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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 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






2. Subtract the smallest from the largest and add 1






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






4. 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






5. Combine like terms






6. The whole # left over after division






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






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






9. 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






10. 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






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






12. 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






13. 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.






14. 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






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






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






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






18. 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






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






20. 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






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






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






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






24. 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






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






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






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






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






29. 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






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






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






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






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






34. 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






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






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






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






38. 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






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






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






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






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






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






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






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






46. 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






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






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






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