Vladimir Luzgin

Math Lessons for Gifted Students

Level D

(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 1

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1. Complete mentally these flow charts.

2. How many of the numbers between 100 and 300 begin or end with 2?

3. Express your answers in lowest terms.

1) ¹⁹/₂₀ - (¹/₄ + ²/₅) aaaaaaaaaa 2) (⁵/₈ - ²/₅) + ³/₂₀

3) ¹/₄ + 0.7 - ¹/₅ aaaaaaaAaaaaa 4) ⁴/₅ - ¹/₃ + 0.2

5) 0.9 - 0.3 - ²/₅ aaaaaaaaaaaaaa 6) ⁷/₉ + ¹/₁₈ - 0.3

7) ⁷/₁₂ + (⁵/₆ - ³/₄) aaaaaaaaaaaa 8) ⁷/₉ - 0.4 - ⁴/₁₅

4. Write the reciprocal. [The reciprocal of any fraction ^m/_n (where m, n do
not equal to 0) is defined to be the fraction ⁿ/_m.]

1) ⁵/₈ aaaaaaaaaa 2) 4 aaaaaaaaaa 3) ¹/₇ aaaaaaa 4) 3 ¹/₃

5) 1 ²/₁₁ aaaaaaa 6) 6.25 aaaaaaaa 7) 1.4 aaaaaaa 8) 0.125

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

1)   3   1   6   6   =   150

2)   2   3   8   6   =   230

3)   6   6   2   7   =   40

6. What percentage is

1) 125 of 25? aaaaaa 2) 40 of 32?

    What percentage of

3) 2 is 2.5? aaaaaaaa 4) 0.8 is 1.5?

    What percent of

5) 0.5 is ¹/₄? aaaaaaa 6) 3.5 is 0.56?

7. Draw a line segment, 12 cm long, and mark a point P, 5 cm from one end. Using a ruler and
compasses, construct a perpendicular to the line segment at P.

8. Simplify and evaluate.

1) (2x + 5y) - (x + 4y) for x = 0.4 and y = 0.6;

2) (3a - 4b ) - (2a - 3b) for a = 0.12 and b = 1.28;

3) (5c - 6b) - (3c - 5b) for c = - 0.25 and b = 2.5;

4) (7x + 8y) - (5x - 2y) for x = - ³/₄ and y = 0.025.

9. Place the given numbers into the squares of the magic crosses to get the given sums in their row
and column.

a) Numbers: - 8, - 7, - 5, - 4, 3, 5, 6, 9, 10.       b) Numbers: - 10, - 5, - 3, - 1, 1, 2, 3, 4, 8.

    Row sum = 5, column sum = -3.                         Row sum = - 2, column sum = 5.

                             

10. The Greek mathematician Eratosthenes (276 -195 B.C.) developed the following method of finding
prime numbers (Sieve of Eratosthenes). To find the prime numbers from 1 to 100:

a) Write the numbers in ten columns.

1	2	3	4	5	6	7	8	9	10
11	12	13	14	15	16	17	18	19	20
21	22	23	24	25	26	27	28	29	30
31	32	33	34	35	36	37	38	39	40
41	42	43	44	45	46	47	48	49	50
51	52	53	54	55	56	57	58	59	60
61	62	63	64	65	66	67	68	69	70
71	72	73	74	75	76	77	78	79	80
81	82	83	84	85	86	87	88	89	90
91	92	93	94	95	96	97	98	99	100

b) Cross out 1; it is not a prime.

c) Circle 2; it is a prime. Cross out all the multiples of 2.

d) Circle 3; it is prime. Cross out all the multiples of 3.

e) Repeat this process for all numbers until only circled numbers remain. These are all prime
numbers in this set.

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Lesson 2

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1. Complete mentally these flow charts.



