Extended Constructed Response (ECR) Item - Released in 2005 |
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Aisha used squares to make the pattern of figures below.
Complete the following in the Answer Book:
- Using the pattern, draw Figure 5 and Figure 6 in the Answer Book.
- Complete the table in the Answer Book to determine the perimeter of each figure.
- Write an expression that can be used to determine the perimeter of the nth figure in this pattern.
- If this pattern continues, which figure will have a perimeter of 140 centimeters? Use mathematics to explain how you determined your answer. Use words,
symbols, or both in your explanation.
/share/clg/xml/public_release/mathematics/2005_112_alg12.xml |
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Selected Response Item - Released in 2005 |
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A fish tank empties at a constant rate. The table below shows the volume of water left in the fish tank after each minute.
Which of these equations describes the volume of water in the tank as a function of time?
- v = -8t + 622
- v = -8t + 630
- v = 8t + 622
- v = 8t + 630
/share/clg/xml/public_release/mathematics/2005_112_alg18.xml |
Correct Answer:
B
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Selected Response Item - Released in 2001 |
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Wind makes the air feel colder than the actual temperature. This is called wind
chill. The table below shows the effect that a 20-mile-per-hour wind has on the
actual air temperature.
Which of these equations represents the relationship between the actual
temperature (t) and the wind-chill temperature (w)? |
- w = 0.714t – 7
- w = 0.714t + 7
- w = 1.4t – 38
- w = 1.4t + 38
/share/clg/xml/public_release/mathematics/2001_112_alg43.xml |
Correct Answer:
C
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Selected Response Item - Released in 2002 |
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| The table below shows a relationship between x and y.
Which of these equations represents this relationship? |
/share/clg/xml/public_release/mathematics/2002_112_alg06.xml |
Correct Answer:
C
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Extended Constructed Response (ECR) Item - Released in 2002 |
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| Stephanie must complete class projects for history and mathematics. Each project is worth a maximum of 100 points if she turns it in on time. Each teacher uses a different method to calculate the maximum number of points that a student can earn for a late paper. The tables below show the two methods.
Complete the following in the answer box below:
- Complete the tables to show the number of possible points for projects that are 4 and 5 days late.
- How many days late can Stephanie turn in each project and still possibly receive a score of 65 or better on each project? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- Stephanie can complete only one project on time. The second project will be only one day late. To receive the maximum total number of possible points, which project should she complete first? Use mathematics to justify your answer.
- Describe the method that each teacher uses to determine the maximum possible points that a student can earn for a late paper.
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/share/clg/xml/public_release/mathematics/2002_112_alg07.xml |
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Selected Response Item - Released in 2005 |
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Look at the graph below.
Which of these tables corresponds to the line that is graphed?
/share/clg/xml/public_release/mathematics/2005_112_alg03.xml |
Correct Answer:
A
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Extended Constructed Response (ECR) Item - Released in 2001 |
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Certain ice crystals have six sides. Flakes are formed when these six-sided ice
crystals connect. One pattern is shown below.
Complete the following in the answer box below:
- Complete the table to show the total number of crystals in each of the first
6 stages of flake growth.
- Based on the drawing at Stage 3, draw the pattern for the same flake at Stage 4.
- Draw a scatter plot using the data in the completed table.
- Write an equation that represents the total number of crystals (c), at each
stage number (n). Use mathematics to explain how you determined your
equation. Use words, symbols, or both in your explanation.
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/share/clg/xml/public_release/mathematics/2001_112_alg15.xml |
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Selected Response Item - Released in 2001 |
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Tommy used building blocks to create the designs below.
The table below shows the number of blocks in each design.
Which of these equations shows the relationship between the design number (d)
and the number of blocks (b) in the design? |
- b = d + 6
- b = 2d + 5
- b = 3d + 2
- b = 4d + 3
/share/clg/xml/public_release/mathematics/2001_112_alg23.xml |
Correct Answer:
B
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Selected Response Item - Released in 2002 |
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| A library is trying to decrease the number of overdue books by increasing the fines. They plan to charge $0.25 for the first day a book is late and $0.10 for each additional day. Which of these tables represents the fines for the first five days a book is late? |
/share/clg/xml/public_release/mathematics/2002_112_alg28.xml |
Correct Answer:
C
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Selected Response Item - Released in 2003 |
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| The table below shows a relationship between x and y.
Which of these equations represents this relationship? |
- y = 2x - 1
- y = 2x - 2
- y = -2x + 3
- y = -2x - 1
/share/clg/xml/public_release/mathematics/2003_112_alg11.xml |
Correct Answer:
C
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Extended Constructed Response (ECR) Item - Released in 2003 |
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Park rangers determined that the current deer population in a park is 78. Ranger Jones predicted that the deer population will increase by 6 deer each year. Ranger Percy predicted that the deer population will increase by 8 deer each year.
