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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 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






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






3. 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.






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. 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






6. Multiply the exponents






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






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






9. 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






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






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






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






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






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






15. Factor out the perfect squares






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






17. pr^2






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






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






20. Part = Percent x Whole






21. Volume of a Cylinder = pr^2h






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






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 whole # left over after division






25. 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






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






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






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






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






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






31. 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






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






38. 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






39. 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






40. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






41. 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






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






43. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






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






45. Subtract the smallest from the largest and add 1






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






47. 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






48. 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






49. Combine like terms






50. 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