 JUNIOR MATHS

## Week 10 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

Express the following fractions as percentages:

(a) $$\dfrac{1}{2}$$

(b) $$\dfrac{1}{4}$$

(c) $$\dfrac{3}{4}$$

(d) $$\dfrac{1}{8}$$

(e) $$\dfrac{3}{8}$$

(a) $$50\%$$

(b) $$25\%$$

(c) $$75\%$$

(d) $$12.5\%$$

(e) $$37.5\%$$

## Question 2

Express the following percentages as fractions in their simplest form:

(a) $$50\%$$

(b) $$40\%$$

(c) $$10\%$$

(d) $$15\%$$

(e) $$17\%$$

(a) $$\dfrac{1}{2}$$

(a) $$\dfrac{2}{5}$$

(a) $$\dfrac{1}{10}$$

(a) $$\dfrac{3}{20}$$

(a) $$\dfrac{17}{100}$$

## Question 3

Express the following decimals as percentages:

(a) $$0.26$$

(b) $$0.99$$

(c) $$0.2$$

(d) $$0.3$$

(e) $$0.03$$

(a) $$26\%$$

(a) $$99\%$$

(a) $$20\%$$

(a) $$30\%$$

(a) $$3\%$$

## Question 4

Express the following percentages as decimals:

(a) $$50\%$$

(b) $$40\%$$

(c) $$10\%$$

(d) $$15\%$$

(e) $$17\%$$

(a) $$0.5$$

(b) $$0.4$$

(c) $$0.1$$

(d) $$0.15$$

(e) $$0.17$$

## Question 5

Calculate the following:

(a) $$10\%$$ of $$20$$

(b) $$5\%$$ of $$100$$

(c) $$40\%$$ of $$500$$

(d) $$90\%$$ of $$300$$

(a) $$2$$

(b) $$5$$

(c) $$200$$

(d) $$270$$

## Question 6

Calculate the following:

(a) $$12\%$$ of $$10$$

(b) $$3\%$$ of $$5$$

(c) $$13\%$$ of $$50$$

(d) $$90\%$$ of $$25$$

(a) $$1.2$$

(b) $$0.15$$

(c) $$6.5$$

(d) $$22.5$$

## Question 7

Calculate the following:

(a) $$35$$ as a percentage of $$70$$

(b) $$15$$ as a percentage of $$75$$

(c) $$20$$ as a percentage of $$25$$

(d) $$49$$ as a percentage of $$50$$

(a) $$50\%$$

(b) $$20\%$$

(c) $$80\%$$

(d) $$98\%$$

## Question 8

Calculate the following:

(a) $$15$$ seconds as a percentage of $$1$$ minute

(b) $$18$$ seconds as a percentage of $$1.5$$ minutes

(c) $$45$$ minutes as a percentage of $$2$$ hours

(d) $$3$$ minutes as a percentage of $$1.25$$ hours

(a) $$25\%$$

(b) $$20\%$$

(c) $$37.5\%$$

(d) $$4\%$$

## Question 9

(a) Decrease $$200$$ by $$10\%$$

(b) Increase $$200$$ by $$10\%$$

(c) Decrease $$50$$ by $$22\%$$

(d) Increase $$50$$ by $$22\%$$

(a) $$180$$

(b) $$220$$

(c) $$39$$

(d) $$61$$

## Question 10

(a) If $$10\%$$ of a particular number is $$20$$, what is that number?

(b) If $$64\%$$ of a particular number is $$20$$, what is that number?

(c) If $$40\%$$ of a particular number is $$5$$, what is that number?

(d) If $$80\%$$ of a particular number is $$5$$, what is that number?

(a) $$200$$

(b) $$31.25$$

(c) $$12.5$$

(d) $$6.25$$

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 students on a sports team.

\begin{align}\{15, 17, 14, 14, 17, 16, 18, 14, 13, 13, 15, 16, 14, 16, 15, 16, 17, 17, 15, 15, 15 \}\end{align}

(a) Represent this data on a frequency table.

(b) What is the mean of this data?

(c) What is the mode of this data?

(d) What is the median of this data?

(e) What is the range of this data?

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

(b) $$15\frac{1}{3}$$

(c) $$15$$

(d) $$15$$

(e) $$5$$

## Question 2

Below are the ages that students of a particular classroom were when they completed their Junior Cycle.

\begin{align}\{15, 15, 15, 14, 14, 15, 15, 15, 13, 15, 15, 14, 14, 14, 16, 15, 15, 15, 15, 14\}\end{align}

(a) Represent this data on a frequency table.

(b) What is the mean of this data?

(c) What is the mode of this data?

(d) What is the median of this data?

(e) What is the range of this data?

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

(b) $$14.65$$

(c) $$15$$

(d) $$5$$

(e) $$3$$

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 1

Prove that vertically opposite angles are equal in measure.

This proof will be shown during the grind!

## Theorem 2

Prove that, in an isosceles triangle, the angles opposite the equal sides are equal.

Conversely, If two angles are equal, then the triangle is isosceles.

This proof will be shown during the grind!

## Theorem 3

Prove that, if a transversal makes equal alternate angles on two lines, then the lines are parallel.

This proof will be shown during the grind!

## Theorem 4

Prove that the angles in any triangle add to $$180^{\circ}$$.

This proof will be shown during the grind!

## Theorem 5

Prove that two lines are parallel if and only if for any transversal, corresponding angles are equal.

This 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

Solve the following inequality:

\begin{align}2x>10\end{align}

$$x>5$$

## Question 2

Solve the following inequality

\begin{align}2x>10\end{align}

where $$x \in \mathbb{N}$$.

$$x>5, x \in \mathbb{N}$$

## Question 3

Represent the following inequalities on number lines:

(a) $$2x>10, x \in \mathbb{N}$$

(b) $$2x>10, x \in \mathbb{R}$$

(c) $$2x\geq 10, x \in \mathbb{R}$$

These number lines will be shown during the grind!

## Question 4

Solve the following inequality

\begin{align}4x+8 > 7x+2, x \in \mathbb{N}\end{align}

and represent the solution on a number line.

$$x \in\{0,1,2\}$$

The number line 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

Express the following as a single fraction:

\begin{align}\frac{1}{4}+\frac{1}{6}\end{align}

$$\dfrac{5}{12}$$

## Question 2

Express the following as a single fraction:

\begin{align}\frac{x}{4}+\frac{x}{6}\end{align}

$$\dfrac{5x}{12}$$

## Question 3

Express the following as a single fraction:

\begin{align}\frac{9x}{2}-\frac{4x}{3}\end{align}

$$\dfrac{19x}{6}$$

## Question 4

Express the following as a single fraction:

\begin{align}\frac{x+2}{4}+\frac{x-3}{6}\end{align}

$$\dfrac{5x}{12}$$

## Question 5

Express the following as a single fraction:

\begin{align}\frac{x+1}{5}-\frac{2-x}{15}+\frac{x}{3}\end{align}

$$\dfrac{9x+1}{15}$$

## Question 6

Solve the following equation:

\begin{align}\frac{x}{5}=4\end{align}

$$x=20$$

## Question 7

Solve the following equation:

\begin{align}\frac{x+2}{5}=4\end{align}

$$x=18$$

## Question 8

Solve the following equation:

\begin{align}\frac{x+2}{5}-\frac{x-1}{10}=3\end{align}

$$x=25$$

## Question 9

Solve the following equation:

\begin{align}\frac{x+2}{5}-\frac{x-1}{10}=\frac{3}{15}\end{align}

$$x=-3$$