Maths Practice Questions

<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P18 Q10 Practice Questions</h4><ol><li>Alex has a collection of stamps that can be evenly divided into groups of 5, 10, and 20. If half of the stamps are international stamps and half are local stamps, determine the minimum value of the collection if the international stamps are worth $1 each and local stamps are worth $0.50 each.</li><li>Sarah collects marbles that can be divided into groups of 6, 9, and 18 without any leftovers. If 1/4 of her marbles are blue, 1/4 are red, and 1/2 are green, calculate the minimum total value of her collection if blue marbles are $0.10 each, red marbles are $0.25 each, and green marbles are $0.50 each.</li><li>Liam has different colored balls that can be grouped into sets of 4, 8, and 16. If one third of the balls are red, one third are blue, and one third are yellow, find the minimum total value of the balls if red balls cost $0.75 each, blue balls cost $0.50 each, and yellow balls cost $0.25 each.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P19 Q12 Practice Questions</h4><ol><li>Each box in stack X is 15cm in height, while each box in stack Y is 20cm in height. What is the minimum height for each stack so that both stacks will be of the same height? How many boxes are required for stack X to reach this minimum height?</li><li>Each book in shelf A is 3 inches in height, while each book in shelf B is 4 inches in height. What is the minimum height for each shelf so that both shelves will be of the same height? How many books are required for shelf A to reach this minimum height?</li><li>Each vial in rack 1 is 10cm in height, while each vial in rack 2 is 15cm in height. What is the minimum height for each rack so that both racks will be of the same height? How many vials are required for rack 1 to reach this minimum height?</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P24 Q25 Practice Questions</h4><ol><li>John has two ribbons, one 72 cm long and the other 48 cm long. What are two possible integer lengths for the pieces he can cut, and what is the longest possible length?</li><li>Emily has two cables, one measuring 60 cm and the other measuring 90 cm. Determine two potential integer widths for the cables that can be cut into smaller sections and find the maximum width possible.</li><li>David has two wooden planks, one measuring 120 cm and the other 150 cm. Give two possible integer lengths of pieces he can cut, as well as the maximum possible length.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P24 Q26 Practice Questions</h4><ol><li>There was a long queue of 600 people for a gift distribution. Every 120th person will receive a tablet, every 50th person will receive a portable charger, and every 25th person will receive a $30 gift card. How many people will receive a tablet and a portable charger simultaneously? And how many will receive all three items simultaneously?</li><li>A line of 500 people is waiting for a concert. Every 80th person will receive a concert T-shirt, every 35th person will receive a VIP pass, and every 20th person will receive a $100 gift card. How many people will receive a concert T-shirt and a VIP pass simultaneously? And how many will receive all three items simultaneously?</li><li>In a marathon of 1000 runners, every 200th runner will receive a medal, every 75th runner will receive a water bottle, and every 50th runner will receive a $20 cash prize. How many runners will receive a medal and a water bottle simultaneously? And how many will receive all three items simultaneously?</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P25 Q27 Problems and Practice Questions</h4>According to scientific research, it is found that the cicada insects have life cycles of prime numbers. A particular breed of cicada breeds every 13 years.Suppose a cicada’s predator has a life cycle in a particular year.(a) Find the number of years, A, before a predator’s life cycle coincides with that of the cicada’s again.(b) Suppose the life cycle of cicadas change to a non-prime number, 12 years or 10 years. Find the value of B and C.(c) In general, different predators of the cicadas can have life cyclesof2,3,4,6 and 12 years. Briefly explain, based on the results2above, how it is an advantage for cicadas to have a life cycle of13 years, which is prime.<img src="https://knowt-user-attachments.s3.amazonaws.com/cea55568-e075-4220-8844-60eb57be9be3.png" data-width="100%" data-align="center">Practice Questions1. A certain type of cicada breeds every 17 years. If a predator breeds every 15 years, find the number of years, A, before the predator’s life cycle coincides with that of the cicada’s again.2. Suppose a cicada’s life cycle changes to the non-prime number of 14 years. Calculate the years, B, before the predator’s life cycle coincides with that of the cicada’s again if the predator breeds every 3 years.3. Discuss the implications of cicadas with an 11-year life cycle when faced with predators that have life cycles of 2, 5, and 10 years. How might this prime cycle provide advantages against these predators?