Лузгин Владимир Николаевич : другие произведения.

Math-C (grade 6)

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  • Аннотация:
    Math lessons for students, grade 6

Vladimir Luzgin

 Math Lessons for Gifted Students

Level C

(grade 6)

Center Impulse

Week-end and evening classes for gifted students grades 5-9
Canada, ON, L4K 1T7, Vaughan (Toronto),
80 Glen Shields Ave., Unit 10,
Phone (416)826-7270
[email protected]

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Content

Click on the lesson!


Lesson 01.
Lesson 02.
Lesson 03.
Lesson 04.
Lesson 05.
Lesson 06.
Lesson 07.
Lesson 08.
Lesson 09.
Lesson 10.



Lesson 01


1. Solve the problems.
1) A bag contains 80 jellybeans, 20 of which are red, 20 are black, 20 are green, and 20 are yellow. What is the least number that a blindfolded person must eat to be certain of having eaten at least one of each color?
2) Ten pink socks and ten purple socks are all mixed up in a drawer. The twenty socks are exactly alike except for color. The room is pitch dark. How many socks do you need to take out to be sure you have a matching pair?

2. Write as a percent.

0.2 aaaaaaaaaaaa 0.5 aaaaaaaaaaa 0.08 aaaaaaaaaaa 0.15
0.24 aaaaaaaaaaa 0.025 aaaaaaaaa 0.625 aaaaaaaaa 1
3 aaaaaaaaaaaaaa 4.18 aaaaaaaaaa 3/5 aaaaaaaaaaaa 3/4
1/20 aaaaaaaaaaaa 5/8 aaaaaaaaaaa 7/20 aaaaaaaaaaa 17/50
13/25 aaaaaaaaaaa 15/16 aaaaaaaaa 1/3 aaaaaaaaaaaa 11/6

3. Simplify by combining like terms.

1) 5a + 4b - 2b - a aaaaaaaaaaaaaaaaaa. 2) 12p - 5q - 8p + 9q
3) - 9x + 7x - 5x + 2x aaaaaaa.aаaaaaaa 4) - 8y + 7x + 6y + 2x
5) x2 + 3y2 - 4x2 - y2 aaaaaaaaaaaaaaaa 6) 11x2 + 4x - 9x2 - 4x
7) 2y2 - 3y + 2y - 2y2 aaaaaaaaaaaaaaaa 8) a + 6.2a - 6.5a - 0.3a
9) 0.48b + 3 + 0.52b - 3.7b aaaaaaaaaa 10) - a + x + 1.1a - 1.3x
11) - 1.2p + 3.2q + 3.2p - 2.3q aaaaaaa 12) 5.7p - 2.7q + 0.3p + 0.8q + 1.9q - 1.1p

4. Which numbers are divisible aaa a) by 2? aaa b) by 4? aaa c) by 8? aaa List the numbers in increasing order.

259 aaaaaa 850 aaaaaa 1 941 aaaaaa 75 432 aaaaaaa 719 820
324 aaaaaa 955 aaaaaa 3 572 aaaaaa 161 154 aaaaaa 2 772 825
378 aaaaaa 1 005 aa.aa 5 216 aaaaaa 237 583 aa.aaa 5 402 070
701 aaaaaa 1 359 aaaa 16 742 aaaaa 624 226 aaaaaa 24 576 004

5. Solve the following geometric constructions problems.
1) Draw two line segments AB and CD with different lengths. Then using a ruler and a compass, construct a segment with lengths the difference of AB and CD.
2) Draw two angles ABC and DEF. Then using a ruler and a compass, construct an angle with measure the sum of the angles ABC and DEF.

6. Points A, B, and C lie on a straight line, and B is between A and C. The distance from A to C is 1.2 m. Find AB and BC if
a) BC is 30 cm longer than AB.
b) BC is three times as long as AB.
c) AB : BC = 5 : 7.

7. Add. Write answers in simplest form.

1) 1/2 + 9/10 aaaaaaa 2) 1/4 + 3/5 aaaaaaaaaa 3) 7/10 + 1/15 aaaaaaaaa 4) 1/6 + 7/8
5) 1/5 + 5/6 aaaaaaaa 6) 5/12 + 1/4 aaaaaaaaa. 7) 5/6 + 1/2 aaaaaaaaaaa 8) 7/8 + 3/10
9) 5/36 + 7/24 aaaaaa 10) 11/35 + 8/49 aaaaaa 11) 13/72 + 11/54 aaaaaa 12) 53/54 + 59/72

8. Place numbers in the empty boxes, so that the number in each box equals to the sum of the two numbers in the boxes above it.

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9. Fill in the blanks to correctly total each row and column based on the given operations.

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10. Find the value of the following (do without a calculator and show all your work).

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Answers


1. aa a) 61. aaaaaaaaaaa b) 3.

