Accuplacer Math Review

**This packet is meant as a rough overview of topics that are included in the Accuplacer. Cleary there is no way to fit 12 years of mathematics into a 5 page review. If there is any topic you would like to brush up on, please see Math Coach Erick or College Readiness Specialist Shelli.***

You CANNOT use a calculator on the Accuplacer

Decimals

Adding

Line up the decimal pts

Subtracting

Line up the decimal pts

Add zeros is necessary on top number

Multiplying

Do NOT line up dec pts

ADD # of digits to right of dec pt for top and bottom numbers, count over from right to left in answer

Dividing

Cannot have dec pt in divisor number outside. Move over dec pt in divisor to make a whole #, move same # of places on dividend. Bring dec pt straight up and divide as normal.

42.3 + 5.34

42.30

+ 5.34

47.64

Subtract: 5.1 - 4.68

5.10 (notice the added 0) - 4.68

.42

Multiply: .15 x.5

.15 (2 digits to right of dec pt)

x.5 +(1 digit to right of dec pt)

.075 ( 3 places to count over)

Divide: .0713 .23

=

= 23

Answer = .31

Your turn:

1. 6.32 + 4.9+ 0.23 =_____________________

2. 34.1 5.23 = ________________________

3. .25 x .11 = ____________________________

4. 42 .07 =__________________________

Fractions- part over whole

Numerator = Part

Denominator Whole

Simplify or Reducing

Divide numerator and denom by the same number

Improper to Mixed

-Divide numerator by denom

-Remainder becomes numer.

-Keep same denom.

Mixed to Improper

-Multiply denom by whole number, add numerator -Keep same denom

7 out of 10 = 7

10

Simplify

6 3 = 2

9 3 3

=

=

Your turn:

5. Write $.13 as a fraction =____________________ 6. Reduce = _______________________________

7. Change to a mixed number_______________ 8. Change to an improper fraction =___________

Adding Fractions

-Write equivalent fractions with like denominators

-Add the numerator, keep

the same denominators

-reduce

Subtracting Fractions

-Write equivalent fractions with like denominators

-Subtract the numerator, keep the same denominators

-reduce

Multiplying Fractions

-Write all fractions as improper fractions

-multiply numerators

-multiply denominators

-reduce

Dividing Fractions

-Write all fractions as improper fractions

-Invert or flip the fraction on the right

-multiply numerators

-multiply denominators

-reduce

1/4 + 5/16 =

1_ x4 = 4_

4 x4 = 16

+ 5_ x1= + 5_

16 x1= 16

Ans = 9/16

5/16 - 1/4 =

5 x1= _ 5_

16 x1= 16

-1 x4 = - 4_

4 x4 = 16

Ans = 1/16

3 x 4 =

13 x 9 = 117

4 2 8

Reduce

3 4 =

13 x 2 = 26

4 9 36

Reduce

Your turn:

9. =____________________ 10. = ________________________

11. = _______________ 12. =__________________________

Percents - means out of 100

Decimal to percent

-Move the dec pt 2 place to the right

Percent to decimal

-Move the dec pt 2 places to the left

Percent to fraction

-place the percent over 100, drop the % sign, simplify

.75 becomes 75%

.08 becomes 8%

35% becomes .35

7% becomes .07

35% = =

Change each percent to a decimal and a fraction, simplify

13. 82% dec=________fraction____________ 14. 36% dec=________fraction____________

15. 9 % dec=________fraction___________

16. 1% dec=________fraction____________

Remember: of means multiply

is means equal

Equation Method

% x Whole = Part

-Set up problem in equation

-solve

What percent of 40 is 8?

Proportion Method

Set up the equation, solve.

What percent of 40 is 8?

?% x 40 = 8

Divide both sides by 8

Ans = 20%

Cross Multiply: 8 x 100 = 40 x ?% Divide by 40:

Ans = 20%

Your turn:

17. 6% of 20 =____________________ 18. 20 is 40% of what number= ________________________

19. What percent of 160 is 128 = ___________ 20. What percent of 128 is 160=__________________________

Ratios a comparison of two quantities-- can be written 3 ways. First terms mentioned goes on top.

Write 8 men to 10 women as a ratio

8/10 = 8 : 10 = 8 to 10 reduce 4/5 = 4 : 5 = 4 to 5

Your turn:

21. Ratio of hours in a day to hours in a week =__________ 22. Ratio of inches in foot to inches in a yard= ________

23. Ratio of 7 red markers to 28 blue markers= ___________ 24. Ratio of 8 desks to 8 chairs=_________________

Proportion- an equation stating two ratios are equal- cross multiply and solve resulting equation

Cross Multiply: 8 * 100 = 40 * X

Divide both sides by 40: 800 = 40x

20 = x

Joanie bought 6 feet of speaker wire for $21.66. How much would 10 feet cost?

**both ratios must be the same comparisons**

(Wire ) = _6_= _10 or (Cost) = 21.66 = _x_

(Cost) 21.66 x (Wire ) 6 10

Cross multiply: 6 * x = 21.66 * 10

Divide by 6: 6x = 216.6

x = 31.6

Your turn:

25. x=__________ 26. If 4 candy bars cost $1.22, how much would 32 candy bars cost?_____ __

27. Out of every 5 students surveyed, 2 play sports. At that rate, how many students play sports out of 800 ?________

28. Randy can mow a 1000 square foot lawn in 2 hours. How long would it take him to mow a 3500 sq ft lawn?____

Exponents tell how many times to multiply the base

6 means 6 x 6 x 6 x 6

6 = 6x6x6x6x6x6x6 = 279,936

4 = 4x4x4= 64

-Any base with exponent of 1, equals the base

6 = 6 20 = 20 36 = 36

Multiplication with Exponents

-if they have the same base, add the exponents and keep the same base

5 x 5 = 5 3 x 3 = 3

Power raised to a power

-multiply the exponents together and keep the same base

Division with Exponents

-if they have the same base, subtract the exponents and keep the same base

-Any base with exponent of 0, equals 1

6= 1 20 = 1 36 = 1

(5) = 5 (3) = 3

Your turn:

29. (7) =__________

30. 4 x 4 = ____________

31. = ___________

32. (5) =_________________

Square Roots- what number times itself ..

-This is asking, What is the square root of 64?

-It means, What number times itself is 64

-Answer = 8

Simplifying Square Roots

Try to find factors of the number under the square root sign(radical) that are perfect squares(have square roots)

Key to Simplifying: x

= 5 x = 5

Your turn:

33. =__________

34. = ____________

35. Simplify = ___________

36. Simplify =_________________

Order of Operations- Please Excuse My Dear Aunt Sally

Parentheses you get do parentheses first

Exponents You get to eliminate the exponents next

Multiply & Divide Must go from left to right next

Add & Subtract- Last. Must go from left to right

Evaluate: 3(1+4)

= 3(5)

= 15

Evaluate: 3 + 5

=9 + 5

= 14

Evaluate: 3 x 6 9

= 18 9

= 2

Evaluate: 4 + (12 + 3) 5

=4 + 15 5

=16 + 15 5

=16 + 3

= 19

Your turn:

37. =__________

38. =____________

39. 3 x 6 + (12 x 2 6) = ___________

40. 10 + 3 -3 +3 =_________________

Evaluating Expressions wit