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. Factor out the perfect squares






2. 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






3. To solve a proportion - cross multiply






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






5. Combine like terms






6. 2pr






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






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






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






10. Multiply the exponents






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






12. 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






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






14. 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






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






16. 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






17. 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






18. Add the exponents and keep the same base






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






20. 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






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






22. 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






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






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






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






26. 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






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






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






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






30. 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






31. 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






32. 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)






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






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






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






37. Volume of a Cylinder = pr^2h






38. pr^2






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






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






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






42. 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






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






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






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






46. 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






47. Probability= Favorable Outcomes/Total Possible Outcomes






48. 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






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






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