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






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






3. To multiply fractions - multiply the numerators and multiply the denominators






4. 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






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






6. Factor out the perfect squares






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






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






9. 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






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






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






12. 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






13. Subtract the smallest from the largest and add 1






14. 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






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






16. 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






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






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






19. 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






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






21. 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






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






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






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






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






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. 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






28. 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)






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






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






31. Volume of a Cylinder = pr^2h






32. 2pr






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






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






36. 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






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






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






39. Add the exponents and keep the same base






40. 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






41. 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






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






43. 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






44. 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






45. Combine like terms






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






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






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






49. The whole # left over after division






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