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Pascal's Triangle and Investment Worth

Solve problems related to Pascal's triangle, investment growth, and mathematical concepts. Identify patterns and make calculations to find solutions.

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Pascal's Triangle and Investment Worth

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  1. The figure to the right shows a partial view of Pascal’s triangle. Which row of numbers best represents the seventh row in Pascal’s triangle? A 1 5 10 10 5 1 B 1 6 15 20 15 6 1 C 1 7 21 35 35 21 7 1 D 1 8 28 56 70 56 28 9 1 Problem #1 Obj 10 - TAKS 2004 9th [8.16(A)]

  2. Mr. Collins invested some money that will double in value every 12 years. If he invested $5,000 on the day of his daughter’s birth, how much will the investment be worth on his daughter’s 60th birthday? A $300,000 B $160,000 C $80,000 D $320,000 Problem #2 Obj 10 - TAKS 2004 9th [8.16(A)]

  3. The table to the right shows the number of sides and diagonals in certain polygons. Based on the table, how many diagonals should a 9-sided polygon have? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Problem #3 Obj 10 - TAKS 2004 9th [8.16(A)]

  4. The amount of material needed to make a basketball best represents the ball’s: A volume B surface area C circumference D perimeter Problem #4 Obj 10 - TAKS 2004 9th [8.15(A)]

  5. Which of the following is a valid conclusion based on the diagram shown below? A All rhombuses are squares. B All rhombuses are rectangles. C All quadrilaterals are parallelograms. D All rectangles are parallelograms. Problem #5 Obj 10 - TAKS 2004 9th [8.16(A)]

  6. Sean is an Algebra I student who believes that xy2 = (xy)2. Rudy informs Sean that this theory is not always true. Which pair of values for x and y could Rudy use to disprove Sean’s theory? A x = 0 and y = 2 B x = 1 and y = 2 C x = 2 and y = 0 D x = 2 and y = 1 Problem #6 Obj 10 - TAKS 2004 9th [8.16(B)]

  7. Adam’s age is 4 years less than twice Blanca’s age. If Adam is 16 years old, which equation can be used to determine Blanca’s age? A 2(x – 4) = 16 B 2x – 4 = 16 C 4 – 2x = 16 D 2(4 – x) = 16 Problem #7 Obj 10 - TAKS 2004 9th [8.14(A)]

  8. Jake’s square backyard covers an area of 104 square meters. How can Jake best determine the length of each side of his backyard? A Divide the area by the number of sides B Square the area C Find the square root of the area D Divide the area in half Problem #8 Obj 10 - TAKS 2004 9th [8.14(C)]

  9. A middle school band must be at the contest site by 8:00 A.M. to participate in a competition. It takes 45 minutes to load the bus with the band’s equipment, and it takes 1 hour 45 minutes to travel to the contest site. What should be the first step in determining the band’s departure time? A Add the time it takes to travel to the contest site to 8:00 A.M. B Add the time it takes to load the bus to 8:00 A.M. C Add the travel time and loading time together D Subtract the loading time from the travel time Problem #9 Obj 10 - TAKS 2004 9th [8.15(A)]

  10. Mr. Harmon is planning to sell his house and wants to paint all the rooms. A can of paint costs $12.95 plus 7.75% sales tax and covers about 476 square feet. What other information is needed to determine the number of cans of paint Mr. Harmon needs to purchase? A The number of rooms in the house B The area in square feet to be painted C The total cost of each can of paint D The name of the store where Mr. Harmon will buy the paint Problem #10 Obj 10 - TAKS 2004 10th [8.14(A)]

  11. The school drama club plans to attend a Shakespeare festival in 6 weeks. The total cost per person is $185.75. The club has $296 in its account and will divide the money equally among the 8 members who attend the festival. Troy is planning to attend the festival and has already saved $55. How much more money does Troy need in order to cover his cost to attend the festival? A $93.75 B $110.25 C $148.75 D Not here Problem #11 Obj 10 - TAKS 2004 10th [8.14(B)]

  12. A rectangle has an area of 144 square inches and a perimeter of 50 inches. What are the dimensions of the rectangle? A 10 in. by 15 in. B 9 in. by 16 in. C 8 in. by 18 in. D 4 in. by 36 in. Problem #12 Obj 10 - TAKS 2004 10th [8.14(C)]

  13. Linda owns a set of seven wrenches. The wrenches come in consecutive increments of ⅛ inch. Linda has misplaced a wrench. The sizes she has are ⅛ inch, ¼ inch, ½ inch, ⅝ inch, ¾ inch, ⅞ inch Which size wrench is missing from Linda’s set? A B C D Not here Problem #13 Obj 10 - TAKS 2004 10th [8.16(A)]

  14. A circle and its diameter are shown to the right. The value of π is the result of which of the following ratios comparing a circle’s circumference to its diameter? A B C D Problem #14 Obj 10 - TAKS 2004 10th [8.15(A)]

