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






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






3. pr^2






4. 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






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






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






7. Part = Percent x Whole






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






9. Combine like terms






10. Add the exponents and keep the same base






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






12. Factor out the perfect squares






13. Volume of a Cylinder = pr^2h






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






15. 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)






16. 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






17. 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






18. 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






19. 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






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






21. 2pr






22. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






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






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






25. Subtract the smallest from the largest and add 1






26. 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






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






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






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






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






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






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






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






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






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






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






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






39. 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)






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






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






43. Probability= Favorable Outcomes/Total Possible Outcomes






44. 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






45. 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






46. 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






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






48. 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






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






50. 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