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






2. 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






3. 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






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






5. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






6. 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)






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






8. Subtract the smallest from the largest and add 1






9. 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






10. Factor out the perfect squares






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






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






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






14. 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)






15. 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






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






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






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






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






20. 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






21. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






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






23. 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






24. The whole # left over after division






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






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. 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






28. 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






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






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






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






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






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






34. 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






35. 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






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






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






38. Volume of a Cylinder = pr^2h






39. 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






40. 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






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






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






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. Multiply the exponents






45. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






49. 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






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