L.C. MATHS

## Week 9 Grinds

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!

## Question 1

(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

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

(b) $$7$$

(c) $$1$$

(d) $$1$$

(e) $$(-1.5,0)$$

(f) $$(0,3)$$

(g) $$2$$

## Question 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.

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

(b) $$(3,4)$$

## Question 3

(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.

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

(b) It does not pass through the origin.

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

## Question 4

(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.

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

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

## Question 5

(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 $$2x^2-x-3=0$$.

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

(b) $$-1.5$$ and $$1$$

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!

## Theorem 12

Let $$\Delta ABC$$ be a triangle. If a line $$l$$ is parallel to $$BC$$ and cuts $$[AB]$$ in the ratio $$s : t$$, then it also cuts $$[AC]$$ in the same ratio.

The proof will be shown during the grind!

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!

## Question 1

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?

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

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

(c) $$39$$

(d) $$27$$

(e) $$34$$

## Question 2

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?

(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) $$60\%$$

## Question 3

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?

(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 $$47$$

## Question 4

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?

(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.

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!

## Question 1

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?

€$$926.10$$

## Question 2

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?

€$$318.37$$

## Question 3

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?

€$$115.93$$

## Question 4

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.

$$1.92\%$$

## Question 5

€$$5{,}000$$ 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.

(a) €$$5{,}020.37$$

(b) €$$5{,}123.48$$

(c) €$$5{,}292.87$$