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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. Change in y/ change in x rise/run






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






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






4. 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






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






6. 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






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






8. Multiply the exponents






9. 2pr






10. 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






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






12. 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






13. Volume of a Cylinder = pr^2h






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






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






16. 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






17. 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)






18. Subtract the smallest from the largest and add 1






19. 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






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






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






22. 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






23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






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






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. To solve a proportion - cross multiply






27. 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






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






29. 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






30. 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






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






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






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






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






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






36. 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.






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






38. 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






39. 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






40. pr^2






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






42. Probability= Favorable Outcomes/Total Possible Outcomes






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






44. Add the exponents and keep the same base






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






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






47. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






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






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