2. aa 1) 20% aaaaaаaaaaa 2) 50% aaaaaaaaaaaaa 3) 8% aaaaaaaaaaaa 4) 15%
aaa.a 5) 24% aaaаaaaaaaa 6) 2.5% aaaaaaaaaaaa 7) 62.5% aaaa.aaaaa 8) 100%
aa.aa 9) 300% aaaa.aaaaa 10) 418% aaaa.aaaaaa 11) 60% aaaaaaaaaa 12) 75%
aa.aa 13) 5% aaa.aaaaaaa 14) 62.5% aaaaaaaaaa 15) 35% aaaaaaaaaa 16) 34%
aa.aa 17) 52% aaa.aaaaaa 18) 93.75% aaaaaaaaa 19) 331/3% aaaaaaa. 20) 1831/3%

3. aa 1) 4a + 2b aaaaaaaaaaaaa 2) 4p + 4q aaaaaaaaaaaaaa 3) - 5x aaaaaaaaaaaaaa 4) 9x - 2y
aaaaa 5) - 3x2 + 2y2 aaaaaaaaa 6) 2x2 aaaaaaaaaaaaaaaaaa. 7) - y aaaaaaaaaaaaaaa 8) 0.4a
aaaaa 9) - 2.7b + 3 aaaaaaaaaa 10) 0.1a - 0.3x aaaaaaaaaaa 11) 2p + 0.9q aaaaaaa 12) 4.9p

4. aa a) Divisible by 2: aa 324, a 378, a 850, a 3 572, a 5 216, a 16 742, a 75 432, a 161 154, a 624 226, a 719 820, a 5 402 070, a 24 576 004.
b) Divisible by 4: aa 324, a 3 572, a 5 216, a 75 432, a 719 820, a 24 576 004.
c) Divisible by 8: aa 5 216, a 75 432.

6. aaa a) AB = 45 cm, BC = 75 cm. aaaaaaaaaaaa b) AB = 30 cm, BC = 90 cm. aaaaaaaaa c) AB = 50 cm, BC = 70 cm.

7. aa 1) 12/5 aaaaaaaaa 2) 17/20 aaaaaaaaa 3) 23/30 aaaaaaaa 4) 11/24
5) 11/30 aaaaaaaa 6) 2/3 aaaaaaaaaaa 7) 11/3 aaaaaaaaa 8) 17/40
9) 31/72 aaaaaaaa 10) 117/245 aaaaaa 11) 83/216 aaaaaa 12) 1173/216

8.
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9.
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10. aa 1) 0.2 aaaaaaaaaaaaaaa 2) 9.7



Lesson 02


1. Solve the problems.
1) In your bureau drawer there are 10 blue socks, 8 white socks, and 16 gray socks. You reach into the drawer in the dark, and pull out socks. What is the smallest number of socks you must take to ensure that you have a matching pair?
2) A fly proceeds from one corner of a cube along edges to the diagonally opposite corner. If it does not reverse direction, how many paths can be chosen?

2. Write as a decimal.

1% aaaaaaaaaaaaaaaaa 5% aaaaaaaaaaaaaaaa 13%
90% aaaaaaaaaaaaaaaa 125% aaaaaaaaaaaaa 1.5%
30.5% aaaaaaaaaaaaaa 0.75% aaaaaaaaaaaaa 0.1%
0.05% aaaaaaaaaaaaaa 675.5% aaaaaaaaaaaa 5/8%
16 3/4% aaaaaaaaaaaaa 5 7/20% aaaaaaaaaaa. 1/16%

3. Simplify by combining like terms.

1) a + 0.4a - 1/5 a - 1/2 a aaaaaaaaaaaaaaaaaа 2) 2/9 m + 5/9 m - 1/3 m - 1/9 m
3) 2/3 a - 1/6 a + 1/2 a - 1/12 a aaaaaaaaaaaaa. 4) 0.5 a - 2/3 b - 2/5 a + 5/6 b
5) 1/3 x + 1/2 x - 2/3 a + 1/2 a aaaaaaaaaaaaaa 6) 5/6 y - 1/3 b - 1/6 y + 2/3 b
7) - 2/7 x - 4/9 y - 5/14 x + 2/3 y aaaaaaaaaaaa. 8) 3/2 y2 - 1/16 y2 + 1/32 y2 - 1/4 y2

4. Which numbers are divisible by 5? By 10? List the numbers in increasing order.

259 aaaaaaaa 850 aaaaaaaa. 1 941 aaaaaaaa 75 432 aaaaaaaaa 719 820
324 aaaaaaaa 955 aaaaaaaa. 3 572 aaaaaaaa 161 154 aaaaaaaa 2 772 825
378 aaaaaaaa 1 005 aaaaaa. 5 216 aaaaaaaa 237 583 aaaaaaaa 5 402 070
701 aaaaaaaa 1 359 aaaaaa. 16 742 aaaaaaa 624 226 aaaaaaaa 24 576 004

5. Copy this diagram.

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a) Construct OD, the bisector of the angle AOC.
b) Construct OE, the bisector of the angle BOC.
c) Measure the angle DOE. What conclusion can you make?

