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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. 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






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






3. Volume of a Cylinder = pr^2h






4. 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






5. 2pr






6. 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






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






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






9. 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






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






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






12. Part = Percent x Whole






13. 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






14. 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






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






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






17. 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






18. Probability= Favorable Outcomes/Total Possible Outcomes






19. 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






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






21. 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






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






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






24. 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






25. Subtract the smallest from the largest and add 1






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






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






28. To solve a proportion - cross multiply






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. 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






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






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






33. Multiply the exponents






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. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






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






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






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






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






40. 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.






41. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






42. pr^2






43. 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






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






45. 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






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






47. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






48. 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






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






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