Test your basic knowledge |

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






2. 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






3. 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






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






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






6. 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






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






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






9. Part = Percent x Whole






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






11. Surface Area = 2lw + 2wh + 2lh






12. 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






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






14. For all right triangles: a^2+b^2=c^2






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






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






17. 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






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






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






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






21. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






22. 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






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






24. 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






25. 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






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






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






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






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






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






31. 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






32. 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)






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






34. 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






35. pr^2






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






38. The whole # left over after division






39. 2pr






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






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






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






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






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






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






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






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






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






49. 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






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