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Exam Review 1 – Squares, Square Roots, & Pythagorean TheoremMultiple ChoiceIdentify the choice that best completes the statement or answers the question.____1.Which of these numbers is not a perfect square: 121, 2, 100, or 4?a.121b.2c.100d.4____2.Which of these numbers is a perfect square: 50, 20, 25, or 15?a.50b.20c.25d.15____3.What is the side length of a square with area 25 cm2?a.5 cmb.12.5 cmc.6.25 cmd.20 cm____4.Which 2 consecutive square numbers is 54 between?a.53 and 55 b.28 and 32c.49 and 64d.12 and 16 ____5.What is the area of a square with side length 10 units?a.200 square unitsc.20 square unitsb.40 square unitsd.100 square units____6.Find the square of 11.a.121b.22c.44d.242____7.Find a square root of 64.a.32b.8c.16d.32____8.Find 82.a.8b.64c.16d.32____9.Find .a.105b.500c.15d.10____10.The area of a square is 8 m2. Find its side length.a. mb. mc. md.2 m____11.The area of a square is 24 m2. Find its side length.a. mb. mc. md.6 m____12.Find .a.25b.5c.625d.156.25____13.Between which 2 consecutive whole numbers is ?a.27 and 28b.110 and 112c.100 and 121d.10 and 11____14.What is the greatest whole number less than ?a.27b.7c.8d.13____15.Find the area of the indicated square.a.50 square unitsc.400 square unitsb.30 square units d.7.1 square units____16.Find the length of the hypotenuse.a.9 mb.10 mc.11 md.12 m____17.The areas, in square centimetres, of the smaller squares on the sides of a right triangle are given. Determine the area of the largest square.a.61 cm2 b.22 cm2 c.11 cm2 d.330 cm2 ____18.Ingrid is making a quilt using equal sized squares. Each square has side length 40 cm. What is the diagonal length of a square? Round your answer to the nearest tenth.a.28.3 cmb.113.2 cmc.69.3 cmd.56.6 cmShort Answer19.Which whole numbers between 67 and 141 are perfect squares?20.Find a square root of 900.21.List the factors of 70 in ascending order.22.Find 92 + 52.23.Order from least to greatest: 52, 42, , 1924.The side length of a square is m. Find its area.25.Between which 2 consecutive whole numbers is ?26.Which of the following square roots does not lie between 15 and 16?, , , 27.Is 5 greater than, less than, or equal to ?28.Find the approximate side length of a square with area 242 cm2.29.Label the hypotenuse on this right triangle.30.The hypotenuse of a right triangle is 13 cm.The length of one of the legs is 7 cm.Find the length of the other leg.31.Which has the longer diagonal, the rectangle or the square?32.A square has area 169 cm2. Determine the length of the sides and the length of the diagonal.33.Is this set of numbers a Pythagorean triple? How do you know?2, 21, 2934.Determine whether a triangle with each set of side lengths is a right triangle. a)9 cm, 12, cm, 15 cmb)24 cm, 10 cm, 26 cmc)22 cm, 21, cm, 30 cmd)21 cm, 20 cm, 29 cm35.The area, in square centimetres, of the square on each side of a triangle is given. Is the triangle a right triangle? How do you know?36.Kalsa wants to determine if her garden is a rectangle. The garden has side lengths 24 m and 10 m and diagonal length 26 m.Determine whether the garden is a rectangle.37.Randall drew a right triangle with sides cm and cm.How long is the third side? Give your answer to 1 decimal place.Give 2 possible answers.38.An airplane is 105 km due south of an airport. Another airplane is 80 km due west of the airport. How far apart are the planes? Give your answer to the nearest kilometre.39.A rectangular carpet measures 6 m by 5 m. What is the distance between opposite corners? Give