Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 Chapter 9 Items marked A, B, C are increasing in difficulty. Group A questions are the most basic while Group C are the most difficult and require higher levels of thinking skills. The level of difficulty is only relative to the same section. Most problems include random number generation within individual problems. [n] indicates n problems types are available in the topic. Note: Some problems require rounding. At each step, round to the specified decimal. For example, if has triangle sides a and b, round c after finding its value and before continuing any further calculations. Section 9.1 Objective: Students will be able to find and approximate square roots. 9_1 Square Roots [4] Find positive and negative square roots of perfect squares. 9_1 Approximate Square Roots [4] Approximate positive and negative square roots. 9_1 Solve Using Square Roots A [2] Solve x^2 = b form. Enter multiple solutions separated by a semi colon. Ex. x^2 = 9. Solutions would be entered as 3; 3. 9_1 Solve Using Square Roots B [3] Solve using one step. 9_1 Solve Using Square Roots C [3] Solve using one step and approximate a decimal value. Section 9.2 Objective: Students will be able to define and work with irrational numbers. 9_2 Classify Real Numbers [4] Multiple Selection Choose all rational or irrational values. 9_2 Order Real Numbers A [5] Use <, >, or = to compare rational and irrational numbers. 9_2 Order Real Numbers B [4] Compare rational and irrational numbers involving square roots. Section 9.3 Objective: Students will be able to use the Pythagorean Theorem to solve problems. 9_3 Find Leg of Rt. Triangle A [2] Find leg of right triangle. Integer solutions. 9_3 Find Hyp. of Rt. Triangle A [1] Find hypotenuse of right triangle. Integer solutions. 9_3 Determine Right Triangle [3] Multiple selection. Select all values which form a right triangle. 9_3 Find Leg of Rt. Triangle B [4] Find leg of a right triangle. Decimal solutions. 9_3 Find Hyp. of Rt. Triangle B [2] Find the hypotenuse of a right triangle. Decimal solutions. Section 9.4 Objective: Students will be able to use the Pythagorean Theorem to solve real life problems. 9_4 Determine Pythagorean Triple [3] Multiple selection. Select each set of values which is a Pythagorean Triple. 9_4 Perimeter and Area A [2] Given two legs of a triangle, find the perimeter and area. Note: Round all answers to one decimal place when a side of the triangle is found. Use the rounded value in the determination of perimeter and area. 9_4 Perimeter and Area B [2] Given a side and hypotenuse, find the perimeter and area. 9_4 Perimeter and Area C [2] Given the area and a leg of the triangle, find the perimeter. 9_4 Word Problems [3] Solve right triangle word problems to find length of a side or area of a right triangle.
Lincoln Public Schools Math 8 McDougal Littell Middle School Math Course 3 Please note: This demo is a one problem sample from each topic. Most problems are random number problems and consist of multiple types for each topic. Some fraction problems are not properly formatted in this demo due to the conversion to Word form. They will appear properly formatted when used in EDU. 9_1 Square Roots [4] Find positive and negative square roots of perfect squares. Find 4 Your Answer: 2 Correct Answer: 2 Find 4 4 = 2 2 = 2 9_1 Approximate Square Roots [4] Approximate positive and negative square roots. Find 457 Round answers to the nearest tenth. Your Answer: 21.4 Correct Answer: 21.4 Find 457 Round answers to the nearest tenth. = 21.377558 457 Round to the nearest tenth. 21.4
9_1 Solve Using Square Roots A [2] Solve x^2 = b form. Enter multiple solutions separated by a semi colon. Ex. x^2 = 9. Solutions would be entered as 3; 3. Solve the equation. x 2 = 256 Your Answer: 16; 16 Correct Answer: 16; 16 Solve the equation. x 2 = 256 Take the square root of both sides. x = ± 256 x = ± 16 Enter the answers as 16; 16 9_1 Solve Using Square Roots B [3] Solve using one step. Solve the equation. x 2 + 87 = 208 Round to the nearest tenth when necessary. Your Answer: 11; 11 Correct Answer: 11; 11 Solve the equation. x 2 + 87 = 208 Subtract 87 from both sides. x 2 = 121 Take the square root of both sides. x = ± 121 x = ± 11 Enter the answers as 11; 11
9_1 Solve Using Square Roots C [3] Solve using one step and approximate a decimal value. Solve the equation. x 2 59 = 10 Round to the nearest tenth when necessary. Your Answer: 8.3; 8.3 Correct Answer: 8.3; 8.3 Solve the equation. x 2 59 = 10 Add 59 to both sides. x 2 = 69 Take the square root of both sides. x = ± 69 x = ± 8.3 Enter the answers as 8.3; 8.3 9_2 Classify Real Numbers [4] Multiple Selection Choose all rational or irrational values. Check each box beside a value which is rational. Choice Selected Points 0.565565556... No 16 Yes +1 6.226226226... Yes +1 43 No Total correct answers: 2 Partial Grading Explained 16 0.565565556... 43 is a rational number because 16 is a perfect square. The square root of 16 is 4; is an irrational number since the decimal does not repeat the same pattern each time. is an irrational number since the square root of 43 is not a perfect square and the decimal 6.557439 does not terminate or repeat. 6.226226226... is a rational number since the decimal does repeat the same pattern 226 each time. 9_2 Order Real Numbers A [5] Use <, >, or = to compare rational and irrational numbers.
