. 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






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






22. To solve a proportion - cross multiply






23. 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.






24. 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






25. 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






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






27. Multiply the exponents






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






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






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. 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






32. 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)






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






34. Add the exponents and keep the same base






35. 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






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






37. 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






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






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






40. 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






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






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






43. Part = Percent x Whole






44. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






47. 2pr






48. 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






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






50. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)