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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. 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






2. 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






3. 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






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






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






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






7. Factor out the perfect squares






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






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






10. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






13. 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






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






16. The whole # left over after division






17. Subtract the smallest from the largest and add 1






18. 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






19. 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






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






21. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






22. 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






23. 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






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






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






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






27. 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






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






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






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






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






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






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






34. 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)






35. 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






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






37. Add the exponents and keep the same base






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






39. Volume of a Cylinder = pr^2h






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






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






42. 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






43. To solve a proportion - cross multiply






44. 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






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






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






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






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






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






50. pr^2