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






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






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






4. 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






5. Multiply the exponents






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. The whole # left over after division






8. 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)






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






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






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






12. pr^2






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






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






15. Part = Percent x Whole






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






18. Volume of a Cylinder = pr^2h






19. 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)






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






21. 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






22. 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






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






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






25. 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






26. Probability= Favorable Outcomes/Total Possible Outcomes






27. 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






28. 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






29. 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






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






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






33. 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.






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






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






36. 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






37. 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






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






39. 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






40. Subtract the smallest from the largest and add 1






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






42. 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






43. 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






44. To solve a proportion - cross multiply






45. 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






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






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






48. 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






49. 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






50. 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