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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. Factor out the perfect squares






2. 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.






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






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






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






6. 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






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






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






9. 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






10. Part = Percent x Whole






11. 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)






12. Subtract the smallest from the largest and add 1






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






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






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






16. 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






17. The whole # left over after division






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






19. 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






20. Volume of a Cylinder = pr^2h






21. 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






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






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






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






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






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






27. 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






28. 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






29. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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. 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






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






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






34. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






38. 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






39. 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






40. 2pr






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






42. 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






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






44. 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






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






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






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






48. 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






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






50. To solve a proportion - cross multiply