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






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






3. 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






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






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






6. 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






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






8. 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






9. Factor out the perfect squares






10. 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






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






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






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






14. Part = Percent x Whole






15. 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






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






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






18. 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






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






20. Probability= Favorable Outcomes/Total Possible Outcomes






21. 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






22. 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)






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






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






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






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






27. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






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






29. 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






30. 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






31. pr^2






32. 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






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






34. Subtract the smallest from the largest and add 1






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






36. 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






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






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






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






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






42. 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






43. 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






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






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






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






48. 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






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






50. 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