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. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






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






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






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






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






7. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






8. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






9. 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






10. 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






11. 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






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






13. 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






14. 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






15. 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






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






17. 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






18. 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






19. 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






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






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






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






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






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






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






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






27. Add the exponents and keep the same base






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






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






30. 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)






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






32. Probability= Favorable Outcomes/Total Possible Outcomes






33. 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






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






35. Multiply the exponents






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






37. 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






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






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






40. 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






41. 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






42. 2pr






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






44. 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






45. 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)






46. 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






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. 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






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