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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. 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






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






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






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






5. 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






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






7. 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)






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






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






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






11. 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






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






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






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






15. 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






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






17. To solve a proportion - cross multiply






18. Part = Percent x Whole






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






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






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






22. The whole # left over after division






23. 2pr






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






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






26. 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






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






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






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






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






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






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






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






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. 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






36. 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






37. Factor out the perfect squares






38. 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






39. Combine like terms






40. Add the exponents and keep the same base






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






42. 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)






43. 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






44. Subtract the smallest from the largest and add 1






45. 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






46. 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






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






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






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






50. 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