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






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






3. 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)






4. 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






5. 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






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






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






8. Factor out the perfect squares






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






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






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






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






13. 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






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






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






16. 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






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






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






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






20. Volume of a Cylinder = pr^2h






21. 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






22. 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






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






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






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






27. 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






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






29. 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






30. 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






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






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






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






34. pr^2






35. 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






36. Part = Percent x Whole






37. 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






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






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






40. 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






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






42. 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






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






44. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






47. 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






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






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






50. 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)