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






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






3. 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






4. 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






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






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






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






8. 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)






9. 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






10. 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






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






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






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






14. 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






15. Subtract the smallest from the largest and add 1






16. 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






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






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






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






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






21. Add the exponents and keep the same base






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






23. 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






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






25. 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






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






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






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






29. The whole # left over after division






30. 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






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






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






33. 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






34. 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






35. 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






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






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






38. 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






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






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






41. 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






42. Probability= Favorable Outcomes/Total Possible Outcomes






43. 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






44. Factor out the perfect squares






45. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






46. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






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






48. To solve a proportion - cross multiply






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






50. 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