Your answer: Your response Compare the values using <, > or =. 0. 18 = 2 11 Correct response Compare the values using <, > or =. 0. 18 = 2 11 Compare the values 0. 18 and using <, > or =. 2 11 2 11 is 0.181818 which is equal to 0.18181818... 9_2 Order Real Numbers B [4] Compare rational and irrational numbers involving square roots. Your answer: Your response Compare the values using <, > or =. Correct response Compare the values using <, > or =. 16 < 5 16 < 5 Compare the values using <, > or =. 16 16 and 5 = 4 and is less than 5
9_3 Find Leg of Rt. Triangle A [2] Find leg of right triangle. Integer solutions. Find the length of the missing leg of the right triangle. Round answers to the nearest tenth when necessary. a =, b = 12, c = 13 Your Answer: 5 Find the length of the missing leg of the right triangle. Round answers to the nearest tenth when necessary. a =, b = 12, c = 13 Pythagorean Theorem Substitute a 2 + 12 2 = 13 2 Evaluate powers a 2 + 144 = 169 Solve for a 2 a 2 = 25 Take the positive square root of both sides. a = 25 = 5 9_3 Find Hyp. of Rt. Triangle A [1] Find hypotenuse of right triangle. Integer solutions. Find the length of the hypotenuse of the right triangle. Round answers to the nearest tenth when necessary. a = 15, b = 20, c = Your Answer: 25 Find the length of the hypotenuse of the right triangle. Round answers to the nearest tenth when necessary. a = 15, b = 20, c = Pythagorean Theorem Substitute 15 2 + 20 2 = c 2 Evaluate powers 225 + 400 = c 2 Add 625 = c 2 Take the positive square root of both sides. c = 625 = 25
9_3 Determine Right Triangle [3] Multiple selection. Select all values which form a right triangle. Place a check beside each set of sides of a triangle which form a right triangle. Choice Selected Points a = 24, b = 32, c = 40 Yes +1 a = 24, b = 45, c = 51 Yes +1 a = 12, b = 35, c = 37 No Total correct answers: 3 Partial Grading Explained Place a check beside each set of sides of a triangle which form a right triangle. For each triangle, use the pythagorean theorem to check if the triangle is a right triangle. a = 12, b = 35, c = 37 144 + 1,225 1,369 1,369 1,369 The statement is true. The triangle is a right triangle. a = 24, b = 32, c = 40 576 + 1,024 1,600 1,600 1,600 The statement is true. The triangle is a right triangle. a = 24, b = 45, c = 51 576 + 2,025 2,601 2,601 2,601 The statement is true. The triangle is a right triangle. 9_3 Find Leg of Rt. Triangle B [4] Find leg of a right triangle. Decimal solutions. 20 ft 26 ft Determine the missing length. Round to the nearest tenth if necessary. Your Answer: 16.6 ft Correct Answer: 16.6 ft
20 ft 26 ft Determine the missing length. Round to the nearest tenth if necessary. Use the pythagorean theorem. Substitute a 2 + 20 2 = 26 2 Evaluate powers a 2 + 400 = 676 Solve for a 2 a 2 = 276 Take the positive square root of both sides. a = 276 = 16.6 and the units will be ft 9_3 Find Hyp. of Rt. Triangle B [2] Find the hypotenuse of a right triangle. Decimal solutions. 16 in 11 in Determine the missing length. Round to the nearest tenth if necessary.
