CONSECUTIVE ODD NUMBERS
This problem gives you the chance to:
- find and test rules in a number pattern.
Wendy is investigating consecutive odd numbers arranged in a triangular
pattern. This is the start of her pattern.
Row
Total
Row 1
1 = 13
1
Row 2
3
Row 3
7
Row 4
13
Row 5
21
5
9
11
15
23
17
25
27
19
29
If I add up the numbers
in each row, I get the
cube numbers.
Wendy
(a)
Show that Wendy’s statement is true for the first five rows.
• Write down a formula for the sum of the numbers in any row.
Be sure to show that you have tested your formula for the rows beyond
Row 5.
Course Test 2 Page 1
(b) Wendy looks for other number patterns in the triangle of numbers.
She thinks about the numbers that go down the middle of the triangle (1,
9, 25,......)
• Find a formula for these middle numbers. Be sure to show that you
have tested your formula for the rows beyond Row 5.
• Does your formula work for every row in the triangular pattern?
Explain your answer.
I think 123 will be a
middle number in the
triangular pattern.
Wendy
• Is Wendy correct?
Explain your answer.
Course Test 2 Page 2
BODY MASS INDEX
This problem gives you the chance to:
- state an inequality
- substitute values into a formula
a. For most people in normal health, their body mass index, I, is at
least 20 and not more than 25.
Express this statement as an inequality.
b. A person’s body mass index, I, is calculated from the person’s
weight, w pounds, and height, h inches, using the formula:
700W
I = -----2
h
Robert weighs 160 pounds. His height is 5 feet 10 inches.
What is his body mass index?
Course Test 2
Page 3
DICEY
This problem gives you the chance to:
- Use probability to solve a problem.
On a red cube one pair of opposite faces is marked with a 1, another
pair of opposite faces is marked with a 6 and a third pair of opposite
faces is marked with an 8.
In a similar way, a blue cube is mared 3,5, and 7 on its pairs of opposite
faces.
red
blue
yellow
1. Write down the probability of throwing a 6 on the red cube. ______
2. Write down the probability of throwing a 7 on the blue cube.______
3. The red and the blue cubes are thrown together.
The diagram on the left shows all of the
Possible outcomes.
rojo
Draw circles around the points on the diagram which show the score on
red cube greater than the score on the blue cube.
Which color cube is more likely to have the higher score?________
4. A yellow cube has 2,4,9 on its pairs of opposite faces.
Draw a diagram to show all the possible outcomes when the yellow
and the blue cubes are thrown together.
Figure out which color cube is more likely to have the higher score.
5.Figure out which color cube is more likely to have the higher score
when the yellow and red cubes are thrown together.
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6.Comment on what you find out. Is there anything surprising in your
results? Explain.
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Course test 2
Page 5
HANG GLIDING
This problem gives you the chance to:
-Find angles and area
-Use a formula in a practical situation.
Alison is designing a new sail for a hang glider.
(a) Find angles x and y.
(b) Find the total area of the sail. Show how you figured it out.
Course Test 2 Page 6.
IS IT TRUE?
This problem gives you a chance to:
- Decide whether or not a statement is true.
Decide whether the following statement is true, sometimes true, or
never true.
If the perimeter of polygon A is larger than the perimeter
of polygon B, then polygon A has the larger area.
You should support your decisions by explaining your reasoning,
and providing examples which show how you figured it out. You may find
it helpful to use algebra.
You may wish to begin by considering some of the polygons shown above.
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Course Test 2 page 7