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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. 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






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






3. The whole # left over after division






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






5. 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






6. Factor out the perfect squares






7. 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






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






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






10. 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






11. Volume of a Cylinder = pr^2h






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






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






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






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






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






17. 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






18. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






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






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






21. Part = Percent x Whole






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






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






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






25. 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






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






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






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






29. 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






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






31. 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)






32. 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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






37. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






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






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






40. 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






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






42. 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






43. 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






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






45. Subtract the smallest from the largest and add 1






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






49. 2pr






50. Combine like terms