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






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






3. Add the exponents and keep the same base






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






5. 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)






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






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






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. 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.






10. Subtract the smallest from the largest and add 1






11. pr^2






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






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






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






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






16. 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






17. 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






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






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






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






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






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






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






24. 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






25. 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






26. 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






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






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






29. 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






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






31. The whole # left over after division






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






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






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






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






36. Part = Percent x Whole






37. 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






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






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






40. Factor out the perfect squares






41. 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






42. 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






43. 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






44. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






47. 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






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






49. 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






50. 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)