Complete the following in the answer box below. You may use paper to complete the grid and otherwise help formulate your response.
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Complete the following in the answer box below for Ranger Jones and Ranger Percy.
- For each ranger's prediction, write an expression that can be used to determine the deer population in the park n years from now.
- What is the difference in the number of deer that Ranger Percy predicted will be in the park 10 years from now compared to Ranger Jones' 10-year prediction? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
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/share/clg/xml/public_release/mathematics/2003_112_alg12.xml |
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Selected Response Item - Released in 2006 |
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Harry works cleaning houses. He charges $15 per hour plus a $10 travel fee to clean
each house. Which of these tables shows the total amount (c) charged, in dollars, to
clean a house for h hours?
/share/clg/xml/public_release/mathematics/2006_112_alg08.xml |
Correct Answer:
C
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Selected Response Item - Released in 2006 |
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The table below shows a relationship between x and y.
Which of these equations represents this relationship?
- y = 6x + 7
- y = 6x - 7
- y = 7x + 6
- y = 7x - 6
/share/clg/xml/public_release/mathematics/2006_112_alg18.xml |
Correct Answer:
D
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Selected Response Item - Released in 2003 |
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| The table below shows a linear relationship between x and y.
Which of these graphs shows this relationship? |
/share/clg/xml/public_release/mathematics/2003_112_alg26.xml |
Correct Answer:
D
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Selected Response Item - Released in 2004 |
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| The table below shows a
relationship between x and y.
Which of these equations represents
this relationship? |
- y = -2x + 7
- y = 2x + 3
- y = 3x + 2
- y = 7x - 2
/share/clg/xml/public_release/mathematics/2004_112_alg31.xml |
Correct Answer:
B
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Extended Constructed Response (ECR) Item - Released in 2006 |
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The table below shows a relationship between x and y.
Complete the following in the Answer Book:
- What are the values of y when x is 10 and x is 11?
- What is the relationship between the x-values and the y-values? Use mathematics to explain the relationship. Use words, symbols, or both in your explanation.
- Fill in the boxes to the right of the table in the Answer Book by finding the difference between the y-values of each of the successive terms. Describe the pattern that exists between the differences that you found.
- What is the difference between the y-values when x is 10 and when x is 11? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
/share/clg/xml/public_release/mathematics/2006_112_alg12.xml |
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Extended Constructed Response (ECR) Item - Released in 2004 |
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Toy blocks are used to build a tower. The surface area and volume of the tower built
with these blocks is shown in the table below.
Complete the following in the answer box below:
- Complete the table in the Answer Book to determine the surface area and the
volume for 5 and 6 blocks.
- Write an algebraic expression to represent the relationship between the number
of blocks and the surface area of the tower. Use mathematics to justify your
answer.
- If 10 blocks are used, what is the surface area and the volume of the tower?
Use mathematics to explain how you determined your answers. Use words,
symbols, or both in your explanation.
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/share/clg/xml/public_release/mathematics/2004_112_alg33.xml |
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Selected Response Item - Released in 2007 |
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The table below shows a relationship between x and y.
Which of these equations describes this relationship?
- y =
 x − 6
- y =
 x − 2
- y = 2x − 4
- y = −2x + 4
/share/clg/xml/public_release/mathematics/2007_112_alg10.xml |
Correct Answer:
D
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Selected Response Item - Released in 2007 |
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A pattern of numbers is determined by the rule shown below.
To find y multiply x by -2. Then add 3.
Which of these graphs represents this pattern?
/share/clg/xml/public_release/mathematics/2007_112_alg27.xml |
Correct Answer:
C
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Extended Constructed Response (ECR) Item - Released in 2007 |
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A triangle, a quadrilateral, a pentagon, and a hexagon are shown below. By drawing a diagonal from 1 vertex, the quadrilateral is divided into 2 non-overlapping triangles. Since the sum of the angle measures of a triangle is 180°, the sum of the measures of the quadrilateral is 360°. By drawing the diagonals from 1 vertex, the pentagon is divided into 3 non-overlapping triangles.
Complete the following in the Answer Book:
- In the Answer Book, draw the diagonals from 1 vertex of the hexagon so that the hexagon is divided into non-overlapping triangles.
- Use the polygons above to complete the table in the Answer Book.
| Polygon |
Number of Sides |
Number of Non-Overlapping Triangles |
Sum of Angle Measures |
| Triangle |
3 |
1 |
180° |
| Quadrilateral |
4 |
2 |
360° |
| Pentagon |
5 |
3 |
? |
| Hexagon |
? |
? |
? |
- Describe how the number of sides of each polygon is related to the number of non-overlapping triangles. Use mathematics to justify your answer.
- Describe how the number of non-overlapping triangles in a polygon is related to the sum of its angle measures. Use mathematics to justify your answer.
/share/clg/xml/public_release/mathematics/2007_112_alg28.xml |
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