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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. 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






2. Part = Percent x Whole






3. 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






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






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






6. 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






7. 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






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






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






10. Multiply the exponents






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






12. 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






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






14. The whole # left over after division






15. 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






16. 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)






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






18. Subtract the smallest from the largest and add 1






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






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






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






22. 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






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






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






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






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






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






28. Combine like terms






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






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






31. Volume of a Cylinder = pr^2h






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






33. 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






34. 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






35. 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






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






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






38. 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






39. pr^2






40. 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






41. 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






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






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






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






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






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






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






48. 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






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






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)