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. 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






2. Combine like terms






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






4. Part = Percent x Whole






5. 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






6. 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.






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






8. 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






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






10. 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






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. 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






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






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






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






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






17. 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






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






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






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






21. 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






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






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






24. The whole # left over after division






25. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






29. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






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






31. 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






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






33. To solve a proportion - cross multiply






34. 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






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






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






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






38. 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






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






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






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






42. pr^2






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






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






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






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






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






48. Volume of a Cylinder = pr^2h






49. 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






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