Question 1
The school library has 36 Drama books, 54 History books, and 90 Science books to be placed on shelves.
a) What is the maximum number of books that can be arranged on each shelf without mixing genres?
b) How many shelves are needed if each shelf contains the maximum number of books from a single genre?
c) If a student can borrow 5 books per day, how many days are needed to borrow all the books?
d) Determine the least common multiple of the given numbers.
Question 2
A gardener has 270 tulips, 225 daisies, and 405 sunflowers. He wants to create flower bouquets with an equal number of flowers from each type.
a) Write the prime factorization of 225.
b) What is the maximum number of flowers each bouquet can contain?
c) How many such bouquets can be prepared?
d) Are 270, 225, and 405 coprime?
Question 3
Raj and his sister reserve seats B12 and B13 for a movie. Using the menu below, determine what they ordered if they spent ₹1550 in total, inclusive of their tickets.
Pizza ₹200
Soda ₹150
Chips ₹130
Ice Cream ₹100
Water ₹30
a) With each ticket priced at ₹400, what snacks might they have bought?
b) How much extra will they need if they also decide to order a combo of Pizza, Ice Cream, and Soda?
Question 4
E, F, G, and H are collinear points in sequence. EF = GH, and G is the midpoint of FH. Prove that:
i) EG = FH
ii) EF = 1/3 EH
Question 5
a) Sketch a rough figure for lines XY and XZ intersecting at X.
b) True or False: Two chords in a circle will always intersect.
c) Sketch a rough outline of quadrilateral MNOP. Illustrate its diagonals and label them. Is the intersection of the diagonals inside or outside the quadrilateral?
Question 6
a) Determine the sum of (-6) + (-2) on the number line.
b) Compute: (-250) + (+324) + (-237) – (-630)
c) If p=12 and q=18, evaluate pq = -|p-q| + 5.
Question 7
a) What is the highest common factor (HCF) of two consecutive even integers?
b) If \( 79^*2845 \) is divisible by 9, where * is a digit, what is the smallest possible value of *?
c) Determine the smallest 4-digit number which, when divided by 15, 25, and 35, leaves a remainder of 4.
Question 8
Subtract the sum of -256 and 152 from the sum of 452 and -782.
Question 9
Describe a trapezium. When is a trapezium referred to as an isosceles trapezium? Illustrate an isosceles trapezium.
Question 10
Determine the following values using appropriate properties:
a) \( 12345 \times 28 + 12345 \times 12 + 12345 \times 60 \)
b) \( 1098 \times 97 \)
Question 11
Find the unknown number: ? + (-9) = 13