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






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






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






4. 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






5. Probability= Favorable Outcomes/Total Possible Outcomes






6. 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






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






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






9. 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






10. 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






11. 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






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






13. 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)






14. Multiply the exponents






15. 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






16. 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






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






18. 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.






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






20. 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






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






22. Add the exponents and keep the same base






23. Combine like terms






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






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






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






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






28. 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






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






30. 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






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






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






33. 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






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






35. 2pr






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






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






38. 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






39. 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






40. Volume of a Cylinder = pr^2h






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






42. 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






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






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






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






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






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






48. 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






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






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