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






2. 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






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






4. 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






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






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






7. 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






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






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






10. 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






11. Combine like terms






12. 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.






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






14. 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






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






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






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






18. 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






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






20. pr^2






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






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






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






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






25. 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)






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






27. 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






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






29. 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






30. To solve a proportion - cross multiply






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






32. Part = Percent x Whole






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






34. Add the exponents and keep the same base






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






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






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






38. 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






39. Factor out the perfect squares






40. 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






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






42. 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






43. 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






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






45. The whole # left over after division






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






47. 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






48. 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






49. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






50. Multiply the exponents