Review Sheet for Math Midterm Exam by liZzkS2

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									                                Review Sheet for Math Midterm Exam


Review Sheet for Math Midterm Exam

Multiple Choice
Identify the choice that best completes the statement or answers the question.

_____ 1. Which number is divisible by 2 but not by 4?
         100, 125, 150, 200
               a. 150              b. 200                                c. 125                        d. 100

_____ 2. Which number is divisible by 3 and by 10?
        606, 110, 260, 420
              a. 606               b. 110                                c. 260                        d. 420

_____ 3. Write an algebraic equation for n multiplied by 5.
                                                                              n
               a. n - 5                    b. n + 5                      c.                            d. 5n
                                                                              5

_____ 4. Evaluate the expression by replacing a with 13.
         a – 10
              a. 23                 b. 3                                 c. 130                        d. 2

_____ 5. If n represents any term number, write a relation for the term.


  Term Number               1               2                 3             4               5              6
     Term                   7              14                21            28              35             42

               a. 7n                       b. 2n + 7                     c. 2n                         d. n+7

_____ 6. Write a relation for the perimeter of the rectangle with length (n + 4) and width n cm.




                                                                                   n




                                                     n+4

               a. (4n + 4) cm              b. (2n + 4) cm                c. n(n + 4) cm                d. (4n + 8) cm



                                                         1
                               The actual test will be very similar to this practice test.
                 Please see the attached pages for study notes to help you do each type of question.
                                Review Sheet for Math Midterm Exam

_____ 7. The are n players on a sports team. Each player gets 3 pairs of sox and 4 pairs are kept
         in reserve. Write a relation for the number of pairs of sox needed.
              a. 4n + 3              b. 3n + 4              c. 7n                 d. 12n

_____ 8. Use algebra. Write a relation for the Input/Output table.

                Input x                   1               2               3              4               5
                Output                   39              38              37             36              35
               a. x – 40                   b. x + 35                     c. 40 – x                     d. 39 – x

_____ 9. Write an equation for “I subtract 13 from a number. The answer is 24.”
                 n
             a.    = 24             b. n + 13 = 24       c. n – 13 = 24         d. 13 – n = 24
                13

_____ 10. Write an equation for the situation.
          Patricia has p posters. She sold 7 and has 19 left.

               a. p = 19 – 7               b. p + 7 = 19                 c. p – 7 = 19                 d. p + 19 = 7

_____ 11. Let one white tile represent +1 and one black tile represent -1.
          Write the integer modeled by this set of tiles.

               ■□□■□□
               □■■□■

               a. +6                       b. +11                        c. +1                         d. -1

_____ 12. Let one white tile represent +1 and one black tile represent -1.
          What sum is modeled by 17 positive tiles and 19 negative tiles?

               a. -1                       b. +2                         c. -2                         d. +36

_____ 13. Add.
          (-5) + (+10)
              a. -15                       b. +15                        c. +5                         d. -5

_____ 14. David gets on an elevator at the 36th floor. The elevator goes down 26 floors then up
          17 floors. At what floor did it finally stop?

               a. -7                       b. 27                         c. 45                         d. 79

_____ 15. Copy and complete.
          (+9) - □ = -18

               a. -9                       b. -27                        c. 9                          d. +27

                                                         2
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                                Review Sheet for Math Midterm Exam



_____ 16. The graph shows the high and low temperatures in a week from Sunday to Saturday.

                                                        High and Low Tem peratures


                                                   20




                                 Degrees Celcius
                                                   15

                                                   10
                                                    5

                                                    0
                                                         Su   M     Tu       W   Th   F    Sa
                                                                         Days


          On which of the following days was the difference between the high and low
          temperature the least?

              a. Sunday                                  b. Monday                     c. Wednesday          d. Friday

_____ 17. A submarine at sea level dives 7m and then another 4 m.
          Write the final depth of the submarine as an integer.

              a. +11m                                    b. +12 m                      c. -11m               d. -12m

                  28
_____ 18. Write      as a decimal. Identify the decimal as terminating or repeating.
                  36

        a. 0.8; terminating                        b. 1.8; terminating           c. 1. 7 ; repeating   d. 0. 7 ; repeating

_____ 19. Subtract.                12.39 – 7.735

              a. -64.96                                  b. 6.496                      c. 4.655              d. 20.125

_____ 20. Calculate.               10.45 + 6.59 – 0.7

              a. 17.74                                   b. 16.97                      c. 16.34              d. 6.35

_____ 21. Add.                     0.9 + 0.89 + 0.789

              a. 0.887                                   b. 2.579                      c. 17.69              d. 7.89

_____ 22. Multiply.                2.4 x 60

              a. 84                                      b. 14.4                       c. 144                d. 1440



                                                                         3
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                                     Review Sheet for Math Midterm Exam



_____ 23. Divide.
          2.12 ÷ 0.4
             a. 5.3                             b. 0.053                      c. 0.53                       d. 53

_____ 24. Evaluate
          17.5 – 5 x 1.4
             a. 10.5                            b. 24.5                       c. 63                         d. 17.5

_____ 25. Write 59% as a decimal.
            a. 5.9                b. 0.059                                    c. 0.59                       d. 59

