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






2. Part = Percent x Whole






3. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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






5. pr^2






6. 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






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. 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)






9. 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






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






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






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






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






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






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






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






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






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






19. Add the exponents and keep the same base






20. 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






21. Multiply the exponents






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






23. Probability= Favorable Outcomes/Total Possible Outcomes






24. Volume of a Cylinder = pr^2h






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






26. 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






27. 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.






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






29. 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






30. 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






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






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






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






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






35. To solve a proportion - cross multiply






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






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






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






39. 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






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






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






42. 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






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. 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






45. Factor out the perfect squares






46. 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






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






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






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