2. The pages of a book are numbered from 1 to 300 inclusive. How many digits are needed to number
the pages of the book?

3. Express your answers in lowest terms.

1) 5 ³/₅ - 3.15 + 7 ¹²/₂₅ aaaaaaaaaaa 2) 3 ⁷/₁₅ + 4.6 - 1 ²/₃

3) (18 ⁷/₁₂ + 3 ¹/₅) - 7 ⁵/₁₂ aaaaaaaa 4) 8 ⁵/₉ - (4 ²/₉ + 2 ¹/₆)

5) ⁵/₂₄ - ⁷/₉₆ - ¹/₁₆ aaaaaaaaaaaaaaaa 6) ⁷/₂₄ + ⁹/₄₀ - ⁵/₃₆

7) ⁵/₆ + ⁴/₉ - ¹/₂ - ²/₃ aaaaaaaaaaaaaa 8) ²/₉ - ⁷/₂₄ + ³/₁₀ - ¹/₆

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

1)   2   3   1   7   =   53

2)   7   6   7   9   =   100

3)   7   6   5   4   =   148

5. Draw a line segment, 12 cm long, and mark a point P about 8 cm above it. Using a ruler and
compasses, construct a perpendicular from P to the line segment.

6. Solve the problems.

a) At one point in the season, the Winnipeg Jets won 9 of the 15 games they played. What percent of
their games did they win?

b) During an election, 630 people were polled to determine how they would vote. The results showed
that 504 people would support the incumbent. What percent of the group questioned supported the incumbent?

7. The Square root method. To determine whether the given number n is a prime or not try all
prime numbers less or equal to the square root of n whether they are factors of n or not. Use
the "square root method" to determine if the following numbers are prime or composite.

a) 487 aaaaaaaaaaa b) 593 aaaaaaaaaaa c) 667

d) 921 aaaaaaaaaaa e) 2789 aaaaaaaaaa f) 6059

8. Simplify and evaluate.

1) - (4.7m + 2.8m - 5.7m) - 3.7m for m = 0.1;

2) 0.5(a - 2b) - (3b + 1.5a) for a = 0.48, b = 0.03;

3) 0.01(2.2x - 0.1) + 0.1(x - 100) for x = -10;

9. Place the given numbers into the squares of the magic crosses to get the given sums in their row
and column.

a) Numbers: - 7, - 6, - 5, - 4, 1, 2, 3, 8, 9.         b) Numbers: - 8, - 6, - 4, - 2, 1, 3, 5, 7, 9.

    Row sum = - 6, column sum = 1.                         Row sum = - 1, column sum = - 2.

                             

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

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Lesson 3

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1. Complete mentally these flow charts.



2. Express your answers in lowest terms.

1) 1 ¹/₈ + ¹/₃ - ¹⁷/₂₄

2) ⁵/₃₆ + ⁷/₈ - ¹/₇₂ - ³/₄

3) ¹/₂ - ¹/₃ + ¹/₄ - ¹/₅ - ¹/₆

4) (7 ¹/₂ - 3 ⁵/₈) - (1 ⁵/₆ + ³/₄) - (2 ²/₃ - 1 ³/₈)

5) (10 - 8 ³/₄) - (6 - 3 ¹/₂) + (5 ²/₃ - 2 ⁵/₁₂)

3. Determine the number of degrees in the measure of the obtuse angle angle formed by the hands of
a cklock at

a) 10 : 15 a.m. aaaaaaaaaaaaaaaaa b) 11 : 18 a.m.

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

1)   6   4   5   3   2   1   =   100

2)   5   6   1   4   3   2   =   100

3)   5   4   6   2   3   1   =   100

4)   6   3   4   2   5   1   =   100

5. Use a ruler to draw any scalene triangle.

a) Using a ruler and compasses, construct the perpendicular from each vertex to the opposite side.
These perpendiculars are calle altitudes of the triangle.

b) State a probable conclusion about the altitudes of a triangle. The point of intersection of the
altitudes is called the orthocenter of the triangle.

6. Find the missing number.

7. Find the prime factorization of the following numbers.

1) 24 aaaaaaaaaaa 2) 52 aaaaaaaaaaa 3) 76

4) 75 aaaaaaaaaaa 5) 98 aaaaaaaaaaa 6) 104

7) 192 aaaaaaaaaa 8) 243 aaaaaaaaaa 9) 720

8. Simplify and evaluate.

1) 8 (1.4 x + 3.6 y) + 13 (0.8 x - 0.9 y) aaa for x = 2.1 and y = 3.4 ;

2) ²/₃ (6 x + 0.3) + ³/₅ (5 x - 1.5) aaa for x = 3.1 ;

3) - 6 (²/₃ y - ¹/₂) - 10 (³/₅ - 1¹/₂ y) aaa for y = -2 ³/₅.

