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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 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






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






3. 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






4. 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






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






6. 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






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






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






9. 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






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






11. 2pr






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






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






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






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






16. 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






17. 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.






18. 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






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






20. Multiply the exponents






21. 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






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






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






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






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






26. Subtract the smallest from the largest and add 1






27. Combine like terms






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






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






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






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






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






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 whole # left over after division






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






36. 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






37. 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)






38. 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






39. 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






40. 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






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






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






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






44. Volume of a Cylinder = pr^2h






45. Factor out the perfect squares






46. 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






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






48. 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






49. 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






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