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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. 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






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






3. Multiply the exponents






4. 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






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






6. 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






7. Part = Percent x Whole






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






9. 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






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






11. 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






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






13. 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






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






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






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






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






18. Add the exponents and keep the same base






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






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






22. 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






23. Combine like terms






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






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






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






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






28. 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






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






30. pr^2






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






32. 2pr






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






36. 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






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






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






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






40. 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






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






42. Subtract the smallest from the largest and add 1






43. 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






44. 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






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






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






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






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






49. 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






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