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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. 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






2. To solve a proportion - cross multiply






3. 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






4. 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






5. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






7. The whole # left over after division






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






9. 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






10. Part = Percent x Whole






11. Subtract the smallest from the largest and add 1






12. Add the exponents and keep the same base






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






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






15. 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






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






17. 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






18. 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.






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






20. 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






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






22. Volume of a Cylinder = pr^2h






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






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






25. 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






26. 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






27. 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






28. 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






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






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






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






33. 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






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






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






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






37. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






40. 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






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






42. 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






43. pr^2






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






45. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






46. 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






47. 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






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






49. 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






50. 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)