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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. 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






2. 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






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






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






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






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






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






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






9. 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






10. 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)






11. Part = Percent x Whole






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






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






14. 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.






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






16. 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






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






18. 2pr






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






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






21. 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






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






23. To solve a proportion - cross multiply






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






25. 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






26. Volume of a Cylinder = pr^2h






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






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






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






31. 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






32. 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






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






34. 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






35. Factor out the perfect squares






36. 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






37. 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






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






39. 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






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






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






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






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






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






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






46. 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






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






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






49. 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)






50. Combine like terms