Grade 9 Math – Final Exam Review Unit 1 – Outcomes Determine the square root of positive rational numbers that are perfect squares. o Determine whether or not a given rational number is a square number and explain the reasoning. o Determine the square root of a given positive rational number that is a perfect square. o Identify the error made in a given calculation of a square root. o Determine a positive rational number given the square root of that positive rational number. Determine an approximate square root of positive rational numbers that are non-perfect squares. o Estimate the square root of a given rational number that is not a perfect square using the roots of perfect squares as benchmarks. o Determine an approximate square root of a given rational number that is not a perfect square using technology. o Explain why the square root of a given rational number as shown on a calculator may be an approximation. o Identify a number with a square root that is between two given numbers. Determine the surface area of composite 3-D objects to solve problems. o Determine the overlap in a given concrete composite 3D object, and explain its effect on determining the surface area (right cylinders, right rectangular prisms, and right triangular prisms) o Determine the surface area of a given concrete composite 3D object. o Solve a given problem involving surface area. 1. Use the diagram to determine the value of the square root of 1 9 . 2. Which numbers below are perfect squares? Explain how you know. a) 25 121 b) 0.004 3. Without the use of a calculator, determine the value of each square root. Show your workings. a) 225 49 b) 2.56 4. The area of a square garden is 12.25 m 2 . (Use a diagram to help you.) a) What is the side length of the garden? b) Determine the perimeter of the garden. 5. Using benchmarks, approximate 11.6 to the nearest tenth.
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Grade 9 Math Final Exam Review Unit 1 Outcomes · Grade 9 Math – Final Exam Review Unit 1 – Outcomes Determine the square root of positive rational numbers that are perfect squares.
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Grade 9 Math – Final Exam Review
Unit 1 – Outcomes
Determine the square root of positive rational numbers that are perfect squares. o Determine whether or not a given rational number is a square number and explain the reasoning. o Determine the square root of a given positive rational number that is a perfect square. o Identify the error made in a given calculation of a square root. o Determine a positive rational number given the square root of that positive rational number.
Determine an approximate square root of positive rational numbers that are non-perfect squares.
o Estimate the square root of a given rational number that is not a perfect square using the roots
of perfect squares as benchmarks.
o Determine an approximate square root of a given rational number that is not a perfect square
using technology.
o Explain why the square root of a given rational number as shown on a calculator may be an
approximation.
o Identify a number with a square root that is between two given numbers.
Determine the surface area of composite 3-D objects to solve problems.
o Determine the overlap in a given concrete composite 3D object, and explain its effect on
determining the surface area (right cylinders, right rectangular prisms, and right triangular
prisms)
o Determine the surface area of a given concrete composite 3D object.
o Solve a given problem involving surface area.
1. Use the diagram to determine the value of the square root of
1
9.
2. Which numbers below are perfect squares? Explain how you know.
a)
25
121 b) 0.004
3. Without the use of a calculator, determine the value of each square root. Show your workings.
a)
225
49 b) 2.56
4. The area of a square garden is 12.25 m2. (Use a diagram to help you.)
a) What is the side length of the garden?
b) Determine the perimeter of the garden.
5. Using benchmarks, approximate
11.6 to the nearest tenth.
6. Each cube has edge length 1 unit. Determine the surface area of the object.
7. In each triangle, determine the unknown length to the nearest tenth of a unit where necessary.
a) b)
8. The local curling rink is shown in the diagram at the right. It is to be painted.
a) Determine the surface area of the structure.
b) The roofs, window, and door are not to be painted.
The door is 1 m by 2 m and the window is 4 m by 2 m.
Determine the surface area to be painted.
c) If it costs $0.32 / m2, determine the cost of the paint
needed.
Unit 2 – Outcomes
Demonstrate an understanding of powers with integral bases (excluding base 0) and whole
numbers by: representing repeated multiplication using powers, using patterns to show that a
power with an exponent of zero is equal to one, and solving problems involving powers.
o Demonstrate the difference between the exponent and the base by building models of a given
power, such as
o Explain using repeated multiplication the difference between two given powers in which the
exponent and base are interchanged (see above example).
o Express a given power as a repeated multiplication.
o Express a given repeated multiplication as a power.
o Explain the role of parentheses in powers by evaluating a given set of powers, eg
( ) ( )
o Demonstrate using patterns, that is equal to 1 for a given value of a ( )
o Evaluate powers with integral bases (excluding base 0) and whole number exponents.
Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and
whole number exponents.
o Explain, using examples, the exponent laws of powers with integral bases and whole number
exponents:
o Evaluate a given expressing by applying the exponent laws.
o Determine the sum and difference of two given powers and record the process.
o Identify the error(s) in a given simplification of an expression involving powers.
9. Write (-3)(-3)(-3)(-3)(-3) as a power?
10. Write 6 4(8 ) (8 ) as a single power.
11. Write 8 4( 7) ( 7) as a single power.
12. Calculate: 5 4 0( 1) ( 1) ( 1) ( 1)
13. Evaluate: 3 0( 3) 4
14. Evaluate:
42
3
15. Complete the table.
Power Base Exponent Repeated Multiplication Standard
Form
53
4( 2)
10 3
(2 2 2 2 2 2)
16. Evaluate each power: a. 4( 3) b. 43
17. Evaluate each of 25 and 5
2 and explain why they are different.
18. Evaluate each expression. Show your work.
a. 2 4 2(18 3 1) 4 b.
4 47 ( 3) (30 6)
19. Write as a single power and then evaluate.
a. 8 2 610 10 10 b.
