## 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. 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**

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

**3. Combine like terms**

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

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

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

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

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

**9. 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**

**10. 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.**

**11. 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**

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

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

**14. 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**

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

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

**17. 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**

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

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

**20. 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**

**21. 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**

**22. 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**

**23. 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**

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

**25. 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)**

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

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

**29. 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**

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

**31. Multiply the exponents**

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

**33. 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**

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

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

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

**37. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b**

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

**39. 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**

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

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

**42. 2pr**

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

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

**45. pr^2**

**46. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3**

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

**48. 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**

**49. 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**

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