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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 whole # left over after division






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






3. 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






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






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






6. 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






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






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






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






10. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






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






12. 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






13. Subtract the smallest from the largest and add 1






14. 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






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






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






17. 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






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






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






20. Part = Percent x Whole






21. Volume of a Cylinder = pr^2h






22. Combine like terms






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






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






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






26. Add the exponents and keep the same base






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






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






29. 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






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






31. Multiply the exponents






32. 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






33. 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






34. 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






35. 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






36. 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






37. 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






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






39. 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






40. 2pr






41. 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






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






43. 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.






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






45. 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






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






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






48. 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






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






50. 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