Grind 9A: Graphing Functions (OL)

**Mr. Kenny will go through the first of these questions during the grind. If time permits, he will then go through the second question. And so on.**

**Any remaining questions are left for you to practice with!**

**(a)** Graph the following linear function:

\begin{align}f(x) = 2x+3\end{align}

in the domain \(-2\leq x \leq 3, x \in \mathbb{R}\).

Using this graph, calculate the following:

**(b)** \(f(2)\)

**(c)** \(f(-1)\)

**(d)** the value of \(x\) for which \(f(x)=5\)

**(e)** the \(x\) intercept

**(f)** the \(y\) intercept

**(g)** the slope of the line

Answer

**(a) **This graph will be shown during the grind!

**(b)** \(7\)

**(c)** \(1\)

**(d)** \(1\)

**(e)** \((-1.5,0)\)

**(f)** \((0,3)\)

**(g)** \(2\)

**(a)** Graph the following linear functions:

\begin{align}f(x) = 2x-2\end{align}

\begin{align}g(x) = x+1\end{align}

in the domain \(-4\leq x \leq 5, x \in \mathbb{R}\).

**(b)** Using this graph, calculate the point of intersection of the two lines.

Answer

**(a) **This graph will be shown during the grind!

**(b)** \((3,4)\)

**(a)** Using the intercept method, graph the following line:

\(2x-4y+8=0\)

**(b)** Explain why this is not a directional proportional graph.

**(c)** State the linear function that 1) has the slope of the above function and 2) has a directly proportional graph.

Answer

**(a) **This graph will be shown during the grind!

**(b) **It does not pass through the origin.

**(c)** \(y=\dfrac{1}{2}x\)

**(a)** Graph the following quadratic function:

\begin{align}f(x) = 2x^2+3x-4\end{align}

in the domain \(-3\leq x \leq 2, x \in \mathbb{R}\).

**(b)** Give two reasons why this is not a directional proportional graph.

Answer

**(a) **This graph will be shown during the grind!

**(b) **It is not linear and does not pass through the origin.

**(a)** Graph the following quadratic function:

\begin{align}f(x) = -2x^2-x+3\end{align}

in the domain \(-2\leq x \leq 2, x \in \mathbb{R}\).

**(b)** Using this graph, calculate the roots of the equation \(2x^2-x-3=0\).

Answer

**(a) **This graph will be shown during the grind!

**(b) **\(-1.5\) and \(1\)

Grind 9B: Theorem 12 (HL)

**Mr. Kenny will go through the first of these questions during the grind. If time permits, he will then go through the second question. And so on.**

**Any remaining questions are left for you to practice with!**

Proof

The proof will be shown during the grind!

Grind 9C: Stem & Leaf Plots (OL)

**Mr. Kenny will go through the first of these questions during the grind. If time permits, he will then go through the second question. And so on.**

**Any remaining questions are left for you to practice with!**

Below is the list of the ages of teachers at a particular primary school.

\begin{align}\{24, 27, 25, 62, 48, 43, 30, 34, 51, 27, 31, 59, 46\}\end{align}

**(a)** Represent this data on an *unordered* stem and leaf plot.

**(b)** Represent this data on an *ordered* stem and leaf plot.

**(c)** What is the mean of this data?

**(d)** What is the mode of this data?

**(e)** What is the median of this data?

Answer

**(a)** This plot will be shown during the grind!

**(b)** This plot will be shown during the grind!

**(c)** \(39\)

**(d)** \(27\)

**(e)** \(34\)

Below is the list of the times taken, in seconds, for different students to complete a \(100\) metres race.

\begin{align}\{45, 16, 26, 27, 41, 28, 19, 40, 27, 30, 84, 30, 44,40,22\}\end{align}

**(a)** Represent this data on an *unordered* stem and leaf plot.

**(b)** Represent this data on an *ordered* stem and leaf plot.

**(c)** What is the mean of this data?

**(d)** What is the mode of this data?

**(e)** What is the median of this data?

**(f)** What was the fastest time?

**(g)** What was the time difference between the fastest and slowest student?

**(h)** What percentage of students completed the race in under \(40\) seconds?

Answer

**(a)** This plot will be shown during the grind!

**(b)** This plot will be shown during the grind!

**(c)** \(34.6\)

**(d)** \(27\)

**(e)** \(30\)

**(f) **\(16\)

**(g) **\(68\)

**(h) **\(60\%\)

Below is the list of the ages of teachers at a particular primary school.

\begin{align}\{24, 27, 25, 62, 48, 43, 30, 34, 51, 27, 31, 59, 46\}\end{align}

Below is the list of the ages of teachers at the nearest secondary school to the primary school above.

\begin{align}\{53, 39, 23, 31, 46, 49, 51, 49, 29, 61, 65, 58, 70\}\end{align}

**(a)** Represent this data on an *ordered* back-to-back stem and leaf plot.

**(b) **What does this plot show about the ages of the teachers in each school?

**(c)** What is the mean of the ages in each school?

**(d)** What is the mode of the ages in each school?

**(e)** What is the median of the ages in each school?

**(f)** What is the range of ages at each school?

Answer

**(a)** This plot will be shown during the grind!

**(b)** The ages at the secondary school are typically higher than at the primary school.

**(c)** \(39\) and \(48\)

**(d)** \(27\) and \(49\)

**(e)** \(34\) and \(49\)

**(f)** \(38\) and \(47\)

Below is the list of the times taken, in seconds, for different students to complete a \(100\) metres race.

\begin{align}\{45, 16, 26, 27, 41, 28, 19, 40, 27, 30, 84, 30, 44,40,22\}\end{align}

Below is the same list but for the teachers at the school.

\begin{align}\{20, 18, 21, 24, 24, 28, 24, 27, 20, 23, 30, 21, 19\}\end{align}

**(a)** Represent this data on an *ordered* back-to-back stem and leaf plot.

**(b)** What does this plot show about the times by both students and teachers?

**(c)** What is the mean of both sets of data?

**(d)** What is the mode of both sets of data?

**(e)** What is the median of both sets of data?

**(f)** What was the fastest time by both students and teachers?

**(g)** What was the time difference between the fastest and slowest student?

**(h)** Does this data contain any outliers?

Answer

**(a)** This plot will be shown during the grind!

**(b)** Teachers were faster and had a much smaller range.

**(c)** \(34.6\) and \(23\)

**(d)** \(27\) and \(24\)

**(e)** \(30\) and \(23\)

**(f) **\(16\) and \(18\)

**(g) **\(68\) and \(12\)

**(h) **Yes, the \(84\) second time.

Grind 9D: Compound Interest (HL)

**Any remaining questions are left for you to practice with!**

An amount of €\(800\) is invested for \(3\) years at \(5\%\) per annum compound interest.

What will the total amount be after the end of the \(3\) year period?

Answer

€\(926.10\)

An amount of €\(300\) is invested for \(3\) years at \(2\%\) per annum compound interest.

What will the total amount be after the end of the \(3\) year period?

Answer

€\(318.37\)

An amount of €\(100\) is invested for \(5\) years at \(3\%\) per annum compound interest.

What will the total amount be after the end of the \(5\) year period?

Answer

€\(115.93\)

A bank offers a return of \(10\%\) total on any amount invested for \(5\) years.

Calculate the AER for such an investment, correct to two decimal places.

Answer

\(1.92\%\)

€\(5{,}000\) is invested in a bank at \(5\%\) AER.

If the interest is added monthly, what will the final value of the investment be after:

**(a)** \(1\) month

**(b)** \(6\) months

**(c)** \(14\) months

to the nearest cent.

Answer

**(a)** €\(5{,}020.37\)

**(b) **€\(5{,}123.48\)

**(c) **€\(5{,}292.87\)

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