9. Write the digits from 1 to 6 to get: a) the smallest answer; b) the largest answer.

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

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Lesson 4

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1. Complete mentally these flow charts.



2. Divide. Express your answers in lowest terms.

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

1)   6   4   1   5   2   3   =   100

2)   6   3   5   2   4   1   =   100

3)   4   4   4   4   4   4   =   100

4. Draw a line l and mark any point P above it. Then using a ruler and compasses,
construct a line through P parallel to l. Follow the steps.

Step 1. Construct a perpendicular PQ from P to l.

Step 2. Construct a perpendicular to PQ at P.

5. Solve the problems.

a) A booklet contains 30 pages. If 9 pages in the booklet have drawings, what percent of the pages
in the booklet have drawings?

b) In a shipment of 55 000 light bulbs, 425 were found to be defective. What percentage
of the light bulbs was defective? Round your answer to the nearest tenth of a percent.

6. Evaluate.

7. Find the prime factorization of the following numbers.

1) 54 aaaaaaaaaaa 2) 162 aaaaaaaaaaa 3) 216

4) 540 aaaaaaaaaa 5) 1500 aaaaaaaaaa 6) 3003

7) 3240 aaaaaaaaa 8) 4608 aaaaaaaaaa 9) 13125

8. A perfect number is a number, which equals the sum of its proper divisors. For example, 6 is a
perfect since 6 = 1 + 2 + 3. Prove that 28 and 496 are perfect numbers.

9. Write the digits from 1 to 6 to get: a) the smallest answer; b) the largest answer.

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

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Lesson 5

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1. Complete mentally these flow charts.

2. Divide. Express your answers in lowest terms.

3. Write each ratio in lowest terms (in simplest form).

1) 24 : 60 aaaaaaaaaaaa 2) 27 : 45

3) 63 : 42 aaaaaaaaaaaa 4) 468 : 594

5) 1 365 : 4 680 aaaaaa 6) 36 : 24 : 54

7) 30 : 75 : 45 aaaaaaaa 8) 32 : 12 : 28

9) 36 : 48 : 96 aaaaaaaa 10) 42 : 105 : 147

4. Draw an acute angle with vertex A and mark two points B and D on its sides. Then using a ruler
and compasses, construct a line through B parallel AD and a line through D parallel AB. Mark their
point of intersection C. The quadrilateral ABCD has both pairs of opposite sides parallel and is
called a parallelogram.

a) Measure the lengths of segments AB and DC, AD and BC. What conclusion can you make about the
opposite sides of a parallelogram?

b) Measure the angles A, B, C, and D. What conclusion can you make about the opposite angles of a
parallelogram? What conclusion can you make about the consecutive angles of a parallelogram?

c) Draw the diagonals AC and BD. mark their points of intersection E. Measure the length of the
segments AE and CE, BE and DE. What conclusion can you make about the diagonals of a parallelogram?

5. Solve the problems.

a) In a curb check of 375 cars it was found that 21 had unsafe brakes. What percentage (to the
nearest tenth) of the cars checked had unsafe brakes?

b) In all of William Shakespeare's work, he used 31 534 different words. Of these, 14 356 were used
only once. What percent of the words did he use only once?

6. Evaluate. Round your answer to two decimal places if necessary.

7. Place the remaining of the numbers 1, 2, 3, 4, 5, 6, and 7 into the squares of the magic letter
H so that the sums in the row and the two columns would be the same:

aaaaaaaaa 1)aaaaaaaaaaaaaaaaaaaaaa 2)aaaaaaaaaaaaaaaaaaaaa 3)

8. The number 7 315 can be written as the product of a pair of two-digit numbers. What are these
numbers?

9. Prove that each of the numbers 220 and 284 equals the sum of the proper divisors of the other
number.

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

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Lesson 6

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1. Divide. Express your answers in lowest terms.

