Algebra and Number Relations Exam Review

Algebra and Number Relations Exam Review

Problem

1. A square has area 40.0 cm2. Determine the perimeter of the square to the nearest tenth of a centimetre.

2. Use factoring to determine whether 4913 is a perfect square, a perfect cube, or neither.

3. 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?

4. Factor this trinomial. Verify that the factors are correct.

5. The area of a shape is given by the expression .

a) Factor the expression.

b) Use both forms of the expression to determine the area of the shape when cm and cm. What do you notice?

6. This composite object is formed by a cone with a hemisphere on top. A formula for the volume of this object is:

a) Factor this formula.

b) Use both forms of the formula to calculate the volume of this composite object with radius 4 cm and height 10 cm.

c) Which formula to do you prefer to use? Why?

7. Find the area of the rectangle.

8. Factor . Explain your steps.

9. Use decomposition to factor . Explain your steps.

10. Write a polynomial to represent the area of this rectangle. Simplify the polynomial.

11. A rectangle has length 14x and width y. Strips of width are cut from the rectangle as shown. Write an expression that represents the area of the rectangle that remains.

12. Factor. Explain your steps.

13. A picture and its frame have dimensions as shown.

a) Find an expression for the area of the frame, in factored form.

b) Determine the area of the frame when cm.

14. Is the cube root of 250 rational or irrational?

Use 2 different strategies to justify your answer.

15. Order these numbers from least to greatest: , , , ,

16. A square has an area of 1134 m. Determine the perimeter of the square. Write the answer as a radical in simplest form.

17. In isosceles DABC, what is the length of BC? Write your answer as a mixed radical.

18. Another formula for the approximate surface area, SA square metres, of a person’s body is , where h is the person’s height in centimetres, and m is the person’s mass in kilograms.

a) Calculate the surface area of a newborn with height cm and mass 7.3 kg. Write the answer as a decimal to the nearest hundredth of a square centimetre.

b) Calculate the surface area of a person with height 170 cm and mass 66 kg. Write the answer as a decimal to the nearest hundredth of a square centimetre.

19. Use exponent laws to simplify . Explain your strategy.