                     12
_____ 26. Write         as a percent.
                     50
                 a. 38%                         b. 24%                        c. 27%                        d. 42%

_____ 27. What fraction of the diagram is shaded?
                                                                                    3                             1
         /////                                                                   a.                           b.
         /////                                                                      8                            24
         /////                                                                       1                           1
                                                                                 c.                           d.
                                                                                    12                           8

_____ 28. What fraction of the diagram is shaded?
          Write the fraction as a percent.
                2                        6
            a.    ; 30%              b.     ; 6%
               10                       100

                       5                              2
                 c.       ; 25%                 d.       ; 20%
                       20                            100



_____ 29. In your last 20 basketball games, you attempted 72 free throws and made 18 of them.
          Express your success in making free throws as a percent.
             a. 25%                  b. 26%               c. 28%               d. 24%

_____ 30. Calculate 50% of 70.
             a. 18                              b. 35                         c. 4                          d. 9

_____ 31. Jason wants to buy a bicycle that costs $395.00. His parents ask Jason to raise 40%
          of the money. How much does Jason have to raise?
              a. $154.00           b. $158.00             c. $118.50             d. $40.00

_____ 32. A circle has a radius of 36.9 cm. What is its diameter?
             a. 18.45 cm             b. 12.3 cm             c. 110.7 cm                                     d. 73.8 cm

                                                              4
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_____ 33. Which is not a relationship between the radius r and the diameter d of a circle?
            a. d ÷ 2 = r            b. d = 2r              c. r + r = d           d. 2d = r

_____ 34. What is the least number in the set?
             11 9      1
          4,   , ,2
              6 4      6

                     1                          9                                                           11
              a. 2                         b.                            c. 4                          d.
                     6                          4                                                            6

_____ 35. Find the next two terms in the pattern.
          0.277, 0.388, 0.499, 0.61…

              a. 0.721, 0.943              b. 0.721, 0.832               c. 0.832, 1.054               d. 0.832, 0.943

_____ 36. Determine the cost of 3.54 kg of apples at $1.05/kg.
            a. $4.59               b. $3.72               c. $0.46                                     d. $37.17

_____ 37. A circle has a diameter of 54.2 m. What is the radius?
             a. 162.6 m             b. 27.1 m              c. 108.4 m                                  d. 18.1 m

_____ 38. Four identical circles of the largest possible size are drawn on a square sheet of
          paper. The side length of the paper is 6.4 cm. What is the radius of each circle?
             a. 1.6 cm               b. 6.4 cm               c. 0.8 cm             d. 3.2 cm

_____ 39. Estimate the circumference of this circle.




              a. 21 m                      b. 42 m                       c. 17 m                       d. 84 m

_____ 40. Estimate the circumference of this circle.




              a. 81 cm                     b. 547 cm                     c. 30 cm                      d. 41 cm




                                                         5
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                                Review Sheet for Math Midterm Exam



_____ 41. The circumference of a circle is 27 cm.
          Calculate the radius. Round your answer to one decimal place.

               a. 5.9 cm                   b. 4.3 cm                     c. 13.5 cm                    d. 8.6 cm

_____ 42. Find the diameter of a circle with a circumference of 35.1 cm.
          Round your answer to one decimal place.

               a. 5.6 cm                   b. 11.2 cm                    c. 22.3 cm                    d. 17.6 cm

_____ 43. Find the area of this parallelogram.




               a. 30 m 2                   b. 50 m 2                     c. 25 m 2                     d. 100 m 2

_____ 44. Find the area of the parallelogram with base 45 cm and height 7.4 cm.

               a. 27.38 cm 2               b. 333 cm 2                   c. 202.5 cm 2                 d. 52.4 cm 2

_____ 45. Find the area of this triangle.




               a. 80 m 2                   b. 18 m 2                     c. 40 m 2                     d. 160 m 2




                                                         6
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                               Review Sheet for Math Midterm Exam



_____ 46. Which triangle has an area of 6 square units?




                                                         Q
                     P




                         R                                        S



              a. Q                        b. R                          c. P                          d. S




_____ 47. Find the area of this circle. Round your answer to two decimal places.




              a. 2678.65 m 2              b. 91.73 m 2                  c. 669.66 m 2                 d. 45.87 m 2




                                                        7
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                                Review Sheet for Math Midterm Exam


The circle graph shows how a college student breaks down her study time in a typical week.

                                             Study Time per Week


                                               English
                                                                 French
                                                11%
                                                                  23%

                                            Math
                                            21%
                                                                     Art
                                                                    14%

                                                   History
                                                    31%




_____ 48. What fraction of the time is spent on English and Math?

                          1                              1                             3                          2
               a. about                    b. about                        c. about                    d. about
                          2                              3                             4                          3

_____ 49. Grade 7 students were surveyed on how many hours per day they spend on various
          activities. About how many hours per day are spent on school and homework?


