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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 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






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






3. Multiply the exponents






4. 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






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






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






7. The whole # left over after division






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






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






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






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






12. 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






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






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






15. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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






17. 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






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






19. 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






20. 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






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






22. 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






23. 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.






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






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






26. 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






27. 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






28. Subtract the smallest from the largest and add 1






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






30. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






31. 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)






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






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






34. 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






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






36. To solve a proportion - cross multiply






37. Part = Percent x Whole






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






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






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






41. Probability= Favorable Outcomes/Total Possible Outcomes






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






43. 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






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






45. 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






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






47. 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






48. 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






49. 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






50. 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