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# This is a test of Brilliant features

1) Absolute Value - Evaluating Expressions

If $$x$$ is a negative real number, what is the value of $$x + |-x|?$$

• $$2x$$
• $$0$$
• $$- 2x$$
• Cannot be determined

I like this because it assumes people are already familiar with the definition of $$|x|$$, and asks them to apply it in a non-trivial setting. It might be too hard for a Q1, in which case I might say "If $$x = -2$$" instead.

2) Completing the Square

Which of the following is equivalent to
$x^2 - 4x + 5?$

• $$(x+2)^2 + 5 - 4$$
• $$(x-2)^2 + 5 + 4$$
• $$(x-2)^2 + 5 - 4$$
• $$(x+2)^2 + 5 + 4$$

I like this because even if someone doesn't know what Completing the square is, then they can start to see what is involved in the process. The options refelct several common misconceptions that people have with the procedure, but they can still expand it out to verify their answer.

3) General Polygons - Area

In the following trapezium, which of the following represents the area?
(Relevant images of isosceles trapezium with base lengths of 2 and 10, slant height of 5 and 5, height of 3)

• $$\frac{1}{2} ( 2 + 10 ) \times 3$$
• $$\frac{1}{2} ( 2 + 10 ) \times 5$$
• $$\frac{1}{2} ( 5 + 5 ) \times 3$$
• $$\frac{1}{2} ( 5 + 5 ) \times 10$$

This is somewhat hard for a Q1, but given the depth that this chapter is in, I think that's fine. I like that it reminds people how to find the area of a trapezium, so even if they forgot the formula they can still figure it out. I might consider adding in a diagonal, so that it's easier to see why the formula works.

4) Trigonometric Functions - Basic Functions

(Image of a right triangle with one angle labelled $$\theta$$, and base of 3 and height of 4.)

Which of the following is equal to $$\sin \theta$$?

• $$\frac{3}{4}$$
• $$\frac{3}{5}$$
• $$\frac{4}{3}$$
• $$\frac{4}{5}$$

I like this because it involves them applying the Pythagorean theorem to get at the hypotenuse. I'm not too happy with this question though, and it might be more suited for a later quiz about "USing right angles to calcualte trigonometric values"

5) Prime Factorization and Divisors

$72 = 8 \times 9$

Which of the following is the largest prime factor of $$72$$?

• 2
• 3
• 8
• 9

This might be too tricky for a Q1. However,

6) Number Bases - Binary Numbers

Given that $$26 = 2 + 8 + 16$$, which of the following is equal to 26 in base 2?

• $$11010_2$$
• $$1101_2$$
• $$1011_2$$
• $$10110_2$$

This reminds / hints at how to do binary conversion, by looking at the powers of 2. If this was the first quiz of the chapter, it would not be an appropriate Q1. But given that this comes after several quizzes, I think it's alright.

7) Taylor Series - Local Linear Approximation

For the function $$f(x) = x^2$$, we have $$f(1) = 1$$ and $$f'(1) = 2$$. Which of the following is the best local linear approximation for $$f(1.1)$$?

• $$f(1) + 0.1 \times f'(1)$$
• $$f'(1) + 0.1 \times f(1)$$
• $$f(1) + 1 \times f'(1)$$
• $$f(1) + 1 \times f'(0.1)$$

This is the first quiz of the chapter. It provides some context for why we have a "local linear approximation". I considered asking for $$f(1+x)$$, but decided that I didn't want to introduce variables for this first problem as yet.

Note by Calvin Lin
2 years, 5 months ago

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test test test Staff · 5 months, 3 weeks ago

So many things at so small an age!! I wish you grow into a great contributor of coordinated knowledge. Normally today knowledge is compartmentalized. One with knowledge of more subjects can see it as a whole. You be one to synthesize. My hearty best wishes. · 1 year, 2 months ago