                                              How Students Spend Their Time



                                                      Socializing
                                                        13%                 Sleeping
                                                                              33%
                                                      School
                                                       25%
                                                                           Homework
                                                                             8%
                                                         Watching
                                                           TV          Eating
                                                          13%           8%




               a. 7 h                      b. 10 h                         c. 9 h                      d. 8 h


_____ 50. Find the central angle of a sector that represents 90% in a circle graph.
          Round to the nearest degree if necessary.

               a. 342°                     b. 306°                         c. 32°                      d. 324°

                                                             8
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                          Review Sheet for Math Midterm Exam


Short Answer

51.




                              Divisible by 3           Divisible by 2

 Place the numbers in the Venn Diagram.

 27, 36, 14, 8, 21, 42, 20, 33

52. Write an algebraic expression for the sentence.
    Subtract 14 from a number, then multiply by 3.

                 x
53. Evaluate       + 9 by replacing x with 30.
                 6

54. The pattern is formed using 1 cm 2 tiles.




           Term 1                   Term 2                     Term 3

      a) What is the perimeter for each term?
      b) Write a relation for the perimeter of the nth term.


55. Write an equation for the sentence.
     Nine less than a number is 14.

56. Which equation has the solution x = 12

      A: x + 6 + 18
      B: 6x = 18
      C: 18 + x = 6




                                                   9
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                           Review Sheet for Math Midterm Exam

57. Let one white tile represent +1 and one black tile represent -1.
    Write the integer modeled by this set of tiles.

       ■               □
      ■ □ ■
          □

58. Let one white tile represent +1 and one black tile represent -1.
    Add.

        □                                                 ■    ■■                    ■
            □□□                                               ■ ■■               ■
        □□□                                    +           ■ ■                    ■■
          □ □                                             ■               ■

59. Add
    (-7) + (-4)

60. Copy and complete.

     (-3) +         = (+5)

61. Write the addition equation modeled by the number line.




62. Write the subtraction equation modeled by the number line.




63. Write 0.48 as a fraction in simplest form.

             7
64. Write      as a decimal.
             4

              5
65. Write 1     as a decimal.
              6

                                                   10
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     66. Use any method. Order the following numbers from least to greatest.

           8 5  3 27
            , ,2 ,
           3 2 5 10

     67. Multiply.
         3.6 x 4.4

     68. Evaluate.
         (14.4 – 2.5) x 4.2 – 2.16 ÷ 0.6

     69. A strip of cardboard measures 3 cm by 36 cm.
             a) What is the diameter of the largest circle you can cut from the strip?
             b) How many circles can you cut from the strip?

     70. A bicycle wheel has a radius of 36 cm.
         How far will the bicycle travel if the wheel makes 400 rotations?

     71. Calculate the area of the semicircle. Round your answer to the nearest
         square centimeter.




                                                 ●

                                              21.2 cm

Problems

     72. Write the least 3-digit number that is divisible by 3 and by 4.

     73. A number is divisible by 5 and by 6. List at least 5 factors of that number.

     74. The diagram consists of a square and a parallelogram. Find the area of the figure.




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75. The outer circle has a diameter of 10 cm. The two smaller circles are identical.
    What is the total area of the shaded regions?
    Round your answer to two decimal places. Show your work.




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                                           Notes and Study Helps


Some notes and special study helps are given to help with individual questions on the review
sheet. These correspond with the question numbers on the review sheet.

1, 2, 51. Divisibility Rules: A number is said to be divisible by another number if the second
number divides evenly into it and there is no remainder. For example 15 is divisible by 5 because
when you divide 5 into 15 the answer is a whole number (3) and there is no remainder.
Divisibility rules are rules that we can use to quickly check if a number can divide evenly into
another number without having to do the actual division.

The divisibility rules that students should know are as follows:

A whole number is divisible by:

2 if the number is even (ends in 0, 2, 4, 6 or 8).
3 if the sum of the digits is divisible by 3.
4 if the number represented by the last two digits is divisible by 4.
5 if the ones digit is 0 or 5.
6 if the number is divisible by both 2 and 3.
8 if the number represented by the last 3 digits is divisible by 8.
9 if the sum of the digits is divisible by 9
10 if the ones digit is 0.

(See Math Makes Sense 7, p. 6-13 for additional information and practice)

3, 4, 52, 53, 55, 56. A variable is a letter, such as n, that represents a number that can vary. An
algebraic expression is a mathematical expression containing a variable; for example, 6x – 4 is an
algebraic expression.

Some examples of algebraic expressions and their meanings are as follows. In each case, n
represents the number.

      Three more than a number: 3 + n or n + 3
      Seven times a number: 7n
      Eight less than a number: n – 8
                                   n
    A number divided by 20:
                                   20
When we replace a variable with a number in an algebraic expression, we evaluate the
expression. That is, we find the value of the expression for a particular value of the variable.

(See Math Makes Sense 7, p. 16-19 for additional information and practice)




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                                Review Sheet for Math Midterm Exam

5, 7. When we compare or relate a variable to an expression that contains the variable, we have a
relation. A relation can be used to describe a pattern and to solve problems. In a growing pattern
of numbers, a relation tells how each term of the pattern relates to the term number, rather than
how each term relates to the term that comes before it.

From a table of values, a relationship can be found. This relationship must be true for all terms in
the table.

