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






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






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






4. To solve a proportion - cross multiply






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






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






7. 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






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






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






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






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






12. 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






13. 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






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






15. 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






16. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






17. 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






18. 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






19. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






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






25. pr^2






26. 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






27. Volume of a Cylinder = pr^2h






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






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






31. Combine like terms






32. 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






33. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






35. 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






36. 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






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






38. 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.






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






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






41. 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






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






43. Subtract the smallest from the largest and add 1






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






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






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






47. 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)






48. The whole # left over after division






49. 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






50. 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