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






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






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






4. 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






5. 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






6. Factor out the perfect squares






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






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






9. 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






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






11. 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






12. Volume of a Cylinder = pr^2h






13. To solve a proportion - cross multiply






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






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






16. 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)






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






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






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






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






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






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






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






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






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






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






27. 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






28. Probability= Favorable Outcomes/Total Possible Outcomes






29. Add the exponents and keep the same base






30. 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






31. 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






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






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






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






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






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






37. 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






38. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






39. 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






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






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






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






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






44. 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






45. 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






46. 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






47. 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)






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






49. Combine like terms






50. 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