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






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






3. 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)






4. 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






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






6. Multiply the exponents






7. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






11. 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)






12. 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






13. 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






14. 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






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






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






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






18. 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






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






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






21. 2pr






22. 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






23. 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






24. The whole # left over after division






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. 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






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






28. 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






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






30. 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






31. 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






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






33. Add the exponents and keep the same base






34. 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






35. Combine like terms






36. 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






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






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






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






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






41. 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






42. 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






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






44. 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






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






46. Subtract the smallest from the largest and add 1






47. 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.






48. 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






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






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