2. Fill in the correct number:

Value	Unit	Value	Unit
538	cm	aaaaaaaaaaaaaaaa	m
6400	m	aaa	km
157	mm	aaa	cm
58	m	aaa	km
35.7	cm	aaa	km
0.02	m	aaa	mm
0.08	km	aaa	dm
26	dm	aaa	m
32	mm	aaa	m
203	mm	aaa	cm
8.96	km	aaa	m
19.5	dm	aaa	mm
0.035	km	aaa	cm
0.0024	km	aaa	mm

3. Simplify the ratios (write each ratio in lowest terms).

1) 0.75 : 0.8 aaaaaaaaaaa 2) 1 : 7.5

3) 3.6 : 1 aaaaaaaaaaaaaa 4) 5 ¹/₄ : 1 ¹/₆

5) 5 304 : 4 : 284 aaaaaaa 6) 42 : 63 : 35

7) 12 : 15 : 18 : 30 aaaaaa 8) 117 : 390 : 260

9) 1.14 : 0.36 : 2.1 aaaaaa 10) 2 ⁵/₈ : 3.5 : 4 ²/₃

4. Using a ruler and compasses, construct rhombus ABCD with an acute angle A in which AB = 6 cm.

a) Measure the angles at which the diagonals intersect.

b) Measure the angles BAC and DAC, ABD and CBD.

c) What conclusion can you make about the diagonals of a rhombus?

5. Solve the problems.

a) On an examination, 27 students passed and 5 students failed. Find the failure rate, in percent.

b) For a day, Bobby keeps a record each time he uses mathematics. He sorts clothes to wash. He
puts four shirts in one pile, three pairs of pants in another, and three towels in a third pile.
What percent of the clothes are shirts?

6. Solve the problems.

1) Prove that 2(3a - 5) - (7 - (5 - 6a)) < 0 for all real a.

2) Prove that difference of the numbers 8m - n and 5m - 4n is divisible by 3 for all integers
m and n.

7. Place the remaining of the numbers 1, 2, 3, 4, 5, 6, and 7 into the squares of the figure below
so that the sums in the row, the two columns, and the two diagonls would be the same:

aaaaaaaaa 1) aaaaaaaaaaaaaaaaaaaaaa 2) aaaaaaaaaaaaaaaaaaaaa 3)

8. Solve the following problems.

1) What is the greatest prime divisor of 1001?

2) Find three consecutive whole numbers with a product 2 184.

9. Determine the smallest perfect square that has three different prime numbers as factors.

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

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Lesson 7

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1. Divide. Express your answers in lowest terms.

2. State each ratio by first expressing both quantities in the same unit.

1) 15 cm to 3 m aaaaaaaaaaaa 2) 2 m to 16 cm

3) 150 m to 2 km aaaaaaaaaaa 4) 48 pennies to 3 dimes

5) 180 days to 1 year aaaaaaaa 6) 54 min to 1 hr

7) 3.6 kg to 800 g aaaaaaaaaaa 8) 80 000 m² to 1 ha

9) 3 L to 600 mL aaaaaaaaaaa 10) 60 c to $3

11) 28 mm to 54 cm aaaaaaaa 12) 750 mL to 1.5 L

13) 45 s to 15 min to 1hr

3. Draw a circle with center O. Draw two non-parallel chords AB and CD.

a) Construct the right bisectors of AB and CD.

b) Where do the right bisectors intersect?

4. Fill in the correct number:

Value	Unit	Value	Unit
14	cm2	aaaaaaaaaaaaaaaa	dm2
500	cm3	aaa	dm3
9 000	cm2	aaa	m2
2 500	mm2	aaa	cm2
600 000	mm2	aaa	m2
500	dm2	aaa	m2
0.75	dm3	aaa	cm3
0.0004	m3	aaa	cm3
3.25	L	aaa	cm3
0.003	km2	aaa	m2

5. Find:

1) 14 is 20% of what number? aaaaaaaaa 2) 35 is 25% of what number?

3) 15 is 60% of what number? aaaaaaaaaa 4) 42 is 30% of what number?

5) 56 is 7% of what number? aaaaaaaaaaa 6) 65 is 13% of what number?

