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. 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






2. 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)






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






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






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






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






7. To solve a proportion - cross multiply






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






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






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






11. The whole # left over after division






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. 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. 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






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






17. 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






18. 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






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






20. 2pr






21. 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






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






23. 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






24. 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






25. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






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






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






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






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






30. pr^2






31. Combine like terms






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






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






34. Factor out the perfect squares






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






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. 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






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






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






40. Subtract the smallest from the largest and add 1






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






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






43. 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






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






45. 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






46. 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






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






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






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






50. 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