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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 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






2. 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






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






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






5. Subtract the smallest from the largest and add 1






6. Volume of a Cylinder = pr^2h






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






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






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






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






11. 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






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






13. 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






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






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






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






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






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






20. Factor out the perfect squares






21. 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






22. 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






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






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






25. 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






26. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






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






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






30. pr^2






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






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






33. 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






34. 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






35. 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






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






37. 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)






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






39. 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






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






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






42. Part = Percent x Whole






43. 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






44. 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)






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






46. 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






47. 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






48. 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






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






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