7) 143 is 110% of what number? aaaaaaaa 8) 32 is 24% of what number?

9) 78 is 52% of what number?

6. Solve equations.

1) (x + 21) + 38 = 73 aaaaaaaaaa 2) ( x + 56) - 78 = 31

3) (x - 45) + 54 = 27 aaaaaaaaaa 4) (x - 83) + 25 = - 49

5) (65 - x) + 23 = 37 aaaaaaaaaa 6) (79 - x) - 25 = 14

7) 75 - (41 - x) = 32 aaaaaaaaaaa 8) 264 - (107 + x) = 122

7. Place the numbers from 1 to 12 in the squares, which are not placed yet, so that each side adds
up to 25.

aaaaaaaaaaaaaaa 1) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 2)

8. Two prime numbers differ by 2 are called twin primes. Some examples are: 3 and 5, 11 and 13, 29
and 31. Solve the following problems:

1) How many pairs of twin primes can you find which are less than 50?

2) Are numbers 1997 and 1999 twin primes?

9. How many different rectangular solids can be made from 24 cubes of equal size by placing the
cubes side by side?

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

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Lesson 8

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1. Divide. Express your answers in lowest terms.

2. A cash register contains 42 $15 bills, 105 $12 bills, and 84 $10 bills.

a) What is the ratio of $15 bills to $12 bills to $10 bills?

b) What is the ratio of the value of the $15 bills to the value of the $12 bills to the value of
$10 bills?

3. Use a ruler and compasses to construct a rectangle with sides 8 cm and 3 cm. Measure the length
of its diagonals. What conclusion can you make about the diagonals of a rectangle?

4. Find the missing number.

5. Solve the problems.

a) In a class survey, it is found that 35% of the students watched more than 2 h of television each
day. Fourteen students said they watched more than 2 h of television each day. How many students
are in the class?

b) When 4131 people attended a concert, the concert hall was 90% full. What is the capacity of the
hall?

6. Solve equations.

1) - 43x - 215 = 473 aaaaaaaaaaaa 2) 5 905 - 27x = 316

3) 14x + 76 = 100 + 2x aaaaaaaaa 4) 21x - 84 = 940 + 5x

5) 7.2 - (7.7 - x) = 2.4 aaaaaaaaaa 6) 93 - (71.8 - x) = 22.48

7) 3.43 - (x - 6.57) = 8.92 aaaaaaa 8) 8.6 - (x + 2.73) = 1.85

7. Place the numbers from 1 to 12 in the squares, which are not placed yet, so that each side adds
up to 25.

aaaaaaaaaaaaaaa 1) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 2)

8. A man loses his place when the book he is reading accidentally closes. He remembers that the
product of the two page numbers showing was 4 032. What is the sum of the page numbers showing?

9. Fill in the correct number:

Value	Unit	Value	Unit
7.43	g	aaaaaaaaaaaaaaaa	mg
800	kg	aaa	t
0.048	kg	aaa	g
0.35	t	aaa	kg
6 000	mg	aaa	g
14.06	g	aaa	kg
0.004	g	aaa	mg
6 256 000	g	aaa	t

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

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Answers

1. aaa 1) ¹/₃ aaa 2) 1 aaa 3) 3²/₃ aaa 4) 3.6 aaa 5) 3³/₈ aaa 6) ¹/₃

2. a a) a 2 : 5 : 4 aaaaaa b) a 3 : 6 : 4

3. a The diagonals of a rectangle are equal.

4. a 22, 90, 1400, 7000.

5. a a) a 40 aaaaa b) a 4590.

6. a 1) a - 16 aaaa 2) a 207 aaaa 3) a 2 aaaa 4) a 64 aaaa 5) a 2.9 aaaa 6) a 1.28 aaaa 7) a 1.08 aaaa 8) a 4.02 aaaa

7. a 1)a11 aa 3 aa 9 aaa 2 aaaaaaaaaaaaa 2)a10 aa 12 aa 2 aa 1 aaa
aaaaaaa 1 aaaaaaaaaaa 12 aaaaaaaaaaaaaaaa 5 aaaaaaaaaaaa 9
aaaaaaa 8 aaaaaaaaaaaa 7 aaaaaaaaaaaaaaaa 6 aaaaaaaaaaaa 8
aaaaaaa 5 aa 6 aa 10 aa 4 aaaaaaaaaaaaaaaa 4 aaa 11 aa 3 aa 7 aaa

8. a 4032 = 63 x 64, a 63 + 64 = 127.

