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






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






3. 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






4. Factor out the perfect squares






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






6. Subtract the smallest from the largest and add 1






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






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






9. 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






10. 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






11. 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






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






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






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






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






16. 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






17. 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






18. Volume of a Cylinder = pr^2h






19. 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






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






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






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






23. To solve a proportion - cross multiply






24. 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






25. 2pr






26. Probability= Favorable Outcomes/Total Possible Outcomes






27. 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






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






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






30. 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)






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






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






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






35. 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






36. 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)






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






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






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






40. 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






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






42. 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






43. Part = Percent x Whole






44. 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






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






46. 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






47. 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






48. 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






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






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