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






2. 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






3. Factor out the perfect squares






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






5. 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






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






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






8. 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)






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






10. Add the exponents and keep the same base






11. 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






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






13. To solve a proportion - cross multiply






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






15. pr^2






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






17. Subtract the smallest from the largest and add 1






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






19. 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






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






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






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






24. 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.






25. 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






26. 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






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






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






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






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






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






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






33. 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






34. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






35. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






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. 2pr






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






39. 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






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






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






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






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






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






45. 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)






46. Part = Percent x Whole






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






48. Combine like terms






49. 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






50. 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