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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. 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






2. 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






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






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






5. Combine like terms






6. Multiply the exponents






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






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






9. 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






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






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






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






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






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






16. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






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






18. 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






19. 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






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






21. 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






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






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






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






25. 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)






26. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






27. 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






28. 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






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






30. Add the exponents and keep the same base






31. Factor out the perfect squares






32. pr^2






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






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






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






36. To solve a proportion - cross multiply






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






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






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






40. 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






41. 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






42. Part = Percent x Whole






43. 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






44. Subtract the smallest from the largest and add 1






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






46. 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






47. 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






48. you can add/subtract when the part under the radical is the same






49. Probability= Favorable Outcomes/Total Possible Outcomes






50. Volume of a Cylinder = pr^2h