IT/IIT100 Unit 1 Practice Test

1. Function Type

Given this graph:

Match the curves to the function type:

	Curves		Possibilities
1.1) ……….	Curve A		a) piece-wise function
1.2) ……….	Curve B		b) discontinous function
1.3) ……….	Curve C		c) constant function
1.4) ……….	Curve D		d) continous function
			e) decreasing function

2. What is a Function?

Given this graph

Which of these curves are true functions?

2.1a ….. 2.1b ….. 2.1c ….. 2.1d ….. 2.1e …..

For each of the other curves state the reason why it cannot be a function.

2.2a ………………..

2.2b ………………..

2.2c ………………..

2.2d ………………..

2.2e ………………..

3. Inverse Functions

Consider the function:

\[y = {x^2}\]

3.1 Sketch the corresponding curve of this function on the graph for the range -5 to 5:

3.2 Specify the domain of this graph.

3.3 Specify the corresponding range of this graph

3.4 Specify the inverse function for this function

3.5 Specify the permissible range for the inverse

4. Function manipulation

Consider the function \(y=f(x)\) represented by this graph:

Add to this graph the curves that represents the following relationships. (Be sure to label the line on the graph.)

4.1 \(y={f(x+2)\over 2}\)

4.2 \(y={f(x)}+ 5\)

4.3 \(y = 2 f(x) + 2\)

5. Prime factors

For each of the following nubmers, what are the prime factors?

5a. 105 …………..

5b. 63 …………..

5c. 192 …………..

6. Numeric conversions.

Raj’s father left him 7.53 crore rupees. However, the inheritance tax is 15 lakh rupees. What is Raj’s inheritance after taxes?

6.1 Express this as crore rupees: …………

6.2 Express this in scientific notation: …….

What is the answer (in standard arabic notation) to this ancient math problem?

\[CMLXII + DCCCXXXIII = ???\]

6.3 …………..

7. Binary, Octal, and Hexadecimal numbers

Fill out the following conversion chart:

Decimal	Binary	Octal	Hexadecimal
	101010		2A
21		25
63		77
129

8. Integer to Real conversions

Given the value of \(-2\pi\) as -6.28318 provide the results of the following functions:

8.1 \(\hbox{ceiling}(-2\pi)\) ………..

8.2 \(\hbox{round}(-2\pi)\) ……….

8.3 \(\hbox{floor}(-2\pi)\) ……….

9. Simplify equation

What is the answer to the following problems?

9.1 \({10^2\times 6 - 3 + 3\times 2\over 3} =\) …….

9.2 \({10^2 - 5\over {5\over 2}} =\) …….

10. Order of precedence

Arrange these symbols by order of precedence:

\[\large - + \div \times () \] > 10.1 …………

11. Exponents

Simplify the following equations:

11.1 \({a^3\over \sqrt{a^7}} =\) ……….

11.2 \({a^5\times b^6 \times a^{-{5\over 2}}\over a^{-{3/2}}\times \sqrt{4b^3}} =\) ………

11.3 \({5.11 \times 10^5 + 1.23 \times 10^3\over 10^2} =\) ……..