6. Points A, B, and C lie on a straight line, and B is between A and C. Find AC if AB : BC = 3 : 5 and AB = 9 cm.

7. Write as a proper fraction or as a mixed number in simplest form.

1) 24/360 aaaaaaaaaa 2) 114/171 aaaaaaaaaaa 3) 198/126 aaaaaaaaaa 4) 168/160
5) 147/210 aaaaaaaaa. 6) 106/318 aaaaaaaaaaa 7) 42/720 aaaaaaaaaaa 8) 3240/972
9) 880/1008 aaaaaaaa 10) 1008/1224 aaaaaaaa 11) 1848/2772 aaaaaaa 12) 2835/7425

8. Place numbers in the empty boxes, so that the number in each box equals to the sum of the two
numbers in the boxes above it.

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9. Fill in the blanks to correctly total each row and column based on the given operations.

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10. Find the value of the following (do without a calculator and show all your work).

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Answers

1. aaa a) 4. aaaaaaaaaaaa b) 6.

2. aa 1) 0.01 aaaaaaaaaaaa 2) 0.05 aaaaaaaaaaа 3) 0.13
4) 0.9 aaaaaaaaaaaaa 5) 1.25 aaaaaaaaaaa. 6) 0.015
7) 0.305 aaaaaaaaaaa 8) 0.0075 aaaaaaaaa 9) 0.001
10) 0.0005 aaaaaaaa 11) 6.755 aaaaaaaaa 12) 0.00625
13) 0.1675 aaaaaaaa 14) 0.0535 aaaaaaaa 15) 0.000625

3. aaa 1) 0.7a aaaaaaaaaaaa 2) 1/3 m aaaaaaaaaaaaa 3) 11/12 a aaaaaaaaaaaaa 4) 0.1a + 1/6 b
aaaaaa 5) - 1/6 a + 5/6 x aaa 6) 1/3 b + 2/3 y aaaaaa. 7) - 9/14 x + 2/9 y aaaaa. 8) 39/32 y2

4. aa a) Divisible by 5: aaa 850, a 955, a 1 005, a 5 402 070, a 719 820, a 2 772 825.
b) Divisible by 10: aa 850, a 719 820, a 5 402 070.

6. aaa AC = 24 cm.

7. aa 1) 1/15 aaaaaaaa 2) 3/3 aaaaaaaaa 3) 14/7 aaaaaaaа 4) 11/20
5) 7/10 aaaaaaaa. 6) 1/3 aaaaaaaa. 7) 7/120 aaaaaaa. 8) 31/3
9) 55/63 aaaaaaa 10) 14/17 aaaaaa 11) 2/3 aaaaaaaa 12) 21/55

8.
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9.
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10. aa 1) 58 aaaaaaaa 2) 18 aaaaaaaa 3) 0.8



Lesson 03


1. Solve the problems.
1) If we wish to tile a 15 m by 8 m rectangular floor using 25 cm by 25 cm square tiles, find how many tiles we will need?
2) A large sheet of paper is 0.01 mm thick. It is cut in half and one piece is placed on the other to make a pile. These are cut in half and all four pieces are placed in a pile. These four are cut in half and placed in a pile, and the process is continued. After the piece have been cut and piled for the tenth time, what is the height of the pile, in cm.

2. Write as a fraction in simplest form.

1% aaaaaaaaaaaaa 4% aaaaaaaaaaaaaaaaa. 5% aaaaaaaaaaaaaaa 20%
25% aaaaaaaaaaaa 50% aaaaaaaaaaaaaaaa 75% aaaaaaaaaaaaaa 40%
45% aaaaaaaaaaaa 120% aaaaaaaaaaaaaaa 170% aaaaaaaaaaaaa 0.1%
0.25% aaaaaaaaaa. 1.75% aaaaaaaaaaaaaa. 331/3% aaaaaaaaaaa. 41/6%
71/7% aaaaaaaaaaa 1/8% aaaaaaaaaaaaaaaa 6 9/11% aaaaaaaaaaa 205/7%

3. Expend and simplify by combining like terms.

1) m - (n + m) aaaaaaaaaaaaaaaaaaaaa. 2) - (n - x) - x
3) p + (- q + r - p) aaaaaaaaaaaaaaaaaa. 4) - a - (m - a + p)
5) - (m - a) - (k + a) aaaaaaaaaaaaaaaaа 6) 3a - (a + 2b)
7) m + (k - a - m) aaaaaaaaaaaaaaaaaaа 8) 5x - (2y - 3x)
9) 8a + (-3b + 5a) aaaaaaaaaaaaaaaaaa 10) 8x - (3x - 2y) - 5y
11) m - (a + m) - (-a - m) aaaaaaaaaaa. 12) 7x + 3y - (-3x + 3y)

