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. 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






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






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






4. 2pr






5. 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






6. 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






7. 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






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






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






10. Multiply the exponents






11. 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






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






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






15. 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






16. To solve a proportion - cross multiply






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






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






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






20. 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






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






23. Volume of a Cylinder = pr^2h






24. 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






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






26. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






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






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






29. Add the exponents and keep the same base






30. Part = Percent x Whole






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






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






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






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






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






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






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






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






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






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






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. Subtract the smallest from the largest and add 1






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






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






46. Combine like terms






47. Factor out the perfect squares






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






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






50. 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