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






2. 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






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






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






5. 2pr






6. 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






7. Subtract the smallest from the largest and add 1






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






9. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






10. Combine like terms






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






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






13. 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






14. 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






15. 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






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






17. Multiply the exponents






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






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






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






22. To solve a proportion - cross multiply






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






24. 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






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






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






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






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






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. Probability= Favorable Outcomes/Total Possible Outcomes






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






33. 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






34. 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






35. Factor out the perfect squares






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






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






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






39. 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)






40. 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






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






42. 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






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






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






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






46. 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






47. 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






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






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






50. 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