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






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






3. 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






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






5. pr^2






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






7. 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.






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






9. Factor out the perfect squares






10. Add the exponents and keep the same base






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






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






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. 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






15. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






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






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






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






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






20. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






21. The whole # left over after division






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. Combine like terms






24. 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






25. Part = Percent x Whole






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






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






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






29. To solve a proportion - cross multiply






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






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






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






36. 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






37. 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






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






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






40. Subtract the smallest from the largest and add 1






41. Multiply the exponents






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






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






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






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






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. 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






48. 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






49. 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






50. 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