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






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






3. Factor out the perfect squares






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






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






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






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






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






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






10. 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






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






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






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






14. 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






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






16. 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






17. 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






18. Multiply the exponents






19. Probability= Favorable Outcomes/Total Possible Outcomes






20. The whole # left over after division






21. 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






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






23. To solve a proportion - cross multiply






24. 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






25. pr^2






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






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






28. 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






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






30. 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






31. Part = Percent x Whole






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






33. 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)






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






35. 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)






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






37. 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






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






39. 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






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






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






42. 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






43. 2pr






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






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






46. 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






47. 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






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






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






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