## 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. 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)**

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

**3. 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)**

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

**5. 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**

**6. 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**

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

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

**9. 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**

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

**11. 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**

**12. 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**

**13. 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**

**14. Volume of a Cylinder = pr^2h**

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

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

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

**18. pr^2**

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

**20. 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**

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

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

**23. 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**

**24. 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**

**25. 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**

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

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

**28. 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**

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

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

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

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

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

**34. 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**

**35. 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**

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

**37. To solve a proportion - cross multiply**

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

**39. Factor out the perfect squares**

**40. 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.**

**41. Add the exponents and keep the same base**

**42. 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**

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

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

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

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

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

**48. 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**

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

**50. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them**