4. Which numbers are divisible by 3? By 9? List the numbers in increasing order.

259 aaaaaaaa 850 aaaaaaaa. 1 941 aaaaaaaa 75 432 aaaaaaaaa 719 820
324 aaaaaaaa 955 aaaaaaaa. 3 572 aaaaaaaa 161 154 aaaaaaaa 2 772 825
378 aaaaaaaa 1 005 aaaaaaа 5 216 aaaaaaaa 237 583 aaaaaaaa 5 402 070
701 aaaaaaaa 1 359 aaaaaaа 16 742 aaaaaaa 624 226 aaaaaaaa 24 576 004

5. Solve the following geometric constructions problem.
a) Construct an isosceles triangle ABC such that AC = BC.
b) Extend AC to D.
c) Construct CE, the bisector of the angle BCD.
d) What can be said about CE and AB? Explain your answer.

6. Points A, B, and C lie on a straight line, and B is between A and C. Find the distance between the midpoints of the line segments AB and BC, if AC = 12 cm.

7. Write as a mixed number.

1) 145/8 aaaaaaaaaaaaaaaa. 2) 137/5 aaaaaaaaaaaaaaaa 3) 37/11 aaaaaaaaaaaaaaa. 4) 68/13
5) 349/15 aaaaaaaaaaaaaaa. 6) 437/24 aaaaaaaaaaaaaaa 7) 3279/32 aaaaaaaaaaaaaa 8) 4389/43
9) 4251/128 aaaaaaaaaaaaa 10) 9836/137 aaaaaaaaaaaa 11) 20151/356 aaaaaaaaaaa 12) 43297/823

8. Place positive numbers in the empty boxes, so that the number in each box equals to the product of the two numbers in the boxes above it. Do not use a calculator and show your work.

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9. Fill in the blanks to correctly total each row and column based on the given operations.

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10. Find the value of the following (do without a calculator and show all your work).

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Answers
1. aa a) 1920. aaaaaaaaaaaa b) 1.024 cm.

2. aa 1) 1/100 aaaaaaa. 2) 1/25 aaaaaaaaaa 3) 1/20 aaaaaaaa 4) 1/5
aaaa. 5) 1/4 aaaaaaaaa. 6) 1/2 aaaaaaaaaaa 7) 3/4 aaaaaaaaa 8) 2/5
aaaaa 9) 9/20 aaaaaaaa 10) 1 1/5 aaaaaaaa 11) 1 7/10 aaaaa. 12) 1/1000
aaaaa 13) 1/400 aaaaaa 14) 7/400 aaaaaaaa 15) 1/3 aaaaaaaa 16) 1/24
aaaaa 17) 1/14 aaaaaaa 18) 1/800 aaaaaaaa 19) 3/44 aaaaaaa 20) 29/140

3. aaa 1) - n aaaaaaaa 2) - n aaaaaaaaaa 3) r - q aaaaaa 4) - m - p
aaaaa 5) - m - k aaaaa 6) 2a - 2b aaaaaa 7) k - a aaaaaa 8) 8x - 2y
aaaaa 9) 13a - 3b aaa 10) 5x - 3y aaaaa 11) m aaaaaaa 12) 10x

4. aa a) Divisible by 3: aa 324, a378, a1941, a1 005, a1 359, a75 432, a161 154, a719 820, a2 772 825, a5 402 070.
b) Divisible by 9: aa 378, a1 359, a161 154, a719 820, a5 402 070.

6. aaa 6 cm.

7. aa 1) 18 1/8 aaaaaaaaaa 2) 27 2/5 aaaaaaaaaaа 3) 3 4/11 aaaaaaaaaaaaa 4) 5 3/13
5) 23 4/15 aaaaaaaaa 6) 18 5/24 aaaaaaaaaa 7) 102 15/32 aaaaaaaaaa 8) 102 3/43
9) 33 27/128 aaaaaaa 10) 71 109/137 aaaaaa 11) 56 215/356 aaaaaaaa 12) 52 501/823

8.
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9.
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10. aa 1) 0.91 aaaaaaaa 2) 2.729



Lesson 04


1. Solve the problems.
1) An organization of 100 people wishes to set up a telephone call system. The initial contact person calls three other persons, each of whom calls three other, and so on, until all persons in the organization have been contacted. What is the maximum number of people who do not need to make a call?
2) Jane was born on June 30, 1974. Alex was born on June 3, 1975. What is the number of days between their birthdays (not included birthdays)?

