




Math Lessons for Gifted Students Level E (grade 7) Center Impulse Weekend and evening classes for gifted students grades 59 Canada, ON, L4K 1T7, Vaughan (Toronto), 80 Glen Shields Ave., Unit #10. Phone (416)8267270 vluzgin@hotmail.com Content Click on the lesson! 
1. Calculate mentally and record your answer. Hint: use the Distributive Laws a(b + c) = ab + ac, a(b  c) = ab  ac. 2. Joan earns $6.40 per hour. She receives an increase in pay of 5%. 3. If M is a point ^{4}/_{7} of the way from A to B on the number line shown, what is the number located at M? 4. Solve the following problems. 5. Study Appendix 2. Apply congruent triangles theorems to solve the following problems. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. Find an algebraic expression that generates each of these sequences of numbers. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. Find the perimeter of the given figure. 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problems below. 12. Find the missing term. 2. aa a) $0.32 aaaaaaaaaa 2) $6.72. 3. aa 62 4. aaa a) 90 miles aaa b) 5.4 miles. 5. a)
b)
c)
or
6. aaa a) ^{1}/_{5}. aaaaaa b) ^{11}/_{24} 7. aaa 1) 36, 38; aaaaaaaa 2) 76, 78; aaaaaaa 3) 56, 72. 8. 9. a 44 cm 10. aa 1) 3 536 aaa 2) ^{1}/_{8} 11. 12. a 1) 3 a 2) 5 a 3) 10 a 4) 18 a 5) 80 a 6) 2 a 7) 6 a 8) 9 
1. Calculate mentally and record your answer. Hint: use the Distributive Laws a(b + c) = ab + ac, a(b  c) = ab  ac. 2. Solve the following problems. 3. Points A, B, C, and D lie on a straight line, and B is between A and C, C is between B and D. 4. Solve the following problems. 5. Solve the following problems. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. Find an algebraic expression that generates each of these sequences of numbers. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. Determine the distance around the outside of the given figure. 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problems below. 12. Find the missing term. 2. aa a) 3.57%. aaaaaaaaaa 2) 23.05%. 3. aa a) 4 cm. aa b) 30 cm. 4. aaa a) 2.54 m aaa b) 5 feet 1 inch. 5. a)
b)
c)
6. aaa a) $1.55 per gallon. aaaaaa b) $369. 7. aaa 1) 256 x 2 = 512, 512 x 2 = 1024; aaaaaaaa 2) 8^{2}  1 = 63, 9^{2}  1 = 80; aaaaaaa 3) 17 + 6 = 23, 23 + 7 = 30. 8. 9. a 58 cm 10. aa 1) 0.64 aaaaaaaaaaaaaaa 2) 47.9 11. 12. a 1) 0.9 a 2) 0.5625 a 3) 3 a 4) 18 a 5) 0.5 a 6) 2 ^{1}/_{3} a 7) 5 a 8) 3.28125 
1. Calculate mentally and record your answer. Hint: use the Distributive Laws a(b + c) = ab + ac, a(b  c) = ab  ac. 2. Solve the following problems. 3. A, B, C, and D are four points on a line such that AB : AC = 3 : 5 and BC : CD = 7 : 12. If CD is 20 cm long, find the length of AB. 4. Solve the following problems. 5. Solve the following problems. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. Find an algebraic expression that generates each of these sequences of numbers. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. Write expressions for the perimeter and the area of the figure below. 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problem below. 12. Find the unknown value in each of the following proportions. 2. aa a) 35.14%; aaaaaaaaaa 2) 6.075 million. 3. aa 17.5 cm. 4. aa a) 42.283 quart aaaaaa b) 197.53 acre. 5. a)
b)
c)
6. aaa a) 56.84 inches. aaaaaa b) $27.5. 7. aaa 1) 63 x 2 + 1 = 127, 127 x 2 + 1 = 255; aaaaaaaa 2) 7^{2} = 49, 8^{2} = 64; aaaaaaa 3) 243 x 3 = 729, 729 x 3 = 2 187. 8. 9. aa 1) P = 2x + 2y; aaaaaaaaaaaaaaa 2) A = xy  (x  z)(y  u) = zu  xu  yz. 10. aa 1) 2 ^{7}/_{9}; aaa 2) ^{4}/_{7; } aaa 3) 0.5 aaa 4) 0.5. 11. 12. a 1) 16.8; aaa 2) 2.5 aaa 3) 6.4 aaa 4) 2.25 
