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






2. 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






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






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






5. 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






6. 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






7. 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






8. 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






9. 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






10. Combine like terms






11. Subtract the smallest from the largest and add 1






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






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






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






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






16. 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






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






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






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






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






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






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






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






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






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






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






27. 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






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






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






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






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 divide fractions - invert the second one and multiply






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






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






35. 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






36. Multiply the exponents






37. pr^2






38. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






39. 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






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






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






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






43. 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)






44. Volume of a Cylinder = pr^2h






45. 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






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






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






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






49. 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






50. 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.