  15. Which statement about the triangles below is true? A All the triangles are scalene. B All the triangles are equiangular. C All the triangles are equilateral. D All the triangles are isosceles. Problem #15 Obj 10 - TAKS 2004 10th [8.16(B)]

  16. In the system of equations 4x + 2y = 10 and 3x + 7y = –18, which expression can be correctly substituted for y in the equation 3x + 7y = –18? A 10 – 2x B 10 + 2x C 5 – 2x D 5 + 2x Problem #16 Obj 10 - TAKS 2004 10th [8.14(B)]

  17. A pattern exists as a result of raising i, an imaginary number, to n, an integer greater than or equal to 1. Based on the table, which of the following best represents i raised to the 16th power? A B -1 C -i D 1 Problem #17 Obj 10 - TAKS 2004 10th [8.16(A)]

  18. Shannon has spent $850 on gasoline and repairs for her car in the last 6 months. Of this total, she spent $300 on repairs. The gasoline she purchased cost $1.29 per gallon. Which of the following can be used to determine how many gallons of gas, g, Shannon has bought within the last 6 months? A 1.29g – 300 = 850 B 1.29g + 300 = 850 C 1.29 – 300g = 850 D 1.29 + 300g = 850 Problem #18 Obj 10 - TAKS 2004 10th [8.15(A)]

  19. How many 2-inch cubes can be placed completely inside a box that is 8 inches long, 2 inches wide, and 6 inches tall? A 8 B 12 C 24 D 48 Problem #19 Obj 10 - TAKS 2004 11th [8.14(C)]

  20. Given: Two angles are supplementary. The measure of one angle is 20° more than the measure of the other angle. Conclusion: The measure of the angles are 70° and 90°. This conclusion: A is contradicted by the first statement given B is verified by the first statement given C invalidates itself because a 90° angle cannot be supplementary to another D verifies itself because 90° is 20° more than 70° Problem #20 Obj 10 - TAKS 2004 11th [8.16(B)]

  21. A wooden pole was broken during a windstorm. Before it broke, the total height of the pole above the ground was 25 feet. After it broke, the top of the pole touched the ground 15 feet from the base. How tall was the part of the pole that was left standing? A 8 ft B 10 ft C 17 ft D 20 ft Problem #21 Obj 10 - TAKS 2004 11th [8.14(B)]

  22. Marsha brought cookies to school. She gave a third of her cookies to Ana. Ana then gave a fourth of her cookies to Cybil. Cybil gave half of her cookies to Betsy. If Betsy has 2 cookies, how many cookies did Marsha have in the beginning? A 18 B 24 C 36 D 48 Problem #22 Obj 10 - TAKS 2004 11th [8.14(C)]

  23. As part of a classroom assignment, Kimberly was given this geoboard to model the slope of ⅔ . If the peg in the lower left-hand corner represents the origin on a coordinate plane, where could Kimberly place a rubber band to represent the given slope? A From peg V to peg W B From peg V to peg X C From peg V to peg Y D From peg V to peg Z Problem #23 Obj 10 - TAKS 2004 11th [8.15(A)]

  24. Chase wanted to find 3 consecutive whole numbers that add up to 81. He wrote the equation (n – 1) + n + (n + 1) = 81. What does the variable n represent in the equation? A The least of the 3 whole numbers B The middle of the 3 whole numbers C The greatest of the 3 whole numbers D The difference between the least and greatest of the 3 whole numbers. Problem #24 Obj 10 - TAKS 2004 11th [8.15(A)]

  25. A leap year occurs when the number of a year is a multiple of 4. However, year numbers that are multiples of 100 are not leap years unless they are multiples of 400. Which is not an example of a leap year? A 2440 B 2400 C 2340 D 2300 Problem #25 Obj 10 - TAKS 2004 11th [8.16(A)]

  26. For a sports banquet Coach Mackey must use the rectangular tables in the school cafeteria. The diagram below shows the seating arrangements that Coach Mackey can use at 1 and 2 tables. Which expression can be used to determine the number of people who can sit as a group if y tables are joined to form 1 long table? A 6y B 4(y + 1) C 3(y + 1) D 2(2y + 1) Problem #26 Obj 10 - TAKS 2004 11th [8.16(A)]

  27. A pizza parlor surveyed 100 customers to determine their favorite pizza topping or combination of toppings. The results are shown to the right. How many of the customers surveyed picked a combination of only 2 toppings as their favorite? A 5 B 7 C 14 D 19 Problem #27 Obj 10 - TAKS 2004 11th [8.16(A)]

  28. ∆LMN is similar to ∆XYZ. Which procedure can be used to find the number of degrees in < N? A Subtract 100 from 360 B Subtract 100 from 180 C Divide 100 by 2 D Divide 180 by 3 Problem #28 Obj 10 - TAKS 2004 8th [8.15(A)]