1. Calculate mentally and record your answer. 2. Greta earns $16.50/h and receives a raise of 4.2%. 3. Solve the following problems. 4. Ray tells his sister, "The metric system is easy because it is based on decimals." If one customary gallon is 3.7852 liters, how many gallons are 10 liters? 5. Prove the following theorems that provide sufficient condicians to have congruent rightangled triangles. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. Find an algebraic expression that generates each of these sequences of numbers. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. What is the perimeter of the figure ABCDEFGHIJ, if AB = 14 cm, AJ = 6 cm, GF = 3 cm, and ED = 4 cm? 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problem below. 12. Find the unknown value in each of the following proportions. 2. aa a) $0.69; aaaaaaaaaa 2) $17.19. 3. aaa 1) 48, 84; aaa 2) 42, 18. 4. aa 2.64 gallons 5. (LL)
(HA)
(LA)
6. aaa a) $0.56; aaaaaa b) 11^{1}/_{3} pounds. 7. aaa 1) 13, 21; aaaaaaaa 2) 5040, 40320; aaaaaaa 3) 216, 343. 8. 9. aa 54 cm. 10. aa 1) 3; aaa 2) 3; aaa 3) ^{49}/_{216} aaa 4) ^{3}/_{8}. 11. 12. a 1) 2.55; aaa 2) 1.25 aaa 3) 17 aaa 4) ^{1}/_{7}. 
1. Calculate mentally and record your answer. 2. A property was purchased for $80 000 and later sold for $100 000. 3. Solve the following problems. 4. Solve the following problems. 5. Solve the following problems. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. Find an algebraic expression that generates each of these sequences of numbers. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. Find expressions for the perimiter and the area of the figure below. 10. Find the value of the following (do without a calculator and show all your work). Round your answer to the nearest hundredth if necessary. 11. Find the missing digits in the problem below. Find two possible solutions. 12. Find the unknown value in each of the following proportions. 2. aa a) 25%; aaaaaaaaaa 2) 125%. 3. aaa a) 343; aaa b) Alex: $770, Fred: $910. 4. aa a) 0.386 sq. miles. aa b) 567 000. 5.
6. aaa a) 26^{2}/_{3} cm; aaaaaa b) $12. 7. aaa 1) 13, 15; aaaaaaaa 2) 28, 36; aaaaaaa 3) 37, 50. 8. 9. aa P = 2(x + y + z) cm, A = xy  zu cm^{2}. 10. aa 1) 3.07; aaa 2) 68.8. 11. 12. a 1) 3; aaa 2) 5; aaa 3) 10.5; aaa 4) 4. 
1. Calculate mentally and record your answer. 2. Solve the following problems. 3. Solve the following problems. 4. Solve the following problems. 5. ABC is an isosceles triangle with AB = AC. 6. Solve the following problems. 7. Predict the next two numbers in each pattern. What expression creates the number pattern? 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. A rectangular flower bed, dimensions 16 yards by 12 yards, is surrounded by a walk 3 yards wide. What is the area of the walk in square yards? 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problem below. 12. Calculate the values of x and y in each of the following proportions. 2. aa a) 762 km; aaaaaaaaaa 2) $ 2 896 175. 3. aaa a) 0.9 m; aaa b) 28^{o}. 4. aa a) 750 miles per hour; aa b) 375 miles per hour. 5.
6. aaa a) ^{2}/_{5}; aaaaaa b) $136.5. 7. aaa 1) 19, 22, 3n  2; aaaaaaaa 2) 33, 38, 5n  2; aaaaaaa 3) 59, 67, 8n + 3. 8. 9. aa 204 sq. yards. 10. aa 1) 78.7; aaa 2) 1. 11. 12. a 1) x = 5, y = 2; aaa 2) x = 12, y = 16; aaa 3) x = 4, y = 9. 
1. Calculate mentally and record your answer. 2. Solve the following problems. 3. Solve the following problems. 4. Solve the following problems. 5. Prove that if ABC is an isosceles triangle, 6. Solve the following problems. 7. Predict the next two numbers in each pattern. What expression creates the number pattern? 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. In a triangle ABC, AD __ BC, BE __ AC, AD = 4 cm, BC = 6 cm, AC = 5 cm. Find the length of BE. 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problem below. 12. Calculate the values of x and y in each of the following proportions. 2. aa a) reduced by 43.75%; aaaaaaaaaa 2) $ 10/h. 3. aaa a) 6.667 kg; aaa b) 30 g. 4. aa a) $ 382.73 aa b) $ 234. 5.
