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






2. 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






3. The whole # left over after division






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






5. To solve a proportion - cross multiply






6. Factor out the perfect squares






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






8. 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






9. 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






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






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






12. Subtract the smallest from the largest and add 1






13. 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






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






17. 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






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






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






20. 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






21. 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)






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






23. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






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






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






27. Add the exponents and keep the same base






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






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






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






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






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






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






36. 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






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






38. 2pr






39. 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






40. 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






41. 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






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






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






44. 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






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






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






47. Part = Percent x Whole






48. 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






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






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