9.

a Value a	a Unit a	a Value a	a Unit a
a 7.43	a g	a 7430 a	a mg
a 800	a kg	a 0.8	a t
a 0.048	a kg	a 48	a g
a 0.35	a t	a 350	a kg
a 6 000	a mg	a 6	a g
a 14.06	a g	a 0.0146	a kg
a 0.004	a g	a 4	a mg
a 6 256 000 a	a g	a 6.256	t

10. aa 1) 0.978 aaa 2) 0.3092

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Lesson 9

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1. Find the missing value.

2. Find each of the following ratios in lowest terms for the numbers 1, 2, 3,..., 99.

a) the number of multiples of 7 to the number of multiples of 8;

b) the number of multiples of 11 to the number of multiples of 4;

c) the number of multiples of 6 to the number of multiples of 8.

3. Using a ruler and compass, construct a 60^o angle.

4. Fill in the correct number:

Value	Unit	Value	Unit
80 000	cm3	aaaaaaaaaaaaaaaa	m3
4	cm3	aaa	L
550	mm2	aaa	dm2
200 000	mm3	aaa	dm3
25 000	L	aaa	m3
3.7	cm2	aaa	m2
0.005	dm2	aaa	mm2
1.3	m3	aaa	dm3
0.237	dm2	aaa	mm2
2.7	dm2	aaa	cm2

5. Solve the problems.

a) In the latest We-All-Win-Lottery, 0.08% of the tickets sold won prizes. How many tickets were sold if four prizes were won?

b) Nan purchased a new bike on sale. She paid 77% of the original price. If she paid $138.60 for the bike, about what was the original price?

c) At a restaurant Mr. X left a tip of $4.50 for the waiter. This was 15% of the bill. How much was the bill?

6. Solve equations.

7. Place the numbers from 1 to 12 in the squares, which are not placed yet, so that each side adds up to 25.

aaaaaaaaaaaaaaa 1) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 2)

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

1)   1   2   3   4   =   0.5

2)   2   3   4   5   =   0.75

3)   2   3   4   5   =   0.3

4)   2   3   4   5   =   0.4

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

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

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Answers

1. aaa 1) 36 aaa 2) 66 ²/₃ aaa 3) 48 aaa 4) ²⁰/₂₁ aaa 5) 1²⁵/₂₇ aaa 6) ¹²/₃₅ aaa 7) ²¹/₅₂ aaa 8) ⁶⁴/₁₂₇ aaa 9) ⁸⁰/₁₆₁

2. a a) a 7 : 6 aaaaaa b) a 3 : 8 aaaaaa c) a 4 : 3

3. a Hint: construct an equilateral triangle.

4.

a Value a	a Unit a	a Value a	a Unit a
a 80 000	a cm3	a 0.08	a m3
a 4	a cm3	a 0.004	a L
a 550	a mm2	aaa 0.055	a dm2
a 200 000 a	a mm3	a 0.2	a dm3
a 25 000	a L	a 25	a m3
a 3.7	a cm2	a 0.00037	a m2
a 0.005	a dm2	a 50	a mm2
a 1.3	a m3	a 1300	a dm3
a 0.237	a dm2	a 2370	a mm2
a 2.7	a dm2	a 270	a cm2

5. a a) a 5000 aaaaa b) a $180 aaaaa C) a $30

6. a 1) a 9 aaaa 2) a 2 aaaa 3) a 3553 aaaa 4) a 3382 aaaa 5) a 20 aaaa 6) a 2 aaaa 7) a 141 aaaa 8) a 19780 aaaa

7. a 1)a10 aa 3 aa 11 aaa 1 aaaaaaaaaaaaa 2)a 9 aa 12 aa 1 aaa 3 aaa
aaaaaaa 9 aaaaaaaaaaaa 12 aaaaaaaaaaaaaaaa 10 aaaaaaaaaaaa 5
aaaaaaa 2 aaaaaaaaaaaaa 5 aaaaaaaaaaaaaaaaa 2 aaaaaaaaaaa 11
aaaaaaa 4 aa 6 aaa 8 aaa 7 aaaaaaaaaaaaaaaaa 4 aaa 8 aa 7 aaa 6

8.