<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P26 Q28 Problems and Practice Problems</h4>A school is planning a learning journey for 3 classes, where the 36 students, 36 students and 40 students in the respective classesA teacher intends to seat the students in different buses such thatevery bus has the same number of students from each class.(a)What is the maximum number of buses which will allow the students from each class to be evenly distributed?(b) Find the total number of students in each bus.Practice Questions1. A school has 24 students in Class A, 36 students in Class B, and 30 students in Class C. The teacher wants to divide the classes into buses so that each bus has the same number of students from each class.(a) What is the maximum number of buses that can be used?(b) Calculate how many students will be in each bus.2. There are 28 students in Class X, 42 students in Class Y, and 56 students in Class Z. A teacher plans to take them on a field trip and wants to use buses that seat the same number of students from each class.(a) How many buses can be used to ensure an equal distribution of students from each class?(b) What will be the number of students in each bus?3. For an event, there are 45 students in Group 1, 30 students in Group 2, and 60 students in Group 3. The organizer wishes to arrange them into buses so that the number of students from each group is the same in every bus.(a) Determine the maximum number of buses that can be used.(b) What is the total number of students per bus?<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P27 Q1 Problem and Practice Problems</h4>For any two numbers x and y, their LCM and HCF are related by the following formula: HCF(x,y) * LCM(x,y) = xyGiven that the product of two numbers is 3240 and their HCF is 2×3², find the LCM in index notation.Practice Questions1. For any two numbers a and b, their LCM and HCF are related by the formula: HCF(a,b) * LCM(a,b) = ab. Given that the product of two numbers is 4800 and their HCF is 4×5, find the LCM in index notation.2. For two numbers m and n, their LCM and HCF can be defined using the relation: HCF(m,n) * LCM(m,n) = mn. If the product of two numbers is 7560 and their HCF is 3×7, determine the LCM in index notation.3. The relationship between the HCF and LCM of any two integers p and q is given by: HCF(p,q) * LCM(p,q) = pq. If the product of two numbers is 2100 and their HCF is 5×3, calculate the LCM in index notation.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P27 Q2 Problems and Practice Problems</h4>The diagram shows a framework of a cube made by wire. The volume of the cube is 729 000 cm³.(a) Express the volume in index notation.(b) Find the length of wire used.Practice Questions<ol><li>The volume of a cube is 1,000,000 cm³.(a) Express the volume in index notation.(b) Calculate the total length of wire used if each edge of the cube is made of wire that measures the same length.</li><li>A cube has a volume of 512,000 cm³.(a) Write the volume in index notation.(b) Determine the length of wire used to create the cube's edges.</li><li>The volume of a cube is 216,000 cm³.(a) Express this volume in index notation.(b) Find out how much wire is needed to outline the cube.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P28 Q3 Problem and Practice Problems</h4>The LCM of three numbers P, Q and R is 2^5 × 3^6 × 5² * 7²Given thatP = 2^4 × 3^5 × 7² andQ = 2^5 × 3² 57,find the smallest value of R, in index notation.Practice Questions1. The LCM of three numbers A, B, and C is 3^4 × 5^3 × 7^2. Given that A = 3^3 × 5^2 and B = 3^2 × 5^1 × 7, find the smallest value of C, in index notation.2. The LCM of three numbers X, Y, and Z is 2^6 × 3^3 × 11^1. Given that X = 2^4 × 3^2 and Y = 2^3 × 3^1 × 11^0, determine the smallest value of Z, in index notation.3. The LCM of three numbers M, N, and O is 2^4 × 3^3 × 5^2 × 13^1. Given that M = 2^3 × 3^2 and N = 2^4 × 5^1, find the smallest value of O, in index notation.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P28 Q4 Problem and Practice Problems</h4>It is given that M = sixth root of 2^p * 2^q is an integer and M is a common factor of 1728 and 648. Find the largest possible values of p and q.Practice Questions<ol><li>Given that N = third root of 3^m * 3^n is an integer and N is a common factor of 729 and 486. Find the largest possible values of m and n.</li><li>Let P = fourth root of 5^a * 5^b be an integer such that P is a common factor of 1250 and 5000. Determine the largest possible values of a and b.</li><li>Suppose Q = fifth root of 4^x * 4^y is an integer and Q is a common factor of 1024 and 256. Find the largest possible values of x and y.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P29 Q1 Practice Problems</h4>Practice Questions<ol><li>Given that x is a prime number, is 4x a prime number? Give a reason for your answer.</li><li>Given that z is a prime number, is 10z a prime number? Give a reason for your answer.</li><li>Given that w is a prime number, is 8w a prime number? Give a reason for your answer.