IA1 Geometry Past Paper PDF

1. Point Q is the midpoint of 𝑃𝑅 and PR = 21.75 yards. What is the length in yards of 𝑄𝑅? _________ yards 2. Ray BC bisects ∠𝐴𝐵𝐷. If 𝑚∠𝐴𝐵𝐷 = 78°, what is 𝑚∠𝐶𝐵𝐷 in degrees? _________ degrees 3. Angles RTG and GTU are adjacent angles. If 𝑚∠𝑅𝑇𝐺 = 5. 8°, and 𝑚∠𝐺𝑇...

1. Point Q is the midpoint of 𝑃𝑅 and PR = 21.75 yards. What is the length in yards of 𝑄𝑅? _________ yards 2. Ray BC bisects ∠𝐴𝐵𝐷. If 𝑚∠𝐴𝐵𝐷 = 78°, what is 𝑚∠𝐶𝐵𝐷 in degrees? _________ degrees 3. Angles RTG and GTU are adjacent angles. If 𝑚∠𝑅𝑇𝐺 = 5. 8°, and 𝑚∠𝐺𝑇𝑈 = 113. 6°, what is 𝑚∠𝑅𝑇𝑈? _________ degrees 4. A city’s boundaries are shown on the grid. Each unit (individual side of each square) equals 5 miles. Part 1 Which measurement is the BEST estimate of the area of the city? A. 38 square miles B. 58 square miles C. 1,438 square miles D. 2,875 square miles Part 2 There are 11,172 people per square mile living in the city shown. Within the next 10 years, the population is expected to decrease to 9,500 people per square mile. How many fewer people are expected to live in the city in 10 years? _________ fewer people 1  5. A fire marshal states that the maximum capacity of a school gym per square yard is 2 students. If the gym is 30 yards by 20 yards, what is the maximum number of students that can attend a dance held in the gym? _________ students 6. Which statement is the converse of the conditional statement? If ray BC bisects ∠𝐴𝐵𝐷, then the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are equal. A. If the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are equal, then ray BC bisects ∠𝐴𝐵𝐷. B. If ray BC bisects ∠𝐴𝐵𝐷, then the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are not equal. C. If the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are not equal, then ray BC does not bisect ∠𝐴𝐵𝐷. D. If ray BC does not bisect ∠𝐴𝐵𝐷, then the measures of ∠𝐴𝐵𝐶 and ∠𝐷𝐵𝐶 are not equal. 7. The length of 𝐾𝐿 is 8𝑥 − 17 units. The length of 𝑆𝑇 is − 2𝑥 + 18 units. For what value of 𝑥 are the segments congruent? ______________ 8. Point P lies on 𝑄𝑅 as shown in the diagram below. Part 1 What is the value of x? 𝑥 = _________ Part 2 What is the length of 𝑄𝑅 in feet? _________ feet 2  9. Angles ABC and CBD are a linear pair. If 𝑚∠𝐶𝐵𝐷 = 90°, what is 𝑚∠𝐴𝐵𝐶 in degrees? _________ degrees 10. In the diagram below, lines TU and EF intersect at point Y. If 𝑚∠𝑈𝑌𝐹 = 42°, what is 𝑚∠𝐹𝑌𝑇? _________ degrees 11. In the figure above, three lines intersect at point P. If x = 65 and y = 75, what is the value of z? A. 140 B. 80 C. 40 D. 20 3  12. Choose the appropriate reasons to fill in the proof. Given: 5𝑡 − 2 = 13 Prove: 𝑡 = 3 Which of these reasons best complete the proof? A. 2. Addition Property of Equality 4. Multiplication Property of Equality B. 2. Addition Property of Equality 4. Division Property of Equality C. 2. Subtraction Property of Equality 4. Division Property of Equality D. 2. Subtraction Property of Equality 4. Multiplication Property of Equality 13. The results of a student survey about a preferred new color for a common room are shown in the two-way relative frequency table. Common Room Color White Yellow Gray Total Class Junior 0.15 0.18 0.15 0.48 Senior 0.33 0.07 0.12 0.52 Total 0.48 0.25 0.27 1 Part A What is the relative frequency of surveyed students who prefer yellow as the common room color given that they are juniors? ____________ Part B 4  Is there an association between seniors and a preferred common room color of white? A. There is an association because seniors are more likely to choose the color white than surveyed students are to choose the color white. B. There is no association because seniors are more likely to choose the color white than surveyed students are to choose the color white. C. There is an association because seniors are as likely to choose the color white as surveyed students are to choose the color white. D. There is no association because seniors are as likely to choose the color white as surveyed students are to choose the color white. 14. The two-way relative frequency table shows the results of a survey that asked shoppers their preferred vegetable. Preferred Vegetable Peas Corn Carrots Total Shop Monday 0.16 0.23 0.18 0.57 ping Day Tuesday 0.12 0.17 0.14 0.43 Total 0.28 0.40 0.32 1 Which statement is true? A. It is more likely that a person who shops on Monday prefers peas than a person who shops on Tuesday prefers corn. B. It is more likely that a person who shops on Monday prefers corn than a person who shops on Tuesday prefers carrots. C. It is more likely that a person who shops on Tuesday prefers peas than a person who shops on Monday prefers carrots. D. It is more likely that a person who shops on Tuesday prefers corn than a person who shops on Monday prefers corn. 15. The time that people spent looking at two different sculptures in a museum is observed. The data are summarized in the histograms. What is the relationship between the standard deviations for the time people spent looking at the sculptures? A. The standard deviations are equal for both sculptures. B. The relationship between the standard deviations cannot be determined. C. The standard deviation for Sculpture G is greater than the standard deviation for Sculpture H. D. The standard deviation for Sculpture H is greater than the standard deviation for Sculpture G. 16. The residents on two different streets recorded how many bags of leaves each house put out for leaf collection day. The data are displayed in the dot plots. 5  Determine whether each statement is true or false. True False Street S has the same number of houses as Street T. Street T has a larger mean number of bags than Street S. Street S has a smaller median number of bags than Street T. Street S and Street T have the same interquartile range for the number of bags put out for leaf collection. 17. A list of 10 data values is shown. 6, 8, 16, 4, 17, 26, 8, 5, 5, 5 What is the mean of this data? 18. The dot plots represent the distributions of values in data sets A and B. Which of the following statements must be true? I. The median of data set A is equal to the median of data set B. II. The standard deviation of data set A is equal to the standard deviation of data set B. A. I only B. II only C. I and II D. Neither I nor II 6