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

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

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

**5. 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**

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

**7. Combine like terms**

**8. Part = Percent x Whole**

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

**10. To divide fractions - invert the second one and multiply**

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

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

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

**14. 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)**

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

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

**17. 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**

**18. 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**

**19. 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**

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

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

**22. 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**

**23. 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.**

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

**26. 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**

**27. 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**

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

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

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

**31. 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**

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

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

**34. 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**

**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. you can add/subtract when the part under the radical is the same**

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

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

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

**40. 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**

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

**42. Multiply the exponents**

**43. 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**

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

**45. 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**

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

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

**48. 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**

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

**50. 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**