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






2. To solve a proportion - cross multiply






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






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






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






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






7. 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






8. 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






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






10. 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






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






12. Add the exponents and keep the same base






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






14. 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






15. Subtract the smallest from the largest and add 1






16. pr^2






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






18. 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






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






20. 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






21. 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






22. 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)






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






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






25. 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






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






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






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






29. Probability= Favorable Outcomes/Total Possible Outcomes






30. 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






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






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






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






34. The whole # left over after division






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






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






37. 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






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






39. 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






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






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






42. 2pr






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






44. 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






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






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






47. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






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






49. 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






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