2. Express these fractions as decimal numbers. Do not use a calculator!

1) 5/8 aaaaaaaaaaaa 2) 17/25 aaaaaaaaaaa 3) 19/40 aaaaaaaaaa 4) 13/20
5) 39/50 aaaaaaaaaa 6) 7/200 aaaaaaaaaaa 7) 6/125 aaaa.aaaaaa 8) 11/125
9) 5/16 aaaaaaaaaaa 10) 7/80 aaaaaaaaaaa 11) 29/32 aaaaaaaaa 12) 213/250
13) 22/80 aaaaaaaaa 14) 73/160 aaaaaaaaa 15) 127/800 aaaaaaa 16) 139/2500

3. Find:

1) 30% of 50 aaaaaaaaaaaaaaaaa 2) 25% of 9
3) 80% of 116 aaaaaaaaaaaaaaaa 4) 38% of 95
5) 18% of 146 aaaaaaaaaaaaaaaa 6) 94% of 5.6
7) 23.5% of 78 aaaaaaa.aaaaaaaa 8) 11.2% of 5.5
9) 3.7% of 1.2 aaaaaaаaaaaaaaaa 10) 5.4% of 270

4. Make the statements true by inserting parenthesis and any of the four operations.

1)   6   5   4   3   =   0.125 aaaaaaaaaaaaaaa 2)   4   3   6   4   =   0.125

5. Expend and simplify by combining like terms.

1) (6a - 2b) - (5a + 3b) aaaaaaa.aaaaaaaa 2) (5a - b) - (2a + 3b)
3) (7a - 2b) - (3b - 7a) aaaaaaaaaaaaaaaa 4) 5m - (3m + 5) + (2m - 4)

6. Use a ruler to draw any scalene triangle ABC.
a) Construct the bisector of each angle of the triangle ABC.
b) State a probable conclusion about the bisectors of the angles of a triangle.
c) Let D be the point of intersection of the three bisectors. Measure angles A, B, C, ADB, ADC, BDC, and find the values of:
    angle BDC - 1/2 (angle A);
    angle ADC - 1/2 (angle B);
    angle ADB - 1/2 (angle C);
d) What conclusion can you make?

7. Write > or < for each square to make a true statement.

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8. Place the numbers from 11 to 16 in the circles, so that the numbers on each side of the triangle add to the same prime number.

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9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Answers
1. aaa a) 67. aaaaaaaaaaaa b) 337.

2. aa 1) 0.625 aaaаaaaaa. 2) 0.68 aaaaaaaaaaaa 3) 0.475 aaaaaaaaaa. 4) 0.65
aaaa. 5) 0.78 aaaaa.aaaaa 6) 0.035 aaaaaaaaaaa 7) 0.048 aaaaa.aaaaa 8) 0.088
aaaa. 9) 0.3125 aaaaaaaa 10) 0.0875 aaaaaaaaa 11) 0.90625 aaaaaaa 12) 0.852
aaaa. 13) 0.275 aaaaaaaa 14) 0.45625 aaaaaaaa 15) 0.15875 aaaaaaa 16) 0.0556

3. aa 1) 15 aaaaaaaaaaaa 2) 2.25 aaaaaaaaaaa 3) 92.8 aaaaaaaaaa 4) 36.1
aaaa. 5) 26.28 aaaaaaaaa 6) 5.264 aaaaaaaaaa 7) 18.33 aaaaaaaaa 8) 0.616
aaaa. 9) 0.0444 aaaaaaaa 10) 14.58

4. aa 1) 6 : (5 + 43) = 0.125 aa 2) 4 : (36 - 4) = 0.125

5. aa 1) a - 5b aa 2) 3a - 4b aa 3) 14a - 5b aa 4) 4m - 9

6. aaa AC = 24 cm.

7. aaa 1) 46/21 > 2 1/7 aaaaaaaa 2) 41/15 > 2 2/3 aaaaaaaaa 3) 37/12 < 31/6 aaaaaaa 4) 3 5/8 < 59/16

8.
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9.
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10. aa 1) 10.9 aaaaaaaa 2) 7.52 aaaaaaaa



Lesson 05


1. Solve the problems.
1) A 6 by 4 rectangle is divided into a number of equal squares as shown. Determine the total number of squares of all sizes in the diagram.

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2) January 1, 1986 occurred on a Wednesday. On what day January 1, 1992, occured?

2. Arrange the following numbers in order from largest to smallest.

1 2/3,    7/6,    1/2,    2/3,    17/12.

3. Add or subtract. Express your answer as in lowest terms.

1) 3 5/12 + 2 7/18 aaaaaaaa 2) 5 7/8 + 27 5/12 aaaaaaaaaa 3) 3 7/25 + 2 9/20
4) 18 1/4 + 43 3/50 aaaaaaa 5) 71 43/45 + 52 73/75 aaaaaa 6) 63 8/9 + 15 11/15
7) 23 2/3 - 21 5/6 aaaaaaaa. 8) 6 1/2 - 3 3/4 aaaaaaaaaaaa. 9) 45 1/5 - 43 9/10
10) 37 2/3 - 34 5/6 aaaaaaa. 11) 9 1/2 - 5/9 aaaaaaaaaaaaa 12) 1 5/12 - 5/6

4. Multiply. Express your answers in lowest terms.

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5. Expend and simplify by combining like terms.

