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






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






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






4. 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






5. Volume of a Cylinder = pr^2h






6. 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






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






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






9. 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)






10. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






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






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






13. 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






14. 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






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






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






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






18. 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






19. 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






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






21. 2pr






22. 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






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






24. 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






25. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






26. pr^2






27. 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






28. 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






29. Probability= Favorable Outcomes/Total Possible Outcomes






30. Subtract the smallest from the largest and add 1






31. Add the exponents and keep the same base






32. 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






33. 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






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






35. 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






36. 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






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






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






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






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






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






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






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






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






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






46. Factor out the perfect squares






47. Combine like terms






48. 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






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






50. 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