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P30 Q7b, Q8 and Q9 Practice Problems</h4><ol><li>The cube of p is 27. Find the value of p. Find the LCM of 2^2 * 5^3 and 2^4 * 3^2 * 5. Find the value of each variable. (a) square root of x = 3^6 (b) cube root of y = 2^2 * 3^5 (c) square root of 11^8 * 13^6 = 11^c * 13^d.</li><li>The cube of r is 64. Find the value of r. Find the LCM of 3^2 * 5^3 and 2^4 * 3^1 * 5^2. Find the value of each variable. (a) square root of m = 5^4 (b) cube root of n = 3^2 * 2^3 (c) square root of 2^12 * 5^4 = 2^a * 5^b.</li><li>The cube of s is 125. Find the value of s. Find the LCM of 2^1 * 5^2 and 2^3 * 3^3 * 5^1. Find the value of each variable. (a) square root of z = 2^5 * 3^1 (b) cube root of x = 5^3 (c) square root of 11^2 * 2^6 = 11^e * 2^f.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P9 Practice Problems</h4>Practice Questions<ol><li>Find the HCF of the numbers in index notation: 3^5 * 2^2 and 3^4 * 2^3.</li><li>Find the HCF of the numbers in index notation: 5^6 * 7^2 and 5^4 * 7^5.</li><li>Find the HCF of the numbers in index notation: 11^3 * 2^8 and 11^2 * 2^5.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P30 Q10 Practice Questions</h4>Practice Questions<ul><li>For 2: HCF(3, a) = a (since a must be less than or equal to 3)</li><li>For 5: HCF(7, 2) = 2</li><li>For 11: HCF(2, 3) = 2 Thus, a can be any value less than or equal to 3 but not equal to 3, therefore possible values of a are 0, 1, or 2.</li></ul><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P31 Q2 Practice Questions</h4><ol><li>Express 243 as a product of its prime factors in index notation.</li><li>Express 120 as a product of its prime factors in index notation.</li><li>Express 540 as a product of its prime factors in index notation.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P31 Q5 B Practice Questions</h4>Practice Questions<ol><li>Find the LCM and HCF of 48 and 180 in index notation given that 48 = 2^4 * 3^1 and 180 = 2^2 * 3^2 * 5^1.</li><li>Find the LCM and HCF of 60 and 120 in index notation given that 60 = 2^2 * 3^1 * 5^1 and 120 = 2^3 * 3^1 * 5^1.</li><li>Find the LCM and HCF of 150 and 225 in index notation given that 150 = 2^1 * 3^1 * 5^2 and 225 = 3^2 * 5^2.</li></ol><h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P31 Q6 Problem and Practice Questions</h4>A scout has three ropes of lengths 70 cm, 112 cm and 280 cm respectively. fe cut equal。lengths from all the three ropes, a maximum number ofequal pieces from each rope without any leftover, Find the total number of pieces of rope of equal lengths that the scout has in the end.Practice Questions1. A carpenter has three pieces of wood measuring 84 cm, 126 cm, and 168 cm respectively. If he cuts equal lengths from each piece, find out how many total pieces of wood he can cut without any leftover. 2. A gardener has three sections of garden hose that are 90 cm, 150 cm, and 270 cm long. If he wants to cut the hoses into equal lengths without leftovers, determine how many total lengths he can create. 3. A chef has three rolls of pastry that are 60 cm, 100 cm, and 180 cm in length. If he divides the rolls into the largest possible equal lengths without any scraps, calculate the total number of pastry pieces he will have. <h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P31 Q8B Problem and Practice Questions</h4>Find two numbers, both smaller than 80, that have a lowest common multiple of 126 and a highest common factor of 21.Practice Questions1. Find two numbers, both smaller than 100, that have a lowest common multiple of 144 and a highest common factor of 36. 2. Find two numbers, both smaller than 50, that have a lowest common multiple of 60 and a highest common factor of 12. 3. Find two numbers, both smaller than 90, that have a lowest common multiple of 210 and a highest common factor of 30.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q1B Problem and Practice Questions</h4>Written as a product of its prime factors,4500=22 x 32 x 53.Find the smallest positive integer k such that 4500k is a perfect cube.Practice Questions1. Written as a product of its prime factors, 3600 = 2^4 * 3^2 * 5^2. Find the smallest positive integer k such that 3600k is a perfect cube. 2. Written as a product of its prime factors, 5400 = 2^3 * 3^3 * 5^2. Find the smallest positive integer k such that 5400k is a perfect cube. 3. Written as a product of its prime factors, 12,600 = 2^2 * 3^2 * 5^2 * 7^1. Find the smallest positive integer k such that 12,600k is a perfect cube.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q2B Problem and Practice Questions</h4>The diagram shows a rectangle of length (32x 53)cm and breadth 5 cm. A square has the same area as the rectangle. Find the length of each side of the square. Give your answer as a product of its prime factors.Practice Questions

A rectangle has a length of (36 x 48) cm and a width of 6 cm. Find the length of each side of the square that has the same area as the rectangle, and express your answer as a product of its prime factors.
