## Test your basic knowledge |

# SAT Math: Concepts And Tricks

**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. 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**

**2. 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**

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

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

**5. Subtract the smallest from the largest and add 1**

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

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

**8. To add or subtract fraction - first find a common denominator - then add or subtract the numerators**

**9. 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)**

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

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

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

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

**14. 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**

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

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

**17. 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**

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

**19. 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)**

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

**21. 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**

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

**23. The whole # left over after division**

**24. 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.**

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

**26. Sum=(Average) x (Number of Terms)**

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

**28. Probability= Favorable Outcomes/Total Possible Outcomes**

**29. pr^2**

**30. 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**

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

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

**33. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.**

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

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

**36. 2pr**

**37. 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**

**38. 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**

**39. Part = Percent x Whole**

**40. 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**

**41. 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**

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

**43. Change in y/ change in x rise/run**

**44. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.**

**45. (average of the x coordinates - average of the y coordinates)**

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

**47. 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**

**48. 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**

**49. 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**

**50. Surface Area = 2lw + 2wh + 2lh**