 Term #           1                 2               3                 4                5                6
  Term            7                14              21                28               35               42

In the above table, if you look at Term 1, you might conclude that Term# + 6 = Term. This
works for Term #1 because 1+6 = 7 but it doesn’t work for Term #2 because 2 + 6 does not equal
14, so this is not the relationship.

You might also conclude that the relationship is Term# x 7 = Term. This works for Term#1,
because 1 x 7 = 7. When we check it with the other Term #’s we see that it also works. i.e.) 2 x7
= 14, 3 x 7 =21 … Therefore we can conclude that we have found the relationship between Term
# and Term for the whole table.

Once we know the relationship for the table, we can use it to find the value for any Term if give
the Term #, without having to calculate all the terms in between. For example, if the above table
were extended the value of the term for Term # 500 would be 500 x 7 = 3500.

(See Math Makes Sense 7, p. 20-24 for additional information and practice)


6. Perimeter is the distance around an object. The formula for the perimeter is:

                             Perimeter = length + width + length + width
                                                  or
                                Perimeter = (2 x length) + (2 x width)



                               x


                                                   x+3

In the rectangle above, Perimeter = x + (x+3) + x + (x+3)
                                  = 4x +6

(See Math Makes Sense 7, p. 20-24 for additional information and practice)



                                                        14
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                                 Review Sheet for Math Midterm Exam

8. When a relation is represented by a table with consecutive Input numbers, a pattern can be
observed in the Output numbers. When a relation is represented as a table of values, we can write
the relation using algebra. Make sure that the relation is true for all pairs of input/output
numbers.

(See Math Makes Sense 7, p. 25-28 for additional information and practice)

9, 10. An equation is a mathematical statement that two expressions are equal. An equation must
contain an “equal” sign. The following are examples of equations:

                     3n – 8 = 55                   x + 5 = 10                 k + 5 = 2k – 7

(See Math Makes Sense 7, p. 35-37 for additional information and practice)

11, 12, 57. The set of integers is as follows:

        I = {…, -4, -3, -2, -1, 0, +1, +2, +3, +4 …}

The numbers farther to the right are the larger numbers.

Colored tiles can be used to represent integers. A tile representing + 1 and a tile representing -1
form a zero pair. These tiles combine to model zero.

                ■■■■■
                □□□□□□

In the example above each white tile represents + 1 and each black tile represents
-1. Each of the five black tiles can be combined with a white tile to form a zero pair, which
equals zero. When this is done there is still one white tile left over, so the total value of all the
tiles combined is +1.

(See Math Makes Sense 7, p. 52-55 for additional information and practice)

13, 14, 58, 59, 60, 61. Colored tiles, as explained above can be used to add integers. Number
lines may also be used. An arrow to the right represents a positive integer. An arrow to the left
represents a negative integer.
The following number line shows the equation (+5) + (-8) = (-3)




                                                         15
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For additional information and practice see the following from Math Makes Sense 7

Adding Integers with Tiles: p.56-59
Adding Integers on a Number Line: p.60-64

Instead of using tiles or a number line, the following rules may be used to add integers:

   1. If the signs are the same, add the numbers and keep the same sign.
               Examples:      (+3) + (+5) = +8
                               (-7) + (-5) = -12

   2. If the signs of the integers are different, subtract the numbers and take the sign of the
      numerically larger number.
               Examples:       (-9) + (+4) = -5
                               (+8) + (-3) = +5

15. Colored tiles can be used to subtract integers. The concept of zero pairs may be used to
subtract integers.

To add integers, we combine groups of tiles. To subtract integers, we do the reverse, we remove
them from a group. Adding a zero pair to a set of tiles does not change its value. For example, (-
3) + 0 = -3. If we do not have enough positive or negative tiles to take away from a group, we
can add zero pairs until we have enough to take away. For example, for the question (+3) – (-2),
we can do the following.

We can represent + 3 as follows:

               □□□

If we want to subtract (-2) from this, we can’t because there are no black tiles to take away.
However, if we add two zero pairs to the model it will look different as shown below but the
value will still be the same.

               □□□□□
                  ■■

Now we have two black tiles, representing (-2) to take away. When we do, we are left with 5
white tiles as shown below, which has a value of (+5).

               □□□□□

Therefore (+3) – (-2) = (+5).



                                                        16
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                                Review Sheet for Math Midterm Exam

In addition to using tiles to subtract, we can also use a number line as explained later, or we can
use the following rule to subtract integers:

Instead of subtracting an integer, we can add its opposite.

       Example: (-6) – (+7) = (-6) + (-7) = (-13)

       Example: (-8) – (-5) = (-8) + (+5) = (-3)

(See Math Makes Sense 7, p. 66-70 for additional information and practice)

16, 17, 61, 62. A number line can be used to subtract an integer. Usually this is done on a
horizontal number line, but it can also be done on a vertical number line as in this question or as
can be found on a thermometer. To subtract a positive integer on a number line, you move to the
left. To subtract a negative integer is the same as adding its opposite, so you move to the right.
On a vertical number line, to subtract a positive integer, you move down. To subtract a negative
integer is the same as adding its opposite, so you move up.

