GRADE 10 ACADEMIC 1St Week Review Package

GRADE 10 ACADEMIC 1st Week Review Package

STUDENT NAME:

Shape / Perimeter / Area/Surface Area / Volume
Circle / /
Parallelogram / P = 2b + 2c / A = bh
Triangle / P = a + b + c /
Rectangular Prism / A = 2(wh + wl + lh) / V = l x w x h
Sphere / /
Cylinder / /
Cone / /

Part A: Number Sense and Algebra (22 marks)

1. Select the expression that is the simplification of (–9x)(3x3).

(a) –6x4

(b) –27x3

(d) –27x4

2. Select the pair of like terms.

(a) 3x2, 4x

(b) 2y, 2a

(d) 7c, –2cd

3. Select the statement that is equivalent to (14m + 35).

(a) 37m

(b) 14m + 5

(d) 2m + 5

4. Select the expression that is the expanded form of 2m(–3m + 8).

(a) –6m2 + 16m

(b) –m + 8

(d) 5m2 + 8

5. Select the simplified form of 8y4 – 7y2 + 3y2 – 6y4.

(a) 10y2 + 14y4

(b) –4y2 + 2y4

(d) –2y6

6. The area of a window is given by the expression 27x6y3 – 12x4y2 units. If one of the dimensions is 3x2y units, the other dimension is ______units.

(a) 9x4 + 3y

(b) –9y2 y2 - 3 x2y

(d) 9x4y2 - 4 x2y

7. Calculate. 

(a)

(b)

(c)

(d)

8. Calculate. 

(a)

(b)

(d) 3

9. is equivalent to:

(a)

(b)

(c)

(d)

10. Calculate and express your answer in simplest form. + 

(a)

(b)

(c)

(d)

11. Simplify the expression.

(a)

(b)

(d) p3q5

12. Select the expression that is equivalent to .

(a) x8y125

(b) x6y15

(d) 3x6y15

13. Select the expression that shows in simplest form.

(a) u2v5

(b)

(d)

14. Simplify the expression.

(a) pq

(b)

(c)

(d) p2q5

15. Simplify. (5x6y7)2

(a) 10x12y14

(b) 5x12y14

(d) 25x8y9

16. In a right triangle, the hypotenuse measures 15 cm and one side measures 12 cm. Select the length of the third side.

(a) 27 cm

(b) 9 cm

(d) 19.2 cm

17. Select the statement that is equivalent to –4(3x2 – 7).

(a) –43x2 – 7

(b) –19x2

(d) –12x2 + 28

18. Select the expression that is the simplification of (2a)(3b).

(a) 5ab

(b) 2a + 3b

(d) 6a + b

19. For the expression 5.7p3q – 2ab – 11, select the statement that is true.

(a) 5.7 is a variable.

(b) 2ab is a constant term.

(d) –2 is a coefficient.

20. Solve: + 1 = –4

(a) k = –7

(b) k = –15

(d) k = –9

21. The solution to –6 + 4a = 14 is:

(a) a = –5

(b) a = 3

(d) a = 5

22. Jorge bought 60g of candies for $1.80. What is his unit cost?

(a) $30.00

(b) $0.03

(d) $33.33

Part B: Linear Relations (8 marks)

23. Select the statement that is NOT true about horizontal lines.

(a) Horizontal lines are parallel to the y-axis.

(b) Horizontal lines are parallel to the x-axis.

(d) Horizontal lines have a slope of zero.

24. Theo paints houses for a summer job. He charges $150 for materials plus $12/h. Select the equation that BEST represents Theo's situation.

(a) y = 150x

(b) y = 150x + 12

(d) y = 12x

25. Select the equation of the line that is perpendicular to y = 8x – 10 and passes through the point (8, 2).

(a) y = –8x + 2

(b) y = 8x + 2

(d) y = – + 3

26. Which of the following can be used to find the slope of a line?

ii)

iii)

(a) i) only

(b) ii) only

(d) i) and ii)

27. Select the equation of the line that is parallel to 3x + 9 = 0.

(a) 3y + 9 = 0

(b) y = 8

(d) 2x + y = 0

28. Write the equation 6x – 2y + 5 = 0 in slope-y-intercept form.

(a) y = 3x + 2.5

(b) y = 3x + 5

(d) 6x – 2y = –5

29. The line 7x – 4y + 3 = 0 has a y-intercept of:

(a) 3

(b)

(d)

30. Write the equation in standard form.

(a) 3y = 4x + 7

(b) 4x – 3y + 7 = 0

(d) 3y – 4x + 7 = 0

Part C: Measurement and Geometry (11 marks)

31. Determine the area of a painting with dimensions as shown. ______

(a) 10 a2b + 6ab2

(b) 10ab + 6b2 + 4a

(d) 5a2 b + 6b2

32. The volume of a cube is found by cubing the length of a side. Which of the following is the volume of a cube with a side length of 7.23 cm?

