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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 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






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. Volume of a Cylinder = pr^2h






4. Multiply the exponents






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






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






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






8. 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






9. 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






10. 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






11. 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






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






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






14. Add the exponents and keep the same base






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






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






18. 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






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






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






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






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






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






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






25. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






26. 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






27. Subtract the smallest from the largest and add 1






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






29. To solve a proportion - cross multiply






30. 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)






31. 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






32. Part = Percent x Whole






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






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






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






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






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






38. 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






39. 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






40. Combine like terms






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






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






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






44. pr^2






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






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. 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)






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






49. 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






50. 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.