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






2. 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






3. 2pr






4. 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






5. Multiply the exponents






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






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






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






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






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






11. 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






12. pr^2






13. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






14. 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






15. 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






16. 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)






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






18. Subtract the smallest from the largest and add 1






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






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






21. 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






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






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






24. 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






25. 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.






26. Probability= Favorable Outcomes/Total Possible Outcomes






27. 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






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






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






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






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






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






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






34. 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






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






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






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






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






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






40. The whole # left over after division






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






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






43. 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






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






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






46. 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






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






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






49. To solve a proportion - cross multiply






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