(a) 51.84 cm3

(b) 21.69 cm3

(d) 14.46 cm3

33. The diagram shows two parallel lines cut by a transversal. What is the measure of x?

(a) 36°

(b) 33.6°

(d) 12°

34. The diagram shows two parallel lines cut by a transversal. What is the measure of a?

(a) 7.5°

(b) 15°

(d) 30°

35. In the diagram, AB = AC. Find the measure of x.

(a) 65°

(b) 80°

(d) 100°

36. In the following diagram, find the value of c.

(a) 45°

(b) 225°

(d) 65°

37. Find the measure of x in the following diagram.

(a) 6°

(b) 60°

(d) The measure changes depending on the size of the triangle.

38. Find the measure of x in the following diagram.

(a) 63°

(b) 117°

(d) 131°

39. The diagram shows two parallel lines cut by a transversal. Find the measure of a.

(a) 20°

(b)

(d) 100°

40. What is the surface area of this sphere if r = 15.0 cm? Answer accurately to the nearest square centimetre. [Use  = 3.14.]

(a) 2826 cm2

(b) 11 304 cm2

(d) 25 896 cm2

41. To the nearest square centimeter, what is the area of the base of this cylinder?

(a) 5 cm2

(b) 25 cm2

(d) 61 cm2

Short Answer:

No marks will be given for answers only.
Show all work.
Justify your answers algebraically or with an explanation.
Trial and error is not an acceptable solution.
Fill in answers in the spaces provided.

Part D: Number Sense and Algebra (25 Marks)

1.In Ontario, the provincial sales tax (PST) is 8% and the goods and service tax (GST) is 6%. The price of a MP3 player is $149.99.

a)Determine the GST and PST. (2 marks)

GST: PST:

b)What is the total price of the MP3 player? (1 mark)

TOTAL PRICE:

2.Solve. Leave answers as fractions if required, no decimals. (2 marks each)

a)3x + 12 = -27b)

Ans: Ans:

3.Find the length of each side of the triangle below. The perimeter of the triangle is 96 m. (3 marks)

x + 3x + 1

4.A warehouse is rectangular in shape. It has a width of 13x, a length of 2x - 1 and a height of 8x. All dimensions are in meters.

a)Draw a diagram to represent the warehouse. Label all dimensions. (1 mark)

b)Determine an expression for the volume of the warehouse. Simplify your expression. (2 marks)

Volume =

c)A similar warehouse has a volume given by the expression Determine the volume of the warehouse when x = 6 m. (1 marks)

d) A shipping company wants to store its large rectangular shipping containers in the warehouse. Each container is 2 x 5 x 9. All dimensions are in meters. The containers are stackable. How many containers will fit in the warehouse in part c? (3 marks)

Number of Containers:

5.Sally has twice as many dimes as nickels. The total value is $4.50. How many nickels does she have? (3 marks)

6.Susan wants to take out the carpet in her room and put down hardwood flooring. Her room is rectangular and has dimensions 7m x 7m. Susan goes shopping and finds a hardwood that she likes. The cost of the hardwood is $35.00 per square meter. The store is going to charge her $18.00 per square meter to install it. How much does Susan have to pay including taxes. PST is 8% and GST is 6%. (5 marks)

Part E: Linear Relations (17 marks)

7.Determine the slope of the line segment AB that has endpoints (do not graph) A(-3,-2) and B(2,4). (2 marks)

Slope AB =

8.The line segment has endpoints A(0, 3) , B(x, 6) and has a slope of 4. Using algebraic methods find x. (2 marks)

x =

9.Find the equation of:

a)a line with x- intercept of -2 and parallel to (3 marks)

Equation:

b)a line that is perpendicular to the line and passes through B(-5,2) (3 marks)

Equation:

10.Solve the following system of equations graphically by following the steps given.

Equation 1: x + y = 7Equation 2: 3x + 4y = 24

a)Plot both relations on the grid below using slope and y-intercept. (4 marks)

b)What is the point of intersection. (1 mark)

Point of Intersection:

c)Verify that your graphical solution (point of intersection) is the solution to this system of equations. (2 marks)

Part F: Measurement and Geometry (5 marks)

11.A standard Canadian football field measures 110 yards X 66 yards (rectangular in shape). During one of the conditioning drills the coach has you run along the perimeter of the field.

a)How far do you have to run in order to complete one lap of the field? (2 marks)

b)A second drill requires you to run diagonally across the field from one corner to the other corner and then return back along the same diagonal. How much farther or shorter is it to run diagonally across and back compared to running around the outside of the field? Draw a sketch of the field. Round final answer to two decimals. (3 marks)

Bonus Questions:A cardboard box has a length of 45 cm, a width of 26 cm and a height of 16 cm. Determine the length of the longest metal rod that you could fit into the box. Use a diagram to assist you. Round your answers to one decimal place. (4 marks)