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






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






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






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






5. 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






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






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






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






9. 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)






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






11. 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






12. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






13. pr^2






14. Combine like terms






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






16. 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






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






18. Factor out the perfect squares






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






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






21. 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






22. Multiply the exponents






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






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






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






26. 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






27. Volume of a Cylinder = pr^2h






28. 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)






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






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






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






32. 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






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






34. 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






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






36. 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






37. 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






38. To solve a proportion - cross multiply






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






40. 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






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






42. 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






43. 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






44. 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






45. 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






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






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. 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






49. 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






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