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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. 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






2. 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






3. 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






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






5. 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






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






7. 2pr






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






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






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






11. Factor out the perfect squares






12. Volume of a Cylinder = pr^2h






13. Part = Percent x Whole






14. 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






15. 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






16. Combine like terms






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






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






19. 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






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






21. 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






22. 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






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






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






25. pr^2






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






27. To solve a proportion - cross multiply






28. 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






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






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






31. Add the exponents and keep the same base






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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. 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






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






37. 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)






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






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






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






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






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. The whole # left over after division






44. 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






45. 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






46. 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






47. 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






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






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