https://file.aiquickdraw.com/mathbot/file/17274487033126ao2nsy4.jpg

Let's go through the mathematical test questions one by one:

### Multiple Choice Questions (10 marks)

**1. Anna's weight relative to Simon**
- Anna weighs 47.5 kg, 5 kg lighter than Simon. Simon’s weight is therefore \( 47.5 + 5 = 52.5 \, \text{kg} \).
- The fraction of Simon's weight that is Anna’s is:
  \[
  \frac{47.5}{52.5} = \frac{95}{105} = \frac{19}{21}
  \]
  **Answer: D. \( \frac{19}{21} \)**

**2. Divisibility by 36**
- 36 = \( 2^2 \times 3^2 \). A number divisible by 36 must have at least two 2’s and two 3’s in its prime factorization.
- Checking each option for divisibility:
  - **Answer: C. 875748** (divisible by 36)

**3. Least number of squares from the sheet**
- Dimensions: 63 cm × 273 cm. We need to find the greatest common divisor (GCD) of 63 and 273 to determine the largest possible square.
  \[
  \text{GCD}(63, 273) = 21
  \]
  - The least number of squares:
  \[
  \frac{63 \times 273}{21 \times 21} = \frac{17199}{441} = 39
  \]
  **Answer: B. 39**

**4. Correct Equations**
- I: \( \frac{4}{7} = \frac{3}{5} \) is false.
- II: True as the arithmetic works out correctly.
- III: Also true.
  **Answer: D. II and III only**

**5. Smallest Value**
- We calculate each option:
  - \( 2 \times 10^4 = 20000 \)
  - \( 20.17^2 = 406.8361 \)
  - \( 200^2 = 40000 \)
  - \( 2017 \times 20.17 \approx 40685.89 \)
  **Answer: B. \( 20.17^2 \) is the smallest value**

### Conventional Questions (20 marks)

**1. (a) Express 1650 in index notation.**
  - 1650 = \( 2 \times 3 \times 5^2 \times 11 \)
  **Answer: \( 2 \times 3 \times 5^2 \times 11 \)**

  **(b) Smallest integer \( k \) such that 1650k is a perfect square**
  - \( 1650 = 2 \times 3 \times 5^2 \times 11 \), so \( k = 2 \times 3 \times 11 = 66 \)

**2. Calculation**
  - Calculate the given expression:
  \[
  4 \left( \frac{1}{10} \left[ 1.56 + 7.5 \times \left( \frac{12}{5} - 2.08 \right) \right] \right) + 0.2
  \]
  Let's break this down step by step to get the answer:
  - \( \frac{12}{5} - 2.08 = 0.32 \)
  - \( 7.5 \times 0.32 = 2.4 \)
  - \( 1.56 + 2.4 = 3.96 \)
  - \( \frac{1}{10} \times 3.96 = 0.396 \)
  - \( 4 \times 0.396 = 1.584 \)
  - Adding 0.2: \( 1.584 + 0.2 = 1.784 \)

Would you like further details on any specific problem or explanation?

Here are 5 related questions:
1. How do you find the greatest common divisor (GCD) of two numbers?
2. What are the steps to check if a number is divisible by 36?
3. How can you express a number in terms of its prime factors?
4. What is the process for calculating a fractional expression involving multiple terms?
5. How do you simplify a nested mathematical expression?

**Tip:** Always simplify complex expressions step by step to avoid calculation errors.

This test covers mathematical concepts including fractions, divisibility by 36, greatest common divisor (GCD), and nested expressions.

This page provides solutions to a variety of mathematical problems on topics including fractions, divisibility, GCD, and nested expressions. Learn how to determine a fraction's value, check divisibility by 36, and calculate the least number of squares from a sheet. Designed for secondary students, this test covers important concepts for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation