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






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






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






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






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






6. 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






7. 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)






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






9. 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






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






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. 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






13. 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






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






15. 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






16. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






19. 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






20. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






21. Part = Percent x Whole






22. 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






23. Subtract the smallest from the largest and add 1






24. 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






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






26. The whole # left over after division






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






28. To solve a proportion - cross multiply






29. 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






30. 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






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






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






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






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






35. pr^2






36. 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






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






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






39. 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






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






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






42. Volume of a Cylinder = pr^2h






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






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






45. 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






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






47. Factor out the perfect squares






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






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






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