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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. 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






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. 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






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






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






6. 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






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






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






9. Add the exponents and keep the same base






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






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






12. 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






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






14. 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






15. 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






16. Subtract the smallest from the largest and add 1






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






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






19. 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






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






21. Factor out the perfect squares






22. 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






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






24. 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






25. 2pr






26. 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






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






28. Part = Percent x Whole






29. 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






30. 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






31. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






32. 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






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






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






35. Volume of a Cylinder = pr^2h






36. 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






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






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






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






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. 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






42. 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






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






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






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






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






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






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






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






50. To solve a proportion - cross multiply