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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 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






2. 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






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






4. 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






5. 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






6. Add the exponents and keep the same base






7. 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






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






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






10. 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






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






12. 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






13. 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)






14. 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






15. pr^2






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






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






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






19. 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)






20. 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






21. 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






22. Combine like terms






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






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






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






26. 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






27. 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






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






29. 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






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






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






32. 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






33. 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






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






35. The whole # left over after division






36. 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






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






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






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






40. 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






41. 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






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






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






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






45. Volume of a Cylinder = pr^2h






46. 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.






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






48. Subtract the smallest from the largest and add 1






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






50. 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