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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. Multiply the exponents






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






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






5. 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)






6. 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






7. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






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






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






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






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






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






13. 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






14. The whole # left over after division






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






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






17. Factor out the perfect squares






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






19. Subtract the smallest from the largest and add 1






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






21. 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






22. To solve a proportion - cross multiply






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






24. 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






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






26. 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






27. 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






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






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






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. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






32. Combine like terms






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






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






35. 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






36. 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






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






38. 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






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






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






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






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






43. 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






44. 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






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






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






48. 2pr






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






50. pr^2