1) 3m - (5m - (2m - 1)) aaaaaaaaaaaaaaa. 2) 4a - (2a - (2 - 3a))
3) a - (b - (a - (b + a))) aaaaaaaaaaaaaaaa 4) a + b - (a - (b - (a - b)))

6. Find:

1) 137% of 0.8 aaaaaaaaaaaaaaa. 2) 0.25% of 102.4
3) 33 1/3% of 75 aaaaaaaaaaaaaa. 4) 0.01% of 2000
5) 65% of 5 1/13 aaaaaaaaaaaaaaa 6) 42% of 5/7
7) 662/3% of 1.5 aaaaaaaaaaaaaaa 8) 0.75% of 60
9) 72.5% of 12.5 aaaaaaaaaaaaaa. 10) 2/3% of 300

7. The perpendicular bisector to a given line segment AB is the line that divides AB at right angles into two equal parts. Draw any line segment AB.
a) Construct a perpendicular bicector of AB, using a ruler and compasses.
b) Locate any point P on the bisector. Join PA and PB.
c) State a probable conclusion about any point on the perpendicular bisector of a line segment.

8. Which numbers are divisible aa a) by 6? aa b) by 12? aaa List the numbers in increasing order.

1 644 aaaaaaaa 4 685 aaaaaaaa 158 457 aaaaaaaa 757 675 aaaaaaaaa 3 289 775
2 108 aaaaaaaa 44 956 aaaaaaa 215 783 aaaaaaaa 835 743 aaaaaaaaa 9 983 709
3 126 aaaaaaaa 67 932 aaaaaaa 555 444 aaaaaaaa 2 487 960. aaaaaaa 21 112 221

9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Answers


1. aaa a) 51. aaaaaaaaaaaa b) Wednesday.

2. aa 1 2/3, aa 17/12, aa 7/6, aa 2/3, aa 1/2.

3. aa 1) 5 29/36 aaaaaaaaaa 2) 33 7/24 aaaaaaaaaaaa 3) 5 73/100 aaaaaaaaaaa 4) 61 31/100
aaaaa 5) 124 209/225 aaaaa. 6) 79 28/45 aaaaaaaaaaa 7) 1 5/6 aaaaaaaaaaaaaa 8) 2 3/4
aaaa. 9) 1 3/10 aaaaaaaaaaa 10) 2 5/6 aaaaaaaaaaaaa 11) 8 17/18 aaaaaaaaaaa 12) 7/12

4. aa 1) 5/8 aaaaaaaaa 2) 2/3 aaaaaaaaaaa 3) 14/15
4) 1/4 aaaaaaaaa 5) 1/6 aaaaaaaaaaa 6) 8/15

5. aa 1) - 1 aaaaaaaaaaa 2) - a + 2 aaaaaaaaaaaa 3) a - 2b aaaaaaaaaaaaa 4) - a + 3b

6. aa 1) 1.096 aaaaaaaaaa 2) 0.256 aaaaaaaaaaa 3) 25 aaaaaaaaaa 4) 0.2
aaaa. 5) 3.3 aaaaaaaaaaaa 6) 0.3 aaaaaaaaaaaaa. 7) 1 aaaaaaaaaaa 8) 0.45
aaaa. 9) 9.0625 aaaaaaaa. 10) 2

8. aa a) Divisible by 6: aaa 1 644, aa 3 126, aa 67 932, aa 555 444, aa 2 487 960.
b) Divisible by 12: aa 1 644, aa 67 932, aa 555 4444, aa 2 487 960.

9.
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10. aa 1) 0.5 aaaaaaaa 2) 51.9



Lesson 06


1. Solve the problems.
1) Find the total number of squares included in the diagram.

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2) An unusual die has its six faces labeled 1, 2, 3, 5, 7, 9. If two such dice are rolled, and the numbers showing on the upper faces are added, then what is the number of possible different sums?

2. Arrange the following numbers in order from largest to smallest.

3/4,    4/5,    5/9,    2/3,    8/11,    11/15.

3. Add. Express your answer as in lowest terms.

1) 3/5 + 7/10 + 1/2 aaaaaaaaaaaaaaaaaaaaaaaaaa 2) 7 1/8 + 5 3/4 + 3 1/2
3) 4 5/12 + 5 2/3 + 1 3/4 aaaaaaaaaaaaaaaaaaaaa 4) 1/2 + 1/3 + 1/4 + 1/5 + 1/6
5) 1 7/9 + 2 5/12 + 5 2/9 + 7/12+ 4 3/4

4. Multiply. Express your answers in lowest terms.

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5. Expend and simplify by combining like terms.