1) a (1 - 2 + 3) / 4 a = a 0.5

2) a 2 3 / 4 - 5 a = a 0.75

3) a (2 x 3) / (4 x 5) a = a 0.3

4) a (2 x 3 - 4) / 5 a = a 0.4

9. a 112

10. aa 1) 1 aaa 2) 0.9 aaa 3) 2 ³²/₆₃ aaa 4) 10

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Lesson 10

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1. Find the missing value.

2. The ratio of boys to girls in a school is 8 : 7. There are 392 boys in the school. How many girls are there?

3. Using a ruler and compass, construct a 45^o angle.

4. Fill in the correct number for the mass of water:

Volume	Unit	Mass	Unit
6	mL	aaaaaaaaaaaaaaaa
7	L	aaa
8	kL	aaa
6.03	L	aaa
0.056	L	aaa
9.364	kL	aaa
6.5	mL	aaa
15.342	kL	aaa

5. Solve the problems.

a) In a recent election with three candidates, Mrs. Jones received 10 575 votes, Mr. Smith received 7 990 votes, and Mr. Green received 2 585 votes. What was the number of eligible votes, if 90% of those eligible to vote did so?

b) On a test of 100 questions, Sue had 50% more right answers than she had wrong answers. Each answer was either right or wrong. How many questions did she answer correctly?

6. Solve equations.

7. Place the numbers from 1 to 12 in the squares, which are not placed yet, so that each side adds up to 25.

aaaaaaaaaaaaaaa 1) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 2)

8. A book falls open at a certain place. The product of the numbers of the two facing pages is 25122. What are the page numbers?

9. Find the number of positive integers that are less than 1000 and that are not divisible by 2 or by 3.

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

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Answers

1. aaa 1) 1 ³/₇ aaa 2) 4.2 aaa 3) 25 aaa 4) 0.9 aaa 5) 0.4 aaa 6) 0.1 aaa 7) 2 ¹/₃ aaa 8) 11.25 aaa 9) 12 ⁵/₆ aaa 10) 23 aaa 11) 10 aaa 12) 8 ¹/₃

2. a 343

3. a Hint: construct an isosceles right-angled triangle or bisect a 90^o-angle.

4.

a Volume a	a Unit a	a Mass a	a Unit a
a 6	a mL	a 6	a g
a 7	a L	aaa 7	a kg
a 8	a kL	aaa 8	a t
a 6.03	a L	aaa 6030	a g
a 0.056	a L	aaa 56	a g
a 9.364	a kL	aaa 9364	a kg
a 6.5	a mL	aaa 6.5	a g
a 15.342	a kL	aaa 15342 a	a kg

5. a a) a 235000 aaaaa b) a 60 aaaaa

6. a 1) a 1 aaaa 2) a 84 aaaa 3) a -21 ²/₇ aaaa 4) a 12 aaaa 5) a 17 aaaa 6) a 25 aaaa

7. a 1)aa8 aa 2 aa 12 aaa 3 aaaaaaaaaaaaaa 2)a 8 aa 11 aa 4 aaa 2 aaa
aaaaaaa 1 aaaaaaaaaaaaa 7 aaaaaaaaaaaaaaaaa 1 aaaaaaaaaaaaa 6
aaaaaa 11 aaaaaaaaaaaaa 9 aaaaaaaaaaaaaaaaa 9 aaaaaaaaaaaa 12
aaaaaaa 5 aa 4 aa 10 aaaa 6 aaaaaaaaaaaaaaaaa 7 aa 10 aa 3 aaa 5

8. a 158, 159.

9. a 333.

10. aa 1) ¹/₄ aaa 2) 7 aaa 3) ¹/_0.5 aaa 4) 0.25

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