Your Answer: 19.4 in Correct Answer: 19.4 in 16 in 11 in Determine the missing length. Round to the nearest tenth if necessary. Pythagorean Theorem Substitute 16 2 + 11 2 = c 2 Evaluate powers 256 + 121 = c 2 Add 377 = c 2 Take the positive square root of both sides. c = 377 = 19.4 and the units would be in 9_4 Determine Pythagorean Triple [3] Multiple selection. Select each set of values which is a Pythagorean Triple. Place a check beside each set of numbers which form a pythagorean triple. Choice Selected Points 12, 35, 37 Yes +1 24, 45, 52 No 24, 32, 39 No Total correct answers: 1 Partial Grading Explained Place a check beside each set of numbers which form a pythagorean triple. For each set of numbers, use the pythagorean theorem to check if The set of numbers is a pythagorean triple.
12, 35, 37 144 + 1,225 1,369 1,369 1,369 The statement is true. The numbers form a pythagorean triple. 24, 32, 39 576 + 1,024 1,521 1,600 1,521 The statement is false. The numbers do not form a pythagorean triple. 24, 45, 52 576 + 2,025 2,704 2,601 2,704 The statement is false. The numbers do not form a pythagorean triple. 9_4 Perimeter and Area A [2] Given two legs of a triangle, find the perimeter and area. Note: Round all answers to one decimal place when a side of the triangle is found. Use the rounded value in the determination of perimeter and area. Your response Find the perimeter and area of the triangle with sides a = 16 cm, b = 21 cm, and c =. Answers should be accurate to the tenths place. Enter square units such as m 2 with a ^ as m^2 Perimeter = 63.4 cm (50%) Area = 168 cm^2 (50%) Correct response Find the perimeter and area of the triangle with sides a = 16 cm, b = 21 cm, and c =. Answers should be accurate to the tenths place. Enter square units such as m 2 with a ^ as m^2 Perimeter = 63.4 cm Area = 168 cm^2 Find the perimeter and area of the triangle with sides a = 16, b = 21, and c =. Answers should be accurate to the tenths place. Enter square units such as m 2 with a ^ as m^2 Find the hypotenuse. 16 2 + 21 2 = c 2 256 + 441 = c 2 697 = c 2 c = 697 = 26.4 Perimeter is the sum of all of the sides. P = 16 cm + 21 cm + 26.4 cm = 63.4 cm
A = ½ base height A = ½ 16 cm 21 cm = 168 cm^2 9_4 Perimeter and Area B [2] Given a side and hypotenuse, find the perimeter and area. Your response Correct response 15 in 27 in 15 in 27 in Find the perimeter and area of the triangle. Round to the nearest tenth if necessary. Enter square units such as m 2 with a ^ as m^2 Perimeter = 64.4 in (50%) Area = 168 in^2 (50%) Find the perimeter and area of the triangle. Round to the nearest tenth if necessary. Enter square units such as m 2 with a ^ as m^2 Perimeter = 64.4 in Area = 168 in^2 15 in 27 in Find the perimeter and area of the triangle. Round to the nearest tenth if necessary. Find the missing side. a 2 + 15 2 = 27 2 a 2 + 225 = 729 a 2 = 504 a = 504 = 22.4 and the units will be in Perimeter is the sum of all of the sides. P = 22.4 in + 15 in + 27 in = 64.4 in A = ½ base height A = ½ 22.4 in 15 in = 168 in^2 9_4 Perimeter and Area C [2] Given the area and a leg of the triangle, find the perimeter.
Find the perimeter of the triangle. Round all decimals to 1 decimal place where necessary. Area = 28 m 2, a = 6 m Your Answer: 26.4 m Correct Answer: 26.4 m Find the perimeter of the triangle. Round all decimals to 1 decimal place where necessary. Area = 28 m 2, a = 6 m Use the area to find side b. Area = ½ base height 28 m 2 = ½ 6 m b 28 m 2 = 3 m b 9.3 m = b Find the hypotenuse. 6 2 + 9.3 2 = c 2 36 + 86.49 = c 2 122.49 = c 2 c = 122.49 = 11.1 Perimeter = sum of all of the sides P = 6 m + 9.3 m + 11.1 m P = 26.4 m
9_4 Word Problems [3] Solve right triangle word problems to find length of a side or area of a right triangle. Surveyors are trying to estimate the area of Welkerville Lake shown in the diagram at the left. The length of W Shore Dr. is 3,600 ft. The length of S Shore Dr. is 5,140 ft. To the nearest square foot, what is the area of the lake Your Answer: 9252000 Correct Answer: 9,252,000 Surveyors are trying to estimate the area of Welkerville Lake shown in the diagram at the left. The length of W Shore Dr. is 3,600 ft. The length of S Shore Dr. is 5,140 ft. To the nearest square foot, what is the area of the lake Area = ½ base height Area = ½ 5,140 3,600 Area = 9,252,000 To the nearest square foot, the lake is 9,252,000 ft 2