The dimensions of a rectangle are (20 x 25) cm for the length and 10 cm for the width. Calculate the side length of the square that has the same area as the rectangle. Provide your answer in the form of prime factors.
A rectangle measures (15 x 40) cm in length and 8 cm in width. Determine the side length of a square that shares the same area as this rectangle and express your answer as a product of its prime factors.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q3 Problems and Practice Questions</h4>Three types of desks, A, B and C, of the same breadth have lengths 60 cm, 80 cm and 120 cm respectively. The desks are arranged along the breadths of each desk as shown, such that the length of each row is the same. (a) Find the minimum length for each row of arranged desks. (b) Given that the breadth of each table is 40 cm, hence, find the minimum total area.Practice Questions
Three types of chairs, X, Y, and Z, of the same width have lengths 70 cm, 90 cm, and 140 cm respectively. The chairs are arranged along the widths of each chair such that the length of each row is the same.(a) Find the minimum length for each row of arranged chairs.(b) Given that the width of each chair is 45 cm, hence, find the minimum total area.
Three models of tables, M, N, and O, with lengths 50 cm, 100 cm, and 150 cm respectively, are displayed in a showroom such that the length of each row is the same.(a) Determine the minimum length required for each row of tables.(b) If the width of each table is 30 cm, calculate the minimum total area of the display.
Three types of cabinets, P, Q, and R, with lengths of 80 cm, 120 cm, and 160 cm respectively are arranged side by side in a storage area.(a) Calculate the minimum length for the arrangement of cabinets.(b) If each cabinet has a width of 50 cm, find the minimum total area occupied by all cabinets combined.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q4 Problems and Practice Questions</h4>(a) There are a total of 231 cubes. The cubes are used to make a cuboid. The length of each cuboid is made of more than one cube. Find the number of cubes on each side of the cuboid. (b) Suppose there are now 693 cubes instead. Find three possibilities for the dimensions of the cuboid.Practice Questions
There are a total of 120 cubes. The cubes are used to create a cuboid. The length of each side of the cuboid is greater than one cube. Determine the number of cubes on each side of the cuboid.
Given 420 cubes, use them to form a cuboid. What are three possible combinations for the dimensions of this cuboid?
You have 512 cubes. They are arranged to form a cuboid where all sides contain more than one cube. Calculate the number of cubes on each side of the cuboid.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q5 Problems and Practice Questions</h4>(a) Express 350 as a product of its prime factors.(b) The number 350k is a perfect square. Find the smallest positive integer of k.(c) y is a number less than 400.The highest common factor of y and 350 is 35.Find the largest possible value of y. Practice Questions1. Express 450 as a product of its prime factors. 2. The number 450k is a perfect square. Find the smallest positive integer of k.3. z is a number less than 500. The highest common factor of z and 450 is 50. Find the largest possible value of z.<h4 collapsed="false" seolevelmigrated="true">Mathematics Tutorial P32 Q6 Problems and Practice Questions</h4><img src="https://knowt-user-attachments.s3.amazonaws.com/db76fb2b-3800-48a5-b82c-d81014f35fa2.png" data-width="100%" data-align="center">Practice Questions<ol><li>Express 144 as a product of its prime factors. Using your answer, explain why 144 is a perfect square. Find the values of p and q such that 144 * p / q is a perfect cube.</li><li>Express 625 as a product of its prime factors. Explain why 625 is a perfect square. Find p and q so that 625 * p / q is a perfect cube.</li><li>Express 729 as a product of its prime factors. Using your answer, discuss why 729 is a perfect square. Determine values for p and q so that 729 * p / q is a perfect cube.</li></ol>