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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 multiply fractions - multiply the numerators and multiply the denominators






2. 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






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






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






5. 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






6. 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






7. 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






8. 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






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






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






12. 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






13. 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






14. Combine like terms






15. 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.






16. 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






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






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






20. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






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






22. Volume of a Cylinder = pr^2h






23. Part = Percent x Whole






24. 2pr






25. pr^2






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






27. 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






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






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






31. 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






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






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






34. The whole # left over after division






35. 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






36. To solve a proportion - cross multiply






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






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






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






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






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






42. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






43. Change in y/ change in x rise/run






44. Multiply the exponents






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






46. 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






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






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






49. Add the exponents and keep the same base






50. Subtract the smallest from the largest and add 1