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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. 2pr






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






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






4. Multiply the exponents






5. Subtract the smallest from the largest and add 1






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






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






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






9. 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






10. 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






11. 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






12. Part = Percent x Whole






13. To solve a proportion - cross multiply






14. 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)






15. Combine like terms






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






17. 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






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






19. 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






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






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






22. pr^2






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






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






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






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






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






28. 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






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






30. 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)






31. 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






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






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






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






35. 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






36. 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






37. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






38. 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






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






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






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






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






43. 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






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






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






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






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






48. 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






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






50. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations