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






3. pr^2






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






5. 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






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






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






8. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






11. 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






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






13. 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






14. Subtract the smallest from the largest and add 1






15. 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






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






17. Volume of a Cylinder = pr^2h






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






19. 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






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






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






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






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






24. 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






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






26. 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






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






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






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






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






31. To solve a proportion - cross multiply






32. 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






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






34. Multiply the exponents






35. 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






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






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






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






39. 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






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






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






42. Factor out the perfect squares






43. 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






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






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






46. Add the exponents and keep the same base






47. 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






48. 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






49. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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