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






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






3. 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)






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. 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






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






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






8. 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






9. To solve a proportion - cross multiply






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






12. 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






13. 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






14. 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






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






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






17. Multiply the exponents






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






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






20. 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)






21. Part = Percent x Whole






22. 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






23. 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






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






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






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






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






28. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






29. 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






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






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






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






33. Add the exponents and keep the same base






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






35. 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






36. 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






37. 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






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






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. 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






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






42. 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






43. The whole # left over after division






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






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






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






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






48. 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






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






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