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






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






3. Volume of a Cylinder = pr^2h






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






5. 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






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






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






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






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






11. 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






12. 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






13. Combine like terms






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






15. Part = Percent x Whole






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






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






18. 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)






19. 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






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. 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






22. Subtract the smallest from the largest and add 1






23. 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






24. 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






25. Factor out the perfect squares






26. 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.






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






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






29. Multiply the exponents






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






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






32. 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






33. 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






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






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






36. 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






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






38. Probability= Favorable Outcomes/Total Possible Outcomes






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






40. 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






41. 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






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






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






44. 2pr






45. 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






46. 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)






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






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






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






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






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