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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. Add the exponents and keep the same base






2. 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






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






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






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






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






7. 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






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






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






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






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






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






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






14. Factor out the perfect squares






15. pr^2






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






17. 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






18. 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






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






20. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






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






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






24. 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






25. Multiply the exponents






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






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






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






29. 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.






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






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






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






33. 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






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






35. 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






36. 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






37. 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






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






39. 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






40. 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






41. 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)






42. 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






43. 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






44. To solve a proportion - cross multiply






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






46. 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






47. Combine like terms






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






49. 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






50. 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)