5 6
7 1
( 3) ( 3)
( 3) ( 3)
20. Identify and then correct any errors in the student’s work below. Explain how you think the errors
occurred.
22
2
( 4) 3 9 3
16 3( 3)
16 3( 9)
16 27
11
Unit 3 – Outcomes
Demonstrate an understanding of rational numbers by comparing and ordering rational numbers
and solving problems that involve arithmetic operations on rational numbers.
o Order a given set of rational numbers, in fraction and decimal form, by placing them on a
number line.
o Identify a rational number that is between two given rational numbers.
o Solve a given problem involving operations on rational numbers in fraction form and decimal
form.
Explain and apply the order of operations, including exponents, with and without technology.
o Solve a given problem by applying the order of operations with and without the use of
technology.
o Identify the error in applying the order of operations in a given incorrect solution.
21. Sketch a number line and mark each rational number on it. Order the numbers from greatest to least.
–3.1, 5
, 3
–1.2,1
7
, 0.6
22. Write the rational number represented by each letter as a fraction.
23. In each pair, which rational number is greater?
a) 7.3, 7.2 b) 4 5
, 5 4
c) 1.2, 1.3 d) 10 10
, 13 11
24. Determine each sum or difference.
a) 3 2
5 3
b) 23 1
18 4
c) 4.1 3.5
d) 53.9 19.4
25. A technician checked the temperature of a freezer and found that it was -15.70C. She noted that the
temperature had dropped 7.80C from the day before. What
was the temperature the day before?
26. Determine each product or quotient.
a) 1 3
4 5
b) 5 2
6 3
c) 1 3
2 45 4
d) ( 0.32) 1.6
e) 0.9 ( 1.2)
27. A thermometer on a freezer is set at -5.50C. Each time the freezer door is opened, the temperature
increases by 0.30C. Suppose there is a power outage. How many times can the door by opened before
the temperature of the freezer increases to 50C? Show how you found your answer.
28. Evaluate
a) 0.84 ( 0.5) ( 2.3)
b) 1 3 9 3
2 5 10 5
Diagram 1 Diagram 2 Diagram 3
c) 5.8 3.1 0.5
d) 2 1 1 2
4 4 33 3 6 5
29. Evaluate with a calculator. Round to the nearest hundredth if necessary.
8.6 14.6 5.3 19.4 8.6
2.9 6.3 9.5
Unit 4 – Outcomes
Generalize a pattern arising from a problem-solving context, using a linear equation, and verify
by substitution.
o Write an expression representing a given pictorial, oral or written pattern.
o Write a linear equation to represent a given context.
o Write a linear equation representing the pattern in a given table of values and verify the
equation by substituting values from the table.
o Solve, using a linear equation, a given problem that involves pictorial, oral and written linear
patterns.
o Describe a context for a given linear equation.
Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.
o Describe the pattern found in a given graph.
o Graph a given linear relation, including horizontal and vertical lines.
o Match given equations of linear relations with their corresponding graphs.
o Interpolate and extrapolate the approximate value of one variable on a given graph given the
value of the other variable.
o Solve a given problem by graphing a linear relation and analyzing the graph.
30. In the equation m = 3n -2, determine the value of m when n =5
Use the diagram below for questions 31 and 32.
31. Determine the expression that relates the number of toothpicks (t) to the diagram number (d).
32. Given the diagrams shown, how many toothpicks would be used to construct Diagram 15 ?
33. Which table of values represents a linear relation?
A) C)
B) D)
34. The fee to ride in King Taxi is $4 plus $1.25 for each km travelled. Determine the equation that relates
the total cost C to the distance travelled d.
35. Which of the lines shown on the graph has the formula y + 4 = 0 ?
A) Line A C) Line C
B) Line B D) Line D
36. Describe the graph of the equation x = -3
37. Which line represents the equation x + y = 5
A) Line A C) Line C
B) Line B D) Line D
38. Which equation describes the graph?
A) x + 2y = 4 C) x + y = 4
B) Y = 4x D) 2x + y = 4
x 0 1 2 3 4
y 2 4 6 4 2
x 0 1 2 3 4
y 0 1 4 9 16
x 0 1 2 3 4
y 2 4 6 8 10
x 0 1 2 3 4
y 2 4 7 11 16
x- 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6
y
- 6
- 5
- 4
- 3
- 2
- 1
1
2
3
4
5
6
A
D
C
B
x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
A
B C
D
x-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x- 8 - 6 - 4 - 2 2 4 6 8
y
- 8
- 6
- 4
- 2
2
4
6
8
Use the graph to the right to answer questions 39-40.
39. Determine the value of y when x = 4
A) 9 C) 3
B) -5 D) 1.5
40. Determine the value of x when y = 7
A) 5 C) -11
B) 3 D) -2
41. A stone if dropped from a bridge. Its speed increases due to the force of gravity. If the speed, s in m/s,
after t second is given by the formula 38.9 ts , what is the speed of the stone at 5 seconds?
A) 0.2041 m/s B) 78.4 m/s C) 49 m/s D) 51 m/s
42. The graph shown represents a linear relation. Determine the value of y when x = 6.
A) 0 C) 1
B) 2 D) 3
43. Look at the pattern and assume it continues.
a) Fill in the table below using the diagrams (complete the pattern of diagrams)
# of Triangles (T) 1 2 3 4 5 6
# of Line Segments (L) 3 5
x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8
y
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
b) Graph the data on the grid below.
c) Find an equation relating T and L.
d) How many line segments would there be if you had: