CSAP Grade 10
Mathematics 1
Daniel owns a swimming pool cleaning service. He charges a flat fee of $75 per month which includes two cleanings per month. Additional cleanings are available for $25 each. Which of these equations represents the cost per month, C, to a customer whose pool is cleaned x times per month? C 25 75x C 25(x 2) 75 C 75(2) 25x C (25 75)x 2
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CSAP Grade 10
Mathematics 2
Use your punch-out ruler and protractor to help you solve this problem. Study the triangle below. B
A
C
Part A Measure the length of each side of triangle ABC to the nearest tenth of a centimeter. On the lines below, record the length of each side.
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AB
centimeters
BC
centimeters
AC
centimeters
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Part B
Measure angle B and angle C to the nearest degree. On the lines below, record the measurement of each angle.
CSAP Grade 10
m∠B
Mathematics degrees
m∠C
degrees
Part C In the space below, draw a triangle that is larger than, but similar to, Triangle ABC. The scale factor between the sides of Triangle ABC and the new triangle should be 1.5.
Part D On the lines below, explain how you know the new triangle is similar to triangle ABC.
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CSAP Grade 10 Mathematics Scoring Guide
CSAP Grade 10
Rubric
Mathematics
Exemplary Response: 3 Points Part A
•
AB = 9.7 cm
BC = 4.5 cm
AC = 6.0 cm
AND Part B
•
m∠B = 26°
m∠C = 136°
NOTE: Allow variation of ± 0.5 cm for linear measures and ± 3° for angle measures. AND Part C
•
B
A
C
NOTE: Allow variation of 0.75 cm for linear measures and 3° for angle measures. AND
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Part D
•
CSAP Grade 10
The triangles are similar by the Angle-Angle Similarity theorem, because, although the lengths of the sides are different, the angles have the same measures.
Mathematics
OR
•
The triangles are similar by the Side-Side-Side Similarity theorem because the side lengths were enlarged by the same factor, so the sides remain in the same proportion.
OR
•
The triangles are similar by the Side-Angle-Side Similarity theorem because I first drew angle A with the same measure as in the original figure, then I drew AB and AC enlarged by the same factor so the sides remain in the same proportion.
NOTE: Give full credit for a response that includes proper reasoning without giving the name of the theorem being used (AA, SSS, SAS, etc.)
Score Points: Apply 3-point holistic rubric.
Standard: 5.1.A Measurement
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CSAP Grade 10
Mathematics 3
Study the graph of y = x2, shown below. y
8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1 0 -1
1
2
3
4
5
6
7
x
8
-2 -3 -4 -5 -6 -7 -8
If the graph is moved up 3 units, what equation will it represent? y ⫽ x2 ⫹ 3 y ⫽ (x ⫹ 3)2 y ⫽ (x ⫺ 3)2 y ⫽ x2 ⫺ 3
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CSAP Grade 10
Mathematics 4
The graph below shows the depth of snow at Blue Mountain Ski Resort last winter.
y
Depth of Snow at Blue Mountain Ski Resort
Depth of Snow (in inches)
100 80 60 40 20 0
20 40 60 80 100 Number of Days Since December 1
x
Part A
On the lines below, explain what the y-intercept of the graph represents.
Part B
On the lines below, explain what the x-intercept of the graph represents.
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CSAP Grade 10 Mathematics Scoring Guide
CSAP Grade 10
Rubric Exemplary Response:
Mathematics
2 Points Part A •
The y-intercept represents the depth of the snow on December 1.
AND Part B •
The x-intercept represents the number of days after December 1 that all the snow has melted.
OR •
The x-intercept represents the number of days after December 1 that the snow level reaches zero.
Score Points: Apply 2-point holistic rubric.
Standard: 2.4.A Patterns, Functions, and Algebra
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CSAP Grade 10
Mathematics 5
Which of the following shows the numbers in order from least to greatest? 5.7 103, 3.9 10–2, 1.8 103, 8.2 10–2 8.2 10–2, 3.9 10–2, 1.8 103, 5.7 103 1.8 103, 3.9 10–2, 5.7 103, 8.2 10–2 3.9 10–2, 8.2 10–2, 1.8 103, 5.7 103
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CSAP Grade 10
Mathematics 6
The table shows the number of bacteria present at 30 minute intervals during a science experiment. Number of Bacteria Over Time
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Time (in minutes)
Number of Bacteria
0 30 60 90 120 150 180 210
3 6 12 24 48 96 192 384
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Which of these graphs best shows the relationship between time and the number of bacteria present?
CSAP Grade 10 y
y
Number of Bacteria
Number of Bacteria
Mathematics
x
0
x
0
Time (in minutes)
Time (in minutes)
y
Number of Bacteria
Number of Bacteria
y
0
x
Time (in minutes)
0
x
Time (in minutes)
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CSAP Grade 10
Mathematics 7
The graph below shows the height of Cindy’s model rocket during the course of its flight. Flight of Cindy’s Rocket
Height (in feet)
y
22 20 18 16 14 12 10 8 6 4 2 0
1 2 3 4 5 6 7 8 9 Time (in seconds)
x
Which of these equations can be used to find the height of the rocket at any time during its flight? y 9x y x2 81 y -x2 9x y 9 9x2
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CSAP Grade 10
Mathematics 8
Laura needs to buy chips and soda for the guests at her party. Each large bag of chips costs $2.40 and each large bottle of soda costs $2.00. She has $48.00 to spend. Which graph represents the number of bags of chips and bottles of soda that Laura can buy? y
36 32 28 24 20 16 12 8 4
Bags of Chips
Bags of Chips
y
0
4 8 12 16 20 24 28 32 36
x
36 32 28 24 20 16 12 8 4 0
y
36 32 28 24 20 16 12 8 4
Bags of Chips
Bags of Chips
y
4 8 12 16 20 24 28 32 36
Bottles of Soda
x
36 32 28 24 20 16 12 8 4 0
4 8 12 16 20 24 28 32 36
13
x
Bottles of Soda
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x
Bottles of Soda
Bottles of Soda
0
4 8 12 16 20 24 28 32 36
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CSAP Grade 10
Mathematics 9
Tara plays a game using 2 bags of game pieces. One bag has 6 blue game pieces and 6 red game pieces. The other bag has ten game pieces numbered 1 through 10. On her turn, Tara must draw one game piece from each bag. What is the probability that she draws a red game piece and an even-numbered game piece?
1 2 1 4 1 30 1 60
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CSAP Grade 10
Mathematics 10 Edgar earned the following scores on his first 10 science tests. 73, 86, 91, 87, 88, 79, 82, 93, 90, 86 Which of these will be affected if Edgar earns a score of 50 on his next test? mean, median, and mode mean and median mean only median only
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CSAP Grade 10
Mathematics 11 Barbara went for a walk in the city park. To cut across the rectangular park, she chose the path shown by the dotted line in the drawing below.
370 feet
294 feet
x
Drawing not to scale
Barbara
At what angle, x, did Barbara cut across the park? Round the answer to the nearest tenth of a degree. 37.4 38.5 51.5 52.6
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CSAP Grade 10
Mathematics 12 Cindy tossed a coin onto the playing board shown below. 12
8
B
3
C
2
D
1
A
What is the probability the coin will land in region C? In the space below, show and explain your thinking and write your answer on the line.
Probability
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CSAP Grade 10 Mathematics Scoring Guide
CSAP Grade 10
Rubric Exemplary Response:
Mathematics
2 Points
•
2 15
OR
•
16 120
AND
•
The area of region C is 16 square units (8 × 2). The entire board has an area of 120 square units (6 × [12 + 8]). Therefore, region C covers 16 out of 120 square units, or 2/15 of the total area of the board. This means that the coin will land in region C an average of 2 out of every 15 tosses.
OR
•
Other valid response indicating that the fractional area of region C represents the probability that a coin will land in region C.
Score Points: Apply 2-point holistic rubric.
Standard: 3.5.E Data Analysis, Probability, and Statistics
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CSAP Grade 10
Mathematics 13 Juan has a bag containing 3 red, 2 blue, and 5 green marbles. He removes one marble from the bag, sets it aside, and draws another marble. What is the probability that he draws a red marble followed by a blue marble? 2 9
2 10 3 10 1 15
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