6. aaa a) ^{1}/_{5}; aaaaaa b) ^{7}/_{12}; 7. aaa 1) 47, 54, 7n  2; aaaaaaaa 2) 51, 66, n^{2} + 2. 8. 9. aa 4.8 cm. 10. aa 1) 6; aaa 2) 45.9. 11. 12. a 1) x = 9, y = 3^{1}/_{3}; aaa 2) x = 4, y = 12; aaa 3) x = 14, y = 2. 
1. Calculate mentally and record your answer. 2. Solve the following problems. 3. Solve the following problems. 4. Solve the following problems. 5. In a quadrilateral ABCD, AB = CB and AD = CD. 6. Solve the following problems. 7. Suppose this pattern were continued: 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. Using a 9 inch x 12 inch sheet of paper lengthwise, a typist leaves a 1inch margin on each side and a 1.5 inch margin on top and bottom. What fractional part of the page is used for typing? 10. Find the value of the following (do without a calculator and show all your work). 11. Find the missing digits in the problem below. 12. Find the number of digits that are required to number the pages of a book from 1 to 250. 2. aa a) $112.70; aaaaaaaa 2) $42.75. 3. aaa a) 610 g; aaaaaaaaa b) 533 g. 4. aa a) ^{1}/_{8}; aaaaa b) 3.629 kg; aaaaa c)1 567.6 kg. 5.
6. aaa a) 9; aaaaaa b) 128. 7. aaa 19, 2n + 1. 8. 9. aa ^{5}/_{9}. 10. aa 1) 145; aaa 2) 125. 11. 12. a 642. 
1. Calculate mentally and record your answer. 2. Solve the following problems. 3. Solve the following problems. 4. Solve the following problems. 5. Prove that 6. Solve the following problems. 7. Suppose this pattern were continued: 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. What is the area of an isosceles rightangles triangle with a hipotenuse 6 cm long? 10. Find the value of the following (do without a calculator and show all your work). 11. Each letter represents a different digit. Find the values of each letter. 12. The number of digits used to number all the pages of a book was 570. Find the number of pages in the book. 2. aa a) $62.62; aaaaaaa 2) $39.95. 3. aa a) 9 : 8; aaaaaaaaa b) 10 and 18. 4. aa a) 6 gallons; aaaaa b) 7 855.4 gallons. 5. a)
b)
6. aaa a) 1800; aaaaaa b) ^{1}/_{6}. 7. aaa 40, 3n + 1. 8. 9. aa 9 cm^{2}. 10. aa 1) 5.003; aaa 2) 100. 11. aa A = 9, B = 2, C = 1. 12. a 226. 
1. Place any of the four operations (+, , x, :) in the empty boxes to make each statement true. 2. Solve the following problems. 3. Solve the following problems. 4. Solve the following problems. 5. In the diagram, AB = DC and AC = DB. Prove that AE = DE. 6. Solve the following problems. 7. A series of cubes are placed together as shown. The total number of faces that show are counted. 8. Make the statements true by inserting grouping symbols (parenthesis) and any of the four operations (+, , x, :). 9. In a triangle ABC, AB = 7 cm, D is a point on BC such that BD = AD. Find the perimeter of the triangle ABC, if the perimeter of the triangle ACD is 15 cm. 10. Find the value of the following (do without a calculator and show all your work). 11. Each letter represents a different digit. Find the values of each letter. 12. Each of the numbers 1, 2, 3, and 4 is represented by one of the letters A, B, C, and D (not necessarily in that order). Find the largest possible sum of the 3digit numbers BAC, CAD, and DAC. 2. aa a) $17 000; aaaaaaa 2) $13.57. 3. aa a) 72, 84; aaaaaaaaa b) 45^{o}, 60^{o}, and 75^{o}. 4. aa a) 2 623; aaaaa b) 0.68 kg. 5.
6. aaa a) 10; aaaaaa b) $ 19 531.25. 7. aaa 79, 5n + 4. 8. 9. aa 22 cm. 10. aa 1) 1.72; aaa 2) 6.875. 11. aa 1) A = 1, B = 5, C = 4, D = 2, E = 0; aa 2) A = 2, B = 3, C = 5, D = 9 12. a 941. 
Triangle's Classification.

Congruent Triangles. Isosceles Triangle.

Conditional Statements. Perpendicular and Angle Bisectors.
A point is on the perpendicular bisector of a line segment iff it is equidistant from the ends of the line segment.


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