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






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






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






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






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






6. Probability= Favorable Outcomes/Total Possible Outcomes






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






8. 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






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






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






11. 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)






12. 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






13. 2pr






14. 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






15. 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






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






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






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






19. 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






20. 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






21. Subtract the smallest from the largest and add 1






22. pr^2






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






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






25. 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






26. 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






27. 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






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






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






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






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






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






34. 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






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






36. 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






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






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






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






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






41. To solve a proportion - cross multiply






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






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






44. 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






45. 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






46. 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






47. 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






48. 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.






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






50. 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