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






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






4. 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






5. Probability= Favorable Outcomes/Total Possible Outcomes






6. 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






7. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






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






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






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






11. 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






12. 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






13. Subtract the smallest from the largest and add 1






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






15. 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






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






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






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






19. 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






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






21. 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






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






23. 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






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






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






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






27. 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






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






29. 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






30. 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)






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






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






33. Add the exponents and keep the same base






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






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






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






37. Combine like terms






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






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






40. 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.






41. 2pr






42. Part = Percent x Whole






43. 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






44. The whole # left over after division






45. Multiply the exponents






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






47. 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






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






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






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