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






2. 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






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






4. 2pr






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






6. 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






7. 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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






10. Sum=(Average) x (Number of Terms)






11. 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






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






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






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






15. 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






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






17. 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






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






19. To solve a proportion - cross multiply






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. Factor out the perfect squares






22. 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






23. 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






24. 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.






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






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






28. 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






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






30. 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






31. Multiply the exponents






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






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






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






35. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






37. 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






38. 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)






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






40. Volume of a Cylinder = pr^2h






41. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






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






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






44. 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






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






46. Add the exponents and keep the same base






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






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






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






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