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






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






3. Add the exponents and keep the same base






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






5. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






6. Combine like terms






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






8. 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






9. 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)






10. 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






11. 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






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






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






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






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






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






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






19. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






20. Multiply the exponents






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






23. Domain: all possible values of x for a function range: all possible outputs of a function






24. 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






25. 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.






26. 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






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






28. 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






29. 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






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






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






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






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






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






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






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






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






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






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






40. 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






41. 2pr






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






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






44. 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






45. 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






46. 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






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






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






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






50. Probability= Favorable Outcomes/Total Possible Outcomes