(See Math Makes Sense 7, p. 71-75 for additional information and practice)

18, 64. To convert a fraction to a decimal, you can divide the numerator (top number in the
fraction) by the denominator (bottom number in the fraction). For example, ¾ as a decimal is
equal to 3 ÷ 4, which equals 0.75. Because this has a definite number of decimal places, it is said
to be a terminating decimal. To change 2/3 to a decimal, we calculate 2 ÷ 3 and get a result of
0.6666666666….When we do this we can never finish the calculation because some of the digits
repeat forever. This is called a repeating decimal and it is written as 0. 6 . Sometimes it is easier
to convert a fraction to a decimal if you first write it in simplest terms. For example 20/36 can be
rewritten as 5/9, which is easier to divide.

(See Math Makes Sense 7, p. 86-90 for additional information and practice)

For certain fractions another method can be used to convert it to a decimal if an equivalent
fraction can be found that has a denominator that is a power of 10 (10, 100, 1000,…) See sheet
Fractions to Decimals.

19, 20, 21. When adding decimals, remember to line up the decimal point. Also remember that
you can use the inverse operation (subtraction) to check addition. You can also use estimation to
check if your answer is reasonable.

When subtracting decimals, remember to line up the decimal points. Also remember that you can
use the inverse operation (addition) to check addition. You can also use estimation to check if
your answer is reasonable.

(See Math Makes Sense 7, p. 96- 99 for additional information and practice)



                                                        17
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                                Review Sheet for Math Midterm Exam

22, 67. When multiplying decimals the decimals don’t have to be lined up. Instead just line up
the numbers and multiply normally. When you have a final answer, you then need to decide
where to place the decimal point. To do this, you add the total number of decimal places in the
factors (the numbers being multiplied). There will be that many decimal places in the answer.
For example if you multiply a number that has one decimal place by a number that has three
decimal places, the product would have a total of four decimal places. Also remember that you
can use the inverse operation (division) to check multiplication. You can also use estimation to
check if your answer is reasonable.

(See assignment Canadian Mathematics 7, p. 94 for additional information and practice)


23. When dividing decimals, you need to start by making sure the divisor is a whole number. If it
isn’t you must multiply both the divisor and the dividend by a power of 10 to make it a whole
number. In the given question, 836.4 ÷3.4, you would begin by multiplying both the dividend
and the divisor by 10 to get a new question, 8364 ÷34. Then you would divide normally. When
you divide, place the decimal in the quotient (the answer) directly above the decimal in the
dividend.

If the divisor had two decimal places, you would have to multiply both the divisor and dividend
by 100. If it had three decimal places, you would have to multiply by 1000, etc.

Also remember that you can use the inverse operation (multiplication) to check division. You
can also use estimation to check if your answer is reasonable.

(See assignment Canadian Mathematics 7, p. 95 for additional information and practice)

24, 68. Order of Operations is the rules that are followed when simplifying or evaluating an
expression. A word that is helpful in remembering the order the steps are to be done in is
BEDMAS. In BEDMAS, each letter stands for an operation:
        B: Brackets
        E: Exponents
        D: Division or M: Multiplication
        A: Addition or S: Subtraction
Division and Multiplication are at the same spot in the order so are simply done left to right.
Addition and Subtraction are the same and are simply worked from left to right.
The order of operations for whole numbers can be applied to decimals.

(See Math Makes Sense 7, p. 108-109 for additional information and practice).




                                                        18
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                                Review Sheet for Math Midterm Exam

25. Any fraction or decimal can be written as a percent, and vice versa. Percent is another name
for hundredths. To change a percent to a decimal, begin by dropping the % sign and then divide
by 100; (move the decimal point 2 places to the left).

Example #1: Write 82% as a decimal.

                                      Begin by dropping the % sign.
                                                   82
                                          Then divide by 100.
                                             82÷100 = 0.82

Example #2: Write 40% as a decimal.

                                      Begin by dropping the % sign.
                                                   40
                                          Then divide by 100.
                                         40 ÷ 100 = 0.40 or 0.4

(See Math Sheet: Decimals to Percents and Math Makes Sense 7, p.111-113 for additional
information and practice).

26. Some fractions can easily be converted to percents by first finding equivalent fractions with a
denominator of 100 and then rewriting it as a percent.

Example: Write 15/20 as a percent.

                      Begin by writing an equivalent fraction for 15/20.
          15/20 = 75/100 (Both the numerator and denominator were multiplied by 5)

                                         Then rewrite as a percent.
                                              75/100 = 75%

If the fraction cannot be written as an equivalent fraction with a denominator of 100, then a
different method is used to convert the fraction to a percent. In such cases, you would divide the
numerator by the denominator to get a decimal. Then you would move the decimal two places to
the right and add a % sign.

Example: Write 3/16 as a percent.
                 Begin by dividing the numerator (3) by the denominator (16)
                                       3 ÷ 16 = 0.1875

             Then move the decimal point two places to the right and add a % sign.
                                          18.75%

(See Math Sheet: Fractions to Percents and Math Makes Sense 7, p.111-113 for additional
information and practice).

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27. To find out what fraction of a diagram is shaded, you would first count the number of shaded
parts. This would be the numerator or top number in your fraction. Then you would count the
total number of parts (shaded + unshaded). This would be your denominator in the fraction. This
assumes that all of the parts are an equal size.