  29. A pattern of equations is shown below. 1% of 800 = 8 2% of 400 = 8 4% of 200 = 8 8% of 100 = 8 16% of 50 = 8 Which statement best describes this pattern of equations? A When the percent is doubled and the other number is halved, the answer is 8. B When the percent is doubled and the other number is doubled, the answer is 8. C When the percent is increased by 2 and the other number remains the same, the answer is 8. D When the percent remains the same and the other number is increased by 2, the answer is 8. Problem #29 Obj 10 - TAKS 2004 8th [8.16(A)]

  30. After careful consideration of the menu shown below, Mireya purchased Charlie’s Value Meal No. 2. Mireya calculated her savings by finding the sum of $2.49 plus 2 times $1.29. What did Mireya do next to calculate her savings? A Add $1.29 to the sum B Divide the sum by 3 C Subtract $4.29 from the sum D Subtract $4.69 from the sum Problem #30 Obj 10 - TAKS 2004 8th [8.16(A)]

  31. Roderick is building a model of an actual airplane with a length of 20 feet. What other information is necessary in order to find x, the length of the model airplane? A The ratio of the length of the model airplane’s tail to the length of its wing. B The speed of the model airplane C The scale factor used D The model airplane’s wingspan Problem #31 Obj 10 - TAKS 2004 8th [8.14(B)]

  32. Mr. Thomas is framing a 28–by–40–foot area for a concrete slab. If the concrete company charges $120.00 per cubic yard of concrete, what other information is needed in order to find c, the cost of the concrete slab? A The area of the slab B The thickness of the slab C The perimeter of the slab D The price per cubic foot of concrete Problem #32 Obj 10 - TAKS 2004 8th [8.14(A)]

  33. Mrs. Avery bought a 5–pound bag of white potatoes for $4.25. If red potatoes sold for $0.89 per pound, why did Mrs. Avery believe that she made the better buy? A The number of red potatoes in a 5–pound bag is greater than the number of white potatoes in a 5–pound bag. B The cost of all kinds of potatoes in 5–pound bags is the same. C The cost per pound of white potatoes is $0.04 less than the cost per pound of red potatoes. D The cost per pound of white potatoes is $0.04 more than the cost per pound of red potatoes. Problem #33 Obj 10 - TAKS 2004 8th [8.16(B)]

  34. The figure below shows three shaded equilateral triangles inside a rectangle. Which statement about this figure is true? A The shaded area is more than 50% of the area of the rectangle. B The shaded area is ¾ of the unshaded area of the rectangle. C The unshaded area is ⅔ of the shaded area of the rectangle. D The shaded area is equal to the unshaded area of the rectangle. Problem #34 Obj 10 - TAKS 2004 8th [8.15(A)]

  35. On Monday Cornelius’s mother gave his school money for the week. He spent $2.80 for lunch every day for 5 school days. He paid a $0.75 book fine at the library and bought school supplies for $3.50. If Cornelius had $1.75 left at the end of the school week, which expression can he use to find the amount of money he received on Monday? A 1.75 + 5(2.80) + 3.50 + 0.75 B 5(2.80) + 3.50 + 0.75 – 1.75 C 1.75 + 2.80 + 0.75 + 3.50 D 5(2.80 + 3.50 + 0.75 + 1.75) Problem #35 Obj 10 - TAKS 2004 8th [8.14(C)]

  36. Valdemar has a spinner like the one shown below. Valdemar would like to increase the chances of the following events: • Spinning an even number • Spinning a number less than 4 •Spinning the square root of 9 Valdemar decides to remove the 5 from the spinner. Which statement best supports his reasoning? A The number 5 takes up more space on the spinner. B Spinning the number 5 has the greatest probability. C The number 5 is the greatest number. D Spinning the 5 is not a desired event. Problem #36 Obj 10 - TAKS 2004 8th [8.16(B)]

  37. The Stars, the Tigers, and the Lobos scored a total of 56 goals during the hockey season. The Stars scored 4 more goals than the Tigers, and the Lobos scored twice as many goals as the Tigers. Which is a reasonable conclusion about the goals the teams scored? A The Stars scored the least number of goals. B The Stars and the Lobos scored an equal number of goals. C The Tigers scored exactly half the total goals. D The Lobos scored the greatest number of goals. Problem #37 Obj 10 - TAKS 2003 8th [8.14(b)]

  38. The figure shows a rectangle inside a circle. Which procedure should be used to find the area of the shaded region? A Find the area of the circle and then subtract the area of the rectangle. B Find the circumference of the circle and then subtract the perimeter of the rectangle. C Find the circumference of the circle and then subtract the area of the rectangle. D Find the area of the rectangle and then subtract the perimeter of the rectangle. Problem #38 Obj 10 - TAKS 2003 8th [8.14(C)]

