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






2. 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






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






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. A square is a rectangle with four equal sides; Area of Square = side*side






6. 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






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






8. Combine like terms






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






10. 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






11. pr^2






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






13. 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)






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






15. 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






16. 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)






17. 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






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






19. 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






20. 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






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






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






23. Volume of a Cylinder = pr^2h






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






25. Factor out the perfect squares






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






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






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






29. 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






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






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






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






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






34. 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






35. 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






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






37. 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






38. 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






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






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






41. The whole # left over after division






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






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






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






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






46. Subtract the smallest from the largest and add 1






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






48. 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






49. Multiply the exponents






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