## 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. 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**

**2. 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**

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

**4. 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**

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

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

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

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

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

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

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

**12. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is**

**13. 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**

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

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

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

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

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

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

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

**21. 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**

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

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

**24. 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)**

**25. Combine like terms**

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

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

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

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

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

**31. 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**

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

**33. 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**

**34. 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**

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

**36. 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**

**37. 2pr**

**38. 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**

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

**40. 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**

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

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

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

**44. 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**

**45. Multiply the exponents**

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

**47. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50**

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

**49. 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**

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