  39. Before the last game of the basketball season, Fernando had scored a total of 73 points. He scored 20 points in the last game, making his season average 15.5 points per game. To find the total number of games he played, first find the sum of 73 and 20 and then — A add the sum to 15.5 B subtract 15.5 from 73 C multiply the sum by 15.5 D divide the sum by 15.5 Problem #39 Obj 10 - TAKS 2003 8th [8.15(A)]

  40. The figures below have a repeating pattern. Which shows a 180° rotation of the 19th figure in the pattern? Problem #40 Obj 10 - TAKS 2003 8th [8.16(A)]

  41. The Venn diagram shows how many of the 400 students at Smith Middle School have a scooter only, a skateboard only, or both a scooter and a skateboard. Use the information in the diagram to find the probability that 1 student chosen at random has neither a scooter nor a skateboard. Problem #41 Obj 10 - TAKS 2003 8th [8.14(A)]

  42. There are 4 children in the Carter family. Roger is 1 ¼ times as tall as Charlie. John is 3 inches taller than Roger. Grace is 58 inches tall, and she is 2 inches taller than Charlie. How tall is John in feet and inches? A B C D Problem #42 Obj 10 - TAKS 2003 8th [8.14(B)]

  43. Antonio and his two brothers equally shared the cost of a new CD with a list price of $18. They received a 20% discount off the list price and paid 8.25% sales tax on the discounted price. Find the approximate amount that each of the 3 brothers paid toward the cost of the CD. A $4.80 B $5.20 C $6.50 D $15.59 Problem #43 Obj 10 - TAKS 2003 8th [8.14(b)]

  44. Rectangle I is similar to rectangle II. The area of rectangle II is 216 square centimeters. Find the area of rectangle I. A 4 cm2 B 12 cm2 C 24 cm2 D 108 cm2 Problem #44 Obj 10 - TAKS 2003 8th [8.14(B)]

  45. The following statements are true about ∆XYZ. • The measure of each angle is evenly divisible by 12. • The measure of < Z is greater than the measure of < Y. • The measure of < Y is greater than the measure of < X. • The measure of < X is greater than 40°. Which choice fits all 4 statements for angles X, Y, and Z? F m < X = 72° m < Y = 60° m < Z = 48° H m < X = 50° m < Y = 60° m < Z = 70° G m < X = 60° m < Y = 72° m < Z = 48° J m < X = 48° m < Y = 60° m < Z = 72° Problem #45 Obj 10 - TAKS 2003 8th [8.16(B)] TAKS 2003 8th

  46. A camp leader plans to buy 3 hot dogs per person for a cookout. If 30 people are going on the cookout and if hot dogs cost $3.99 per package, what other information is needed to find the cost of the hot dogs? A The number of meals at which hot dogs will be served B The cost of mustard and relish C The number of people who eat hot dogs D The number of hot dogs in a package Problem #46 Obj 10 - TAKS 2003 8th [8.14(A)]

  47. Which of the equations below represents the second step of the solution process? A. 5(6x + 1) + 4 = –39 B. 5(6x + 5) = –39 C. 30x + 4 + 1 = –39 D. 30x + 20 + 1 = –39 Step 1. 5(6x + 4) + 1 = –39 Step 2. Step 3. 30x + 21 = –39 Step 4. 30x = –60 Step 5. X = –2 Problem #47 Obj 10 - TAKS 2003 9th [8.14(C)]

  48. Alonso’s family rented a car when they flew to Orlando for a 4-day vacation. They paid $39 per day and $0.09 for each mile driven. How much did it cost to rent the car for 4 days and drive 350 miles, not including tax? A. $70.50 B. $124.50 C. $156.00 D. $187.50 Problem #48 Obj 10 - TAKS 2003 9th [8.14(B)]

  49. The function g(x) = 1.25 + 0.70(x – 1) represents the charge for parking in the mall garage for x number of hours. Which statement best represents the formula for this charge? A. The charge consists of a set fee of $1.25 plus $0.70 for every hour parked. B. The charge consists of a flat rate of $0.70 for every hour parked. C. The charge consists of $1.25 for the first hour parked and $0.70 for each additional hour. D. The charge consists of $1.25 for every hour parked plus a set fee of $0.70. Problem #49 Obj 10 - TAKS 2003 9th [8.15(A)]

  50. A newspaper reported that the mean height of waves in the Norwegian Sea increased by 4 inches per year from 1955 to 1994. What additional information is needed to calculate the mean wave height in 1994? A. The mean height of waves in 1955. B. The range of wave heights from 1955 to 1994. C. The projection of the mean height of waves for the next year. D. The distance from land to where the wave measurements were taken. Problem #50 Obj 10 - TAKS 2003 9th [8.14(A)]

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