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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. 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






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






3. 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






4. 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






5. 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






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






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






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






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






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






11. 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






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






13. 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






14. 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






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






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






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






18. 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






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






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






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






22. 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.






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






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






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






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






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






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






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






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






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






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






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






34. Subtract the smallest from the largest and add 1






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






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






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






38. 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






39. 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






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






41. 2pr






42. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






43. Combine like terms






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






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






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






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






48. The whole # left over after division






49. Volume of a Cylinder = pr^2h






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