Test your basic knowledge |

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






2. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






3. 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






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






5. 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






6. 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






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






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






9. 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.






10. Probability= Favorable Outcomes/Total Possible Outcomes






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






12. 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)






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






14. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






16. 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






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






18. 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






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






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






21. 2pr






22. Factor out the perfect squares






23. 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






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






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






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






27. Subtract the smallest from the largest and add 1






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






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






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






32. 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






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






34. 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






35. 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






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






37. 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






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






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






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






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






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






43. 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)






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






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






46. 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






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






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






49. pr^2






50. The whole # left over after division