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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. The whole # left over after division






2. 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)






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






4. 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






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






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






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






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






10. 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






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






12. 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






13. 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






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






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






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






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






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






19. 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






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






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






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






23. 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






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






25. pr^2






26. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






31. 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






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






33. 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






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






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






36. Factor out the perfect squares






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






38. 2pr






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






40. Multiply the exponents






41. 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






42. 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






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. 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






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






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






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






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






49. Combine like terms






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