Test your basic knowledge |

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. 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






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






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






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






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






6. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






7. 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






8. Factor out the perfect squares






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






10. Multiply the exponents






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






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






13. 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






14. Add the exponents and keep the same base






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






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






17. 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






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






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






20. 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






21. 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






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






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






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






25. 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






26. 2pr






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






28. Combine like terms






29. 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






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






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






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






33. 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






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. The whole # left over after division






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






37. 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






38. To solve a proportion - cross multiply






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






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






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






42. 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






43. 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






44. 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






45. 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






46. 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)






47. 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






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






49. Probability= Favorable Outcomes/Total Possible Outcomes






50. 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