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ReviewProblem Show your Work :) Choose 8 of 9 Questions1.Jordan wants to cut a rectangular carpet with dimensions 32 cm by 80 cm into squares of equal size.a) What is the side length of the largest possible square Jordan can cut?b) How many squares can she cut from carpet?2.Germaine wants to paint a cube with volume 2744 m3. Each tub of paint covers 79 m2. How many tubs of paint does Germaine need to paint the cube?3.Calculate the volume of the largest possible sphere that can fit in a cube with volume 2197.0 cm3. Give the volume to the nearest tenth of a cubic centimetre. Explain your steps.4.a) Here are a student’s solutions for factoring polynomials. Identify the errors in each solution. Write a correct solution.i) Factor: Solution: ii) Factor: Solution: b) What should the student have done to check her work?5.Factor this trinomial. Verify that the factors are correct.6.Use decomposition to factor . Explain your steps.7.Write a polynomial to represent the area of this rectangle. Simplify the polynomial. 8.A student says that the expression represents the volume of this right rectangular prism. Is the student correct? How do you know?ReviewAnswer SectionPROBLEM1.ANS:a)The shorter side of the carpet measures 32 cm. So, the side length of the square must be a factor of 32.The longer side of the carpet measures 80 cm. So, the side length of the square must be a factor of 80.So, the side length of the square must be a common factor of 32 and 80. The side length of the largest square will be the greatest common factor of 32 and 80. Check to see which factors of 32 are also factors of 80. The factors of 32 are: 1, 2, 4, 8, 16, 32The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80The greatest common factor of 32 and 80 is 16.The side length of the largest possible square is 16 cm.b) Find the number of squares Jordan can cut from the carpet:Area, A, of the carpet: Area, A, of the largest possible square is: Divide the area of the carpet by the area of the largest possible square.Jordan can cut 10 squares from the carpet.PTS:1DIF:DifficultREF:3.1 Factors and Multiples of Whole NumbersLOC:10.AN1TOP:Algebra and NumberKEY:Problem-Solving Skills2.ANS:To calculate how many tubs of paint are needed, first determine the surface area of the cube.The edge length, e, of a cube is equal to the cube root of its volume.The surface area, SA, of a cube is the sum of the areas of its 6 congruent square faces.Calculate how many tubs of paint are needed:Germaine needs 15 tubs of paint to paint the cube.PTS:1DIF:ModerateREF:3.2 Perfect Squares, Perfect Cubes, and Their RootsLOC:10.AN1TOP:Algebra and NumberKEY:Problem-Solving Skills3.ANS:To determine the volume of the sphere, first determine the edge length of the cube.The edge length, e, of a cube is equal to the cube root of its volume.The radius, r, of the largest sphere that will fit in the cube is one-half of the edge length of the cube.Use the formula for the volume of a sphere.?he volume of the largest possible sphere that can fit in the cube is approximately 1150.3 cm3.PTS:1DIF:DifficultREF:3.2 Perfect Squares, Perfect Cubes, and Their RootsLOC:10.AN1TOP:Algebra and NumberKEY:Communication | Problem-Solving Skills4.ANS:a) i) Correction:The student did not remove the common factor from the third term correctly. When the common factor is the same as the term, a factor of 1 remains. This must be written as a term in the factored polynomial.ii) Correction:When the student removed the common factor from the third term, she made a sign error. The sign should be negative, not positive. b) The student should have expanded her solutions to check that the trinomial was the same as the original trinomial each time.PTS:1DIF:ModerateREF:3.3 Common Factors of a PolynomialLOC:10.AN5TOP:Algebra and NumberKEY:Communication | Problem-Solving Skills5.ANS:PTS:1DIF:ModerateREF:3.3 Common Factors of a PolynomialLOC:10.AN5TOP:Algebra and NumberKEY:Communication | Problem-Solving Skills6.ANS:Check for common factors; there are none.The product of the coefficient of and the constant term is: Write as the sum of two terms whose coefficients have a product of 324.The two coefficients are , so write the trinomial as .Remove a common factor from the 1st pair of terms, and from the 2nd pair of terms.Each product has a common binomial factor.PTS:1DIF:DifficultREF:3.6 Polynomials of the Form ax^2 + bx + cLOC:10.AN5TOP:Algebra and NumberKEY:Communication | Problem-Solving Skills7.ANS:Use the formula for the area, A, of a rectangle:The expression represents the area of this rectangle.PTS:1DIF:ModerateREF:3.7 Multiplying PolynomialsLOC:10.AN4TOP:Algebra and NumberKEY:Problem-Solving Skills8.ANS:Use the formula for the volume, V, of a right rectangular prism: Since this expression does not match the student’s expression, the student is incorrect.The expression represents the volume of the right rectangular prism.PTS:1DIF:ModerateREF:3.7 Multiplying PolynomialsLOC:10.AN4TOP:Algebra and NumberKEY:Communication | Problem-Solving Skills ................
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