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






2. 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






3. 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






4. 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






5. 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






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






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






8. 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






9. Add the exponents and keep the same base






10. 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)






11. 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






12. Subtract the smallest from the largest and add 1






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






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






15. 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






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






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






18. Combine equations in such a way that one of the variables cancel out






19. 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






20. Multiply the exponents






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






22. 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






23. The whole # left over after division






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






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






26. 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






27. 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






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






29. 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






30. 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.






31. 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






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






33. 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






34. 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






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






36. Combine like terms






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






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






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






40. 2pr






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






42. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






43. Sum=(Average) x (Number of Terms)






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






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






46. 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






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






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






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






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