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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. 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)






2. 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






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






4. 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






5. 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






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






7. 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






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






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






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






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






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






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






14. 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






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






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






17. 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






18. 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






19. Multiply the exponents






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






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






22. 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)






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






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






25. 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






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






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






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






29. 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.






30. The whole # left over after division






31. 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






32. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






33. To solve a proportion - cross multiply






34. 2pr






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






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






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






38. Part = Percent x Whole






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






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






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






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






43. Combine like terms






44. 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






45. 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






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






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






48. Factor out the perfect squares






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






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