/////////////////////// ///////////////////////
/////////////////////// ///////////////////////

In the diagram above 4 parts are shaded, so 4 is the numerator. Altogether there are 10 parts, so
10 is the denominator. The fraction that is shaded then is 4/10. Sometimes fractions can be
simplified into lower terms if there is a number that divides evenly into both the numerator and
denominator. In this case, both 4 and 10 can be divided by 2, to get 2 and 5 respectively.
Therefore, this fraction in lowest terms is 2/5.

28. To find out what fraction of the diagram is shaded, the above method can be used. To extend
this to show the fraction as a percent, the fraction would need to be converted to a percent as
explained in question 26.

(See Math Makes Sense 7, p.111-113 for additional information and practice).

29. To find your success in making free throws as a percent, you would first need to express it as
a fraction. The numerator would be your successful free throws. The denominator would be your
total attempts. Then the fraction would need to be converted to a percent as explained in question
26.

(See Math Makes Sense 7, p.111-113 for additional information and practice).

30, 31. To find a percent of a number, you can convert the percent to a decimal and then
multiply. To change a percent to a decimal, begin by dropping the % sign and then divide by
100; (move the decimal point 2 places to the left).

Example: Write 82% as a decimal.
                              Begin by dropping the % sign.
                                           82
                                  Then divide by 100.
                                     82÷100 = 0.82

For a question such as this you would do the following:

                                                  Calculate 35% of 50.

                                       35% = 0.35                   50 x 0.35 = 17.5

(See Math Sheet, Percents to Decimals and Math Makes Sense 7, p.114-116 for additional
information and practice).

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32, 33, 37. Radius is the distance from the center of a
circle to any point on the circle. Diameter is the distance
across a circle, measured through its center.
Circumference is the distance around a circle, also
known as the perimeter of a circle.

The diameter is twice as long as the radius.
                 d = 2r

The radius is half the length of the diameter.
                  r = d/2

The circumference is equal to 2 times π (pi) times the
radius or π times the diameter. To calculate use 3.14 in place of π.

C=2πr        or     C=πd

      To calculate the diameter if you are given the radius, multiply the radius by 2.
      To calculate the radius if you are given the diameter, divide the diameter by 2.
      To calculate the circumference if you are given the radius, multiply the radius by 2 and
       then by 3.14.
      To calculate the circumference if you are given the diameter, multiply the diameter by
       3.14
      To calculate the radius if you are given the circumference, divide the circumference by 2
       and then by 3.14.
      To calculate the diameter if you are given the circumference, divide the circumference by
       3.14.

(See Math Makes Sense 7, p.130-137 for additional information and practice).

34, 66. Before fractions and decimals can be put in order they must first be converted into similar
units. A few methods can be used to put numbers in order.

      Benchmarks: If a number line is drawn that includes benchmarks such as 1 , 1, 1 1 , 2 …
                                                                                 2      2
       then the numbers to be compared can be positioned on the number line. Then they can be
       put in order by simply reading from the lowest number on the left to the highest number
       on the right.
      Equivalent Fractions: Before fractions can be compared, they must have the same
       denominator. If all of the denominators are the same, then the numerators can be
       compared. The fraction with the lowest numerator is the least and the number with the
       highest numerator is the greatest.




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      Decimals: If all of the numbers are converted to decimals, they can then be compared.
       When comparing decimals, it is sometimes easier if you add zeroes to the end of each
       number to make sure they all have the same number of decimal places.

                                  2
Before mixed fractions (such as 3 5 ) can be compared or converted to equivalent fractions or to
decimals, they should be written as improper fractions ( 17 ). To convert a mixed fraction to an
                                                          5
improper fraction (where the numerator is larger than the denominator), you must first multiply
the denominator by the whole number part of the mixed fraction. Then add this to the numerator
to get a new sum. Then place this sum as the numerator over the original denominator. In the
example above, 5 x 3=15. Then add the numerator: 15+ 2= 17. Then place this over the original
denominator: 175


                                                          2        17
                                              Therefore 3 5 =       5


(See Math Makes Sense 7, p.91-95 for additional information and practice).

35. To complete the missing numbers in sequences, you need to find the pattern of the numbers
that are given and then extend the pattern.

When adding decimals, remember to line up the decimal point. Also remember that you can use
the inverse operation (subtraction) to check addition. You can also use front-end estimation to
check if your answer is reasonable.

When subtracting decimals, remember to line up the decimal points. Also remember that you can
use the inverse operation (addition) to check addition. You can also use front-end estimation to
check if your answer is reasonable. (Front –end estimation is simply ignoring the part of the
number after the decimal point and calculating the rest to get an approximate number. This
won’t give you an exact answer but it will help you to see if your answer is reasonable and to
show you if your decimal point has been reasonably placed. Example) By using front-end
estimation on the question 15.147 + 3.3694, I can simply add 15 + 3 to know that the answer
should be somewhere around 18.

Adding and subtracting decimals are extensions of adding and subtracting whole numbers.
Therefore rules such as carrying and borrowing still apply.

(See Math Makes Sense 7, p.96-99 for additional information and practice).

