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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 30 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. For all right triangles: a^2+b^2=c^2






2. 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






3. Probability= Favorable Outcomes/Total Possible Outcomes






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






6. 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






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






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






9. 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






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






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






12. Multiply the exponents






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






14. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






15. 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






16. Combine like terms






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






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






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






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






21. 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






22. 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






23. 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.






24. Add the exponents and keep the same base






25. 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






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. 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






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






29. 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






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






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






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






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






34. Volume of a Cylinder = pr^2h






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






36. 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






37. 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






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






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






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






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






42. The whole # left over after division






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






44. 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






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






46. 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






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






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






49. Part = Percent x Whole






50. 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