1) 3(2x + 1) + 5(1 + 3x) aaaaaaaaaaaaaaa 2) 4(2 + x) - 3(1 + x)
3) 10(n + m) - 4(2m + 7n) aaaaaaaaaaaaa 4) 7(2x - 3) + 4(3x - 2)
5) -2(4k + 8) - 3(5k - 1) aaaaaaaaaaaaaaa 6) -8(2 -2y) + 4(3 - 4y)

6. Solve the problems.
a) In an election, 73% of the eligible voters voted. 25 700 people were eligible to vote. How many did vote?
b) In a shipment of light bulbs, 7% are defective. How many bulbs would be defective in shipments of 1400 bulbs?

7. Mark two points A and B on your paper. Construct a circle having AB as diameter, using a ruler and compasses.

8. Which numbers are divisible by 15? By 18? By 25?

1 644 aaaaaaaa 4 685 aaaaaaaa 158 457 aaaaaaaa 757 675 aaaaaaaaa 3 289 775
2 108 aaaaaaaa 44 956 aaaaaaa 215 783 aaaaaaaa 835 743 aaaaaaaaa 9 983 709
3 126 aaaaaaaa 67 932 aaaaaaa 555 444 aaaaaaaa 2 487 960 aaaaaaa 21 112 221

9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Lesson 07


1. Solve the problems.
1) You have 50 coins which have a total value of $1.00. How many coins of each type do you have? Is more than one combination possible?
2) Thirty equally spaced points on the circumference of a circle are labeled with the integers 1 to 30, in order. What number is diametrically opposite the number 7?

2. Find the missing value:

1/5    >    ?/40    >    1/6.

3. Subtract. Write your answer in simplest form.

1) 3 4/9 - 1 2/3 aaaaaaa 2) 1 1/6 - 7/9 aaaaaaaaaaa 3) 21 2/5 - 17 5/6
4) 8 2/3 - 4 3/4 aaaaaaa 5) 8 1/2 - 5 4/5 aaaaaaaaa 6) 5 1/3 - 3 5/8
7) 6 2/5 - 4 5/6 aaaaaaa 8) 27 2/5 - 13 7/8 aaaaaaa 9) 35 1/3 - 23 5/8

4. Multiply. Express your answers in lowest terms.

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5. Expend and simplify by combining like terms.

1) (3x - 11)(2) - (4 - 3x)(5) aaaaaaaaaaaaaaa 2) (8a - 1)(- 6) + (3a - 7)(-2)
3) 8(a + 3b) - 9(a + b) aaaaaaaaaaaaaaaaaaaa 4) 3(c + d) - 7(d + 2c)
5) - 0.5(-2x + 4) - (10 - x) aaaaaaaaaaaaaaaa 6) 0.1(x - 2y) + 0.2(x + y)

6. Solve the problems.
a) Jean scored 72% on the test with 75 questions. How many questions did Jean get correct?
b) Bobby and his mother eat lunch at a restaurant. Their total bill is $9.00. Bobby's mother asks him to figure a 15% tip for the waitress. How much money do they leave for the tip?

7. Draw a line segment 12 cm long and divide it into four equal parts, using a ruler and compasses.

8. Place digits in the squares to get the numbers that are divisible by 9.

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9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Lesson 08


1. Solve the problems.
1) Six darts were thrown into the dart board shown in the diagram. The total score was 211. Inside which rings did the six darts land? Is there more than one correct answer?

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2) Find the number of integers between 500 and 700 in which the sum of the digits is 12.

2. Subtract. Write your answer in simplest form.

1) 6 1/8 - 4 5/6 aaaaaaaaaaa 2) 43 1/4 - 28 3/10 aaaaaaaaa 3) 5 7/15 - 3 13/20
4) 15 3/24 - 3 5/36 aaaaaaaa 5) 5 7/24 - 3 11/18 aaaaaaaaa 6) 56 1/12 - 42 5/18
7) 5 31/54 - 3 19/24 aaaaaaa 8) 7 59/108 - 5 31/36 aaaaaaa. 9) 5 5/16 - 3 29/36

3. Insert brackets to make each statement true.

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4. Multiply. Express your answers in lowest terms.

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5. Expend and simplify by combining like terms.

1) 0.2 (6x - 5) - 4 (0.2x - 2) aaaaaaaaaaaaaa 2) 0.4 (1.5y + 3) - 2.5 (3 - 0.6y)
3) - 5 (x + 3) + 4 (x - 2) - 6 (2x + 1) aaaaaa 4) 4 (8a + 3) - 8 (4a - 3) + 7 (5y + 2) - 5 (7y - 2)
5) 1/8 c - (5/9 c - 1/4 c) aaaaaaaaaaaaaaaaaa 6) 2/3 (m - 3n) + 1/3 (n - 2m)

6. Solve the problems.
a) Juanita operates a designer dress shop. Last year, her sales were $ 2 500 000. This year her sales were 115% of the sales last year. What were the sales for this year, to the nearest ten thousand?
b) Monica pays 0.5% of her salary of $250 for additional medical insurance. How much does she pay?