36. When you multiply decimals, you need to line up the numbers rather than the decimal points.
Ignore the decimal points while calculating, but then insert the decimal into your final answer.
To determine where to insert the decimal point in the final product you must count the total
number of decimal places (places after the decimal point) in the each of the numbers being
multiplied. The final product will have this many decimal places. In the following example, a
number with 3 decimal places is multiplied by a number with 1 decimal place. The final product,
then, has 3 + 1 or 4 decimal places.

                                                        22
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                                Review Sheet for Math Midterm Exam



                                2.083
                               x 33.2
                              69.1556

Front-end estimation may also be used to help place the decimal point. In the above example, if
we ignore the numbers after the decimal point, we would multiply
2 x 33 = 66. Therefore, our final product should be somewhere around 66. If we had misplaced
our decimal point so our answer read 6.91556 or 691.556 we could quickly tell that our answer
wasn’t reasonable.

(See Math Assignment, Canadian Mathematics 7, p. 94 for additional information and practice).

37. See Question 32.

38. For some questions, it is easier to visualize what is being asked for if you draw a diagram. A
diagram for this question may look like the following.




                                     6.4 cm

The distance across both circles would be equal to 2 times the diameter or 4 times the radius.
Therefore the radius of one circle is 6.4 cm ÷ 4 or 1.6 cm.

(See Math Makes Sense 7, p.130-132 for additional information and practice).

39, 40. See question 32.         C=2πr            or       C=πd          To calculate use 3.14 for π.

(See Math Makes Sense 7, p.133-137 for additional information and practice).

41. See question 32.    r=C÷2π                         To calculate use 3.14 for π.

(See Math Makes Sense 7, p.133-137 for additional information and practice).




                                                         23
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                                 Review Sheet for Math Midterm Exam

42. See question 32. d = C ÷ π                        To calculate use 3.14 for π.

(See Math Makes Sense 7, p.133-137 for additional information and practice).

43, 44. The area of a parallelogram is equal to the area of a rectangle with the same base and
height. To find the area of a parallelogram, multiply its base by its height. The formula for the
area of a parallelogram is A = b x h.




(See Math Makes Sense 7, p.139-142 for additional information and practice).

45, 46. The area of a triangle is one-half the area of a parallelogram with the same base and
height.




(See Math Makes Sense 7, p.143-147 for additional information and practice).

47. The area of a circle is π (or 3.14) multiplied by the square of its radius r;
                          that is A= π r 2 .


                           For this circle the radius is 4.2 m.
                           The area would be 3.14 x 4.2m x 4.2m = 55.3896 m 2




To round the area to two decimal places (hundredths), you would need to check what number
was in the next decimal place (thousandths). If it were 0-4 you would simply round off. (Drop
everything after the hundredths place). If it were 5-9 you would round the number in the
hundredths place up to the next number. In the example above, there is a 9 in the thousandths
place, so you would round the digit in the hundredths’ place up from an 8 to a nine and drop
everything after that. The area then would be rounded from 55.3896 m 2 to 55.39 m 2 .

C(See Math Makes Sense 7, p.148-152 for additional information and practice).



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                                Review Sheet for Math Midterm Exam



48. A circle graph is a diagram that uses parts of a circle to display data. In a circle graph, data
are shown as parts of one whole. Each sector of a circle represents a percent of the whole circle.
The whole circle represents 100%. If one sector of the graph was to represent 25% of the data,
then it would be represented by a piece that took up 25% of the total circle.

To estimate how much of a circle graph is represented by different data, you need to estimate
how much of the total circle is represented by that data. If the percents are given in each sector,
this can be used to accurately determine how much data is represented by each sector.

(See Math Makes Sense 7, p.156-160 for additional information and practice).


49. To calculate how many stamps Carol has from each country, you need to multiply the percent
given in each sector by the total number of stamps she has. For example, 25% of her stamps are
from Italy so this would be 25% of 500 which equals 125. See question 30 for instructions on
finding the percent of a number). To find how many more stamps she has from one country as
compared with another country you need to find the difference by subtracting.

(See Math Makes Sense 7, p.156-160 for additional information and practice).


50. The central angle of a sector on a circle graph is
the angle located at the center of the circle for that
sector. In a complete circle, there are 360°. On this
circle graph, 25% of the budget is for rent. Therefore,
the sector for rent takes up 25% of the graph and the
central angle for that sector is 25% of 360° or 90°.

To calculate the central angle, you must multiply the
percent that represents the data by 360°.

(See Math Makes Sense 7, p.161-164 for additional information and practice).




                                                        25
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                                Review Sheet for Math Midterm Exam


51.


               1       2    4              6            3                 17
                5       8 10              12              9              19
                11     14    16           18            15
                  13       20


                            Divisible by 2      Divisible by 3

A Venn Diagram is used to compare and contrast different items, in this case numbers. In this
Venn Diagram, the circle on the left contains all of the numbers up to 20 that are divisible by 2.
The circle on the left shows all of the numbers that are divisible by 3. The overlapping region
shows numbers that are divisible by both 2 and 3. Those numbers that do not fit into either circle
because they are not divisible by 2 or 3 are placed outside the circles. See question 1 for
information about divisibility rules.

(See Math Makes Sense 7, p.8-12 for additional information and practice. Also see question 1).