your answer to 1 decimal place.40.The diagonal of a TV screen is 71 cm. The screen is 63 cm wide. What is the height of the screen? Give your answer to 1 decimal place.Problem41.I am a square number less than 400.The sum of my digits is 9.What square numbers might I be?Show your work.42.Tammy wants to install a wallpaper border around the perimeter of her bedroom.The floor area of her bedroom is 361 m2.She has 72 m of wallpaper.Does she have enough wallpaper? How do you know?43.Use 1-cm grid paper.Draw as many different rectangles as you can with area 36 cm2.Find the base and height of each rectangle.Record the results in a table.Base (cm)Height (cm)Perimeter (cm)Which rectangle has the least perimeter?What can you say about this rectangle?44.Find the square of each number.a)8b)9c)745.a)List the factors of each number in ascending order.i)24ii)20iii)25iv)50b)Which number in part a is a square number? How can you tell?46.Which whole number is closer to?47.Sarah says triangle ABC is a right triangle.Is she correct? Justify your answer.48.A triangle has side lengths cm, cm, and cm.Is this triangle a right triangle?Do these side lengths form a Pythagorean triple? Explain.49.A rectangular carpet measures 7.2 m by 5.5 m. Calculate the length of the diagonal. Give your answer to the nearest tenth.50.Find the length of BC to the nearest tenth. Show your work.Exam Review 1Answer SectionMULTIPLE CHOICE1.B2.C3.A4.C5.D6.A7.B8.B9.D10.C11.A12.A13.D14.B15.A16.B17.A18.DSHORT ANSWER19.81, 100, 12120.3021.1, 2, 5, 7, 10, 14, 35, 7022.81 + 25 = 10623.42, , 19, 5224.A = 63 m225.3 and 426.27.5 is less than 28.15.56 cm485775-1111250029.30. cm31.Rectangle: 15.62 unitsSquare: 15.56 unitsThe rectangle has the longer diagonal.32.Side length: 13 cmDiagonal length: 18.4 cm33.No, because .34.a) Right triangleb)Right trianglec)Not a right triangled)Right triangle35.No. 36.242 + 102 = 262The garden is a rectangle because all angles are right angles.37.If the third side is the hypotenuse, the hypotenuse is 6.3 cm.If the third side is a leg, the leg is 2.8 cm.38.132 km39.7.8 m40.32.7 cmPROBLEM41.15 x 15 = 22518 x 18 = 32442.Find the side length of the bedroom:Find a number which, when multiplied by itself, gives 361.19 ? 19 = 361So, the bedroom has side length 19 m.Perimeter is the distance around the bedroom.So, P = 19 m + 19 m + 19 m + 19 m= 76 mThe perimeter of the bedroom is 76 m.Tammy does not have enough wallpaper because the amount of wallpaper she has is less than the perimeter of her bedroom.43.Base (cm)Height (cm)Perimeter (cm)136742184031230492666249426123301824036174The rectangle with side length 6 cm has the least perimeter.The rectangle is a square.44.a) The square of 8 is: b)The square of 9 is: c)The square of 7 is: 45.a) i)24: 1, 2, 3, 4, 6, 8, 12, 24ii)20: 1, 2, 4, 5, 10, 20iii)25: 1, 5, 25iv)50: 1, 2, 5, 10, 25, 50b)25 is a square number because it has an odd number of factors.46.121 < 137 < 144So, < < 11 < < 12 is between 11 and 12.137 is closer to 144 than to 121.So, is closer to , or 12.47.92 + 122 = 15281 + 144 = 225225 = 225Since 225 = 225, triangle ABC is a right triangle.48.2 + 2 = 210 + 21 = 3131 = 31Since 31 = 31, the triangle is a right triangle.No, the side lengths do not form a Pythagorean triple since , , and are not whole numbers.49.Substitute: a = 7.2 and b = 5.5 The length of the diagonal of the carpet is 9.1 m.50.Methods may vary. Sample:?ABD is a right triangle.?BCD is a right triangle.The length of BC is about 11.5 cm. ................
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