7. Use a ruler to draw any scalene triangle.
a) Construct the perpendicular bisector of each side of the triangle.
b) State a probable conclusion about the perpendicular bisectors of the sides os a triangle.

8. Place digits in the squares to get the numbers that are divisible by 24.

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9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Lesson 09


1. Minibuses seating 10, 12 or 15 passengers are used to transport hotel guests from the airport to hotel. A hotel has 5 minibuses of each size available when a party of 120 people arrives. In how many different ways can these guests be transported using some of these minibuses if each buss used must be filled?

2. Express your answers in lowest terms.

1) 4 3/8 - (3 5/7 - 1 5/7) + 1 5/8 aaaaaaaa 2) 12 7/12 - 4 5/12 - (20 3/4 - 19 3/4)
3) 7 5/6 - (3 1/6 - 2 2/3) - 1 1/3 aaaaaaaaa 4) 3 4/9 - (4 5/9 - 5 7/9) - 2 2/3
5) 8 2/3 - 6 1/6 + 1 1/2 aaaaaaaaaaaaaaaa 6) 2 1/2 + 3 1/3 - 4 1/6
7) 2 3/4 + 1 4/5 - 3 3/10 aaaaaaaaaaaaaaa 8) 3 3/4 - 1 1/3 + 1/12

3. Insert brackets to make each statement true.

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4. Multiply. Express your answers in lowest terms.

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5. Expend and simplify by combining like terms.

1) - 6 (2/3 a - 1/6) + 4 (3/4 a - 1/2) aaaaaaaaaaaaaaa 2) 5 (2/5 x - 0.7) - 3 (1/3 x - 0.2)
3) 1/3 (0.3 y - 0.6) - 1/4 (0.4y - 0.8) aaaaaaaaaaaaa 4) 2/9 (1.8m - 5.4) - 3/7 (2.1m - 4.2)
5) 3/4 (4/3 x - 4) - 8 (21/4 x + 3/8)

6. Solve the problems.
a) The population of the town was 40 000 in 1970. Since then it has risen 125%. What is the population today?
b) In a circle with center O, the sector AOB represents 20% of the area of the circle. What is the size of the angle AOB?

7. Use a ruler to draw any scalene triangle ABC.
a) Construct M, the midpoint of AB, and N, the midpoint of AC.
b) Compare the lengths of MN and BC. What do you notice?
c) Compare the measures of angles AMN and ABC. What do you notice?
d) State a probablre conclusion about the line segment joining midpoints of two sides of a triangle.

8. Place digits in the squares to get the numbers that are divisible

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9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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Lesson 10


1. Find the number of integers between 100 and 1000 such that the sum of their digits is 10.

2. Express your answers in lowest terms.

1) 7 2/3 - 5 5/6 + 1 1/2 aaaaaaaa 2) 3 2/3 + 1 1/2 - 2 1/6
3) 5 1/2 - 3 2/3 - 1 5/6 aaaaaaaa 4) 5 - 2 3/4 - 1 3/8
5) 3 5/8 + 2 1/4 - 5 1/2 aaaaaaaa 6) 7 1/4 + 3 1/2 - 6 3/8
7) 1 1/30 + 2 3/5 - 3 1/6 aaaaaaa 8) 3 7/8 - 1 5/18+ 3 1/2

3. Insert brackets to make each statement true.

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4. Simplify.

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5. Find:

1) 3 is what percent of 5? aaaaaaaaaaaaaaa 2) 45 is what percent of 24?
3) 21 is what percent of 36? aaaaaaaaaaaaa 4) 50 is what percent of 2.5?
5) 15/8 is what percent of 13/15? aaaaaaaaaaa 6) What percent of 8 is 12?
7) What percentage is 50 of 32? aaaaaaaaaa 8) What percent of 180 is 621?

6. How many parasites will exist after 4 days if every parasite splits into 2 each day, and a population of 7 exists on day 1?

7. Use a ruler to draw any scalene triangle ABC.
a) Construct the three medians of the triangle. What do you notice?
b) Let M, N, and K be the midpoints of the sides BC, AC, and AB, respectively. Let G be the point of intersection of the three medians. G is called the centroid of the triangle. Measure AG, GM, BG, GN, CG, GK, and find the ratios AG : GM, BG : GN, and CG : GK. What do you notice?
c) State a probable conclusion about the three medians of a triangle.

8. Among grandfather's papers an old bill was found: "72 Turkeys $_ 67.9 _". The first and the last digits of the number that represented the total price of the turkeys are replaced here with blanks as they had faded and are now illegible. What are the missing digits?

9. Find the missing digits in the problem below.

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10. Find the value of the following (do without a calculator and show all your work).

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