52, 53. See question 3.

54. Since all sides of a square are the same length, the perimeter or distance around the square is
equal to 4 times the length of one side. For additional information on relationships in patterns,
see question 5.

55, 56. See Question 3.

57. See Question 11.

58-60. See Question 13.

(See Math Makes Sense 7, p. 20-24 for additional information and practice)

61-62. See Question 16.

63. To change a decimal to a fraction, begin by seeing how many decimal places are in the
decimal. If the decimal has only one decimal place, then write the number as a fraction with a
denominator of 10. If there are two decimal places, write the fraction with a denominator of 100.

After you have written the number as a fraction, it can sometimes be simplified by writing an
equivalent fraction in lower terms. To do this simply divide the numerator and denominator by
the same number, a number that divides evenly into both numbers.

Example #1: Write 0.62 as a fraction.


                                                        26
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                                Review Sheet for Math Midterm Exam

Begin by counting the number of decimal places. There are two decimal places (numbers after
the decimal), which means that the decimal extends to the hundredths’ place, so the fraction will
have a denominator of 100.
                                          0.62 = 62/100
          This can be simplified by dividing both the numerator and denominator by 2.
                                         62/100 = 31/50

Example #2: Write 0.4 as a fraction. 0.4 = 4/10 = 2/5

(See Math sheet Decimals to Fractions and Math Makes Sense 7, p. 86-90 for additional
information and practice).

64. See Question 18.

65. Before converting a mixed number to a decimal you should first change it to an improper
fraction. See notes for questions 34 & 18.

(See Math Makes Sense 7, p. 86-90 for additional information and practice)

66. See Question 34.

67. See Question 22.

68. See Question 24.

69. To solve this problem, it would be good to draw a diagram to help you visualize the problem.
The diameter would be the same as the width of the cardboard. The number of circles that could
be cut from the strip would the same as the number of times 42 cm could be divided by 3.5 cm.
3.5 cm




                                                         42 cm




(See Math Makes Sense 7, p. 86-90 for additional information and practice)



                                                        27
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                                 Review Sheet for Math Midterm Exam

70. A bicycle wheel is a circle. The circumference                                                      of the
wheel is the distance around the outside of the                                                         circle.
The circumference is the distance the bike would                                                        travel in
one rotation of the wheel. See question 32.

C=2πr

To calculate the distance the bike would travel you                                                     have to
multiply the radius by 2 and then by π (3.14) to see                                                    how far
it would travel in one rotation of the wheel. Then                                                      you
would have to multiply that total by 500 because                                                        there
were 500 rotations of the wheel.

(See Math Makes Sense 7, p. 133-137 for additional information and practice)


71. See question 47 for instructions on calculating the area of a circle. Since a semicircle is
simply half of a complete circle, you would need to divide the area of the circle by 2 to find the
area of the semicircle.

(See Math Makes Sense 7, p. 148-152 for additional information and practice).

72. Use divisibility rules to list some of the numbers, starting at 100 (the first 3-digit number)
that are divisible by 5. (The number ends in a 5 or 0). Then check which is the first of these
numbers that is also divisible by 9 (The sum of the digits is divisible by 9). For similar questions,
use the same process, though you will have to use different divisibility rules if different numbers
are used.

(See Math Makes Sense 7, p. 10-13 for additional information and practice).


73. If a number is divisible by two different numbers, then it must also be divisible by any of the
factors of either of those numbers and by any of the factors of one of those numbers multiplied
by any of the factors of the other number.

The factors of 8 are 1, 2, 4 and 8.
The factors of 9 are 1, 3 and 9.

Therefore, any number that is divisible by both 8 and 9 must also be divisible by 1, 2, 3 and 4
and by any of the factors of one of the numbers multiplied by any of the factors of the other
number: by 6 (2 x 3), by 12 (3 x 4), by 18 (2 x 9), by 24 (3 x 8), by 36 (4 x 9) and by 72 (8x9).

(See Math Makes Sense 7, p. 12 for additional information).




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74. To solve this problem, you should break the question into parts.

      Calculate the area of the square first.
       A = L x W or 4 x side (since all sides of a square are the same length.)
      Then calculate the area of the parallelogram.
       A = b x h. (See question 43).
      Then add the area of the square and the parallelogram together.
      Then subtract the area of the triangle since this part is overlapping and you don’t want to
       count it twice. A = 1 b x h (See question 45).
                           2


(See Math Makes Sense 7, p. 139-147 for additional information and practice).

75. To solve this problem, you should break the question into parts.

      First calculate the area of the large circle. (See question 47) A= π r 2 . The diameter of
       this circle is given. To find the radius, you need to divide the diameter by 2.
      Next find the area of one of the smaller circles. Each circle is half the diameter of the
       larger circle and each radius is half the diameter of a smaller circle. Therefore, the radius
       of each of the smaller circles is the diameter of the larger circle divided by 4. A= π r 2 .
      To find the total area of both smaller circles, you need to multiply the area of one of the
       circles by 2.
      Finally, subtract the total area of both smaller circles from the total area of the large
       circle. This will leave the total area of the shaded regions.

(See Math Makes Sense 7, p. 148-152 for additional information and practice).




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