Cambridge IGCSE Maths: Types of Numbers and Symbols

Which statement accurately describes the usage of directed numbers in real-life scenarios?

Consider the numbers $\sqrt{2}$, $\pi$, and $e$. Which of them, when used in the formula for the area or circumference of a circle, would result in an irrational number, and why?

In the context of number theory, how would you classify a number that has more than two factors?

When calculating with numbers, what is the correct order of operations to simplify the expression: $5 + 2 \times (8 - 3)^2 \div 5 - 1$?

When rounding to a specific number of significant figures, at what point does a zero become 'significant'?

Consider two distinct prime numbers, p and q. What is their highest common factor (HCF)?

How does understanding the concept of a 'net' assist in calculating the surface area of a three-dimensional object?

How can you determine whether one number is a factor of another without performing long division?

In practical terms, what does finding the Lowest Common Multiple (LCM) help you achieve in real-world scenarios?

If a larger circle has a radius $R$ and a smaller circle has a radius $r$, and the volume of the larger sphere ($V_R$) is twice the volume of the smaller sphere ($V_r$), what equation connects $r$ to $R$?

How would you determine whether to classify the number 1 as prime, composite, or neither?

When calculating the perimeter of a sector, why must you add twice the radius to the arc length?

What mathematical steps would you take to determine how many whole number boxes of specific dimensions can fit into a storage area with known dimensions, assuming you can't partially fill a box?

A shape can be perfectly divided into smaller shapes—how can you use this property to calculate the total area of the shape?

A symmetrical three dimensional form is rotated around an axis. What characteristic must the cross-section along this axis possess?

A student is trying to determine three numbers' Highest Common Factor (HCF). If not including the trivial factor, what minimal information would allow the student to calculate all three?

Given the equation $x=a^n$, if $n$ is doubled, what transformation must occur to $a$ to keep $x$ constant?

Circle A is fully contained within circle B, and they do not intersect. If you want to calculate the area between these circles, what is the proper method?

Which formula is essential when relating radius, diameter, and calculating a circle's circumference?

Area of Circle = $\pi r^2$. Given this, and if someone knows $\pi$ is irrational, what can correctly be stated about irrationality?

Does the formula to calculate the perimeter of a triangle or the formula to calculate the area of the triangle require right angles or perpendicular lines to function?

When are units most important to your final calculation?

Which is the most accurate method to find the surface area of a complex 3D shape for which no single formula exists?

What should be done, and IN what order should they happen, if one must 'insert brackets' into the following equation to find correct solutions:3 + 8 *4 -2 = 30?

What best explains the practical purpose of 'estimating answers,'

Which is NOT a name for the different parts/types of circles

You attempt to calculate areas of faces on common, complex, solid, geometric shapes. Given "two ends with area equal to the cross-sectional area," what concept has the greatest utility?

How will an irrational number influence the volume of a cylinder when computing?

Is 224 m^2 equal to (1/410)^2 km^2?

In creating/demonstrating the net of a solid, which of the following is most vital?

Which method should you select to measure the length of a rope in a race that will be performed around a track?

What must be remembered when using the Pythagorean Theorem?

What transformation must a, b, and c undergo, where the surface of area for the following is surface area of a cuboid = 2(ab + ac + bc), WHILE the dimensions remain unchnaged.

You are tasked to paint some walls and have a budget. To estimate in your head, which formula or method should be chosen to accurately estimate while shopping?

Which tool would prove of most valuable in solving prime numbers?

What steps are essential to take in order to calculate area, from a set of 2D to create its PERIMETER?

Given that a cylinder consist of many components, which is generally NOT used when describing area?

What does 5! equal