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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 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






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






3. 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






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






5. Part = Percent x Whole






6. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






7. 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






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






9. Probability= Favorable Outcomes/Total Possible Outcomes






10. 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






11. 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






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






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






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






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






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






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






18. 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






19. Multiply the exponents






20. 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






21. 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)






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






23. Factor out the perfect squares






24. 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






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






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






27. 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






28. Add the exponents and keep the same base






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






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






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






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






33. pr^2






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






35. 2pr






36. Subtract the smallest from the largest and add 1






37. 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.






38. To solve a proportion - cross multiply






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






40. Combine like terms






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






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






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






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






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






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






47. 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






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






49. 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






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