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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 whole # left over after division






2. pr^2






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






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






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






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






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






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






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






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






11. 2pr






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






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






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. 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






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






17. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






20. 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






21. 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






22. To solve a proportion - cross multiply






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






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






25. 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






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






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






28. 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






29. Subtract the smallest from the largest and add 1






30. 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






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






32. 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






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






34. 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






35. 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






36. Multiply the exponents






37. 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






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






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






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






41. 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)






42. 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






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






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






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






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






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






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






49. Factor out the perfect squares






50. 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)