JUNIOR MATHS

## Week 6 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

Consider the following number:

\begin{align}1{,}234.567\end{align}

What is the value of each of the following digits?

(a) $$1$$

(b) $$2$$

(c) $$3$$

(d) $$4$$

(e) $$5$$

(f) $$6$$

(g) $$7$$

(a) $$1{,}000$$

(b) $$200$$

(c) $$30$$

(d) $$4$$

(e) $$\dfrac{5}{10}$$

(f) $$\dfrac{6}{100}$$

(g) $$\dfrac{7}{1{,}000}$$

## Question 2

Consider the following number:

\begin{align}3.14159265359…\end{align}

Which of the digits in this number has a denominator of:

(a) $$10$$?

(b) $$10{,}000$$?

(c) $$1{,}000$$?

(d) $$1{,}000{,}000$$?

(a) $$1$$

(b) $$5$$

(c) $$1$$

(d) $$2$$

## Question 3

Write each of the following fractions as decimals:

(a) $$\dfrac{3}{10}$$

(b) $$\dfrac{12}{100}$$

(c) $$\dfrac{4}{100}$$

(d) $$\dfrac{346}{1{,}000}$$

(e) $$\dfrac{27}{1{,}000}$$

(f) $$\dfrac{5}{1{,}000}$$

(a) $$0.3$$

(b) $$0.12$$

(c) $$0.04$$

(d) $$0.346$$

(e) $$0.027$$

(f) $$0.005$$

## Question 4

Calculate the following without using a calculator:

(a) $$4.56+1.23$$

(b) $$3.14159+0.12$$

(c) $$3.1+0.053$$

(a) $$5.79$$

(b) $$3.26159$$

(c) $$3.153$$

## Question 5

Calculate the following without using a calculator:

(a) $$4.56-1.23$$

(b) $$3.14159-0.12$$

(c) $$3.1-0.053$$

(a) $$3.33$$

(b) $$3.02159$$

(c) $$3.047$$

## Question 6

Calculate the following without using a calculator:

(a) $$1.23+2.034+3.0045$$

(b) $$98.7-7.65-0.543$$

(a) $$6.268$$

(b) $$90.507$$

## Question 7

Consider the following number

\begin{align}3.14159\end{align}

What is this number…

(a) Multiplied by $$10$$

(b) Multiplied by $$100$$

(c) Multiplied by $$1{,}000$$

(a) $$31.4159$$

(b) $$314.159$$

(c) $$3{,}141.59$$

## Question 8

Calculate the following without using a calculator:

(a) $$3\times 4$$

(b) $$0.3\times 4$$

(c) $$3\times 0.4$$

(d) $$0.3\times 0.4$$

(a) $$12$$

(b) $$1.2$$

(c) $$1.2$$

(d) $$0.12$$

## Question 9

Calculate the following without using a calculator:

(a) $$1.2\times 3.6$$

(b) $$17.5\times 5.1$$

(a) $$4.32$$

(b) $$89.25$$

## Question 10

Calculate the following without using a calculator:

(a) $$1.46\times 5.3$$

(b) $$11.34\times 26.58$$

(a) $$7.738$$

(b) $$301.4172$$

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

Calculate the area of the following triangle.

$$22\mbox{ cm}^2$$

## Question 2

The area of the below triangle is $$80\mbox{ cm}^2$$.

What is the width of the triangle?

$$10\mbox{ cm}$$

## Question 3

Calculate the area of the shaded region.

$$400\mbox{ cm}^2$$

## Question 4

Calculate the area of the following parallelogram.

$$24\mbox{ cm}^2$$

## Question 5

The area of the following parallelogram is $$85.5\mbox{ cm}^2$$.

What is the parallelogram’s height?

$$9.5\mbox{ cm}$$

## Question 6

A cube has a length of $$4\mbox{ cm}$$.

Calculate the cube’s:

(a) volume

(b) surface area

(a) $$64\mbox{ cm}^3$$

(b) $$96\mbox{ cm}^2$$

## Question 7

A cube has a length of $$1.2\mbox{ m}$$.

Calculate the cube’s:

(a) volume

(b) surface area

(a) $$1.728\mbox{ m}^3$$

(b) $$8.64\mbox{ m}^2$$

## Question 8

A rectangular solid has a length of $$2\mbox{ m}$$, a width of $$3\mbox{ m}$$ and a height $$4\mbox{ m}$$.

Calculate the solid’s:

(a) volume

(b) surface area

(a) $$24\mbox{ m}^3$$

(b) $$52\mbox{ m}^2$$

## Question 9

A rectangular solid has a length of $$3\mbox{ cm}$$, a width of $$14\mbox{ mm}$$ and a height $$2\mbox{ cm}$$.

Calculate the solid’s:

(a) volume

(b) surface area

(a) $$8.4\mbox{ cm}^3$$

(b) $$18.44\mbox{ cm}^2$$

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 circle has a radius of $$5\mbox{ cm}$$.

Calculate the circle’s:

(a) diameter

(b) circumference

(c) area

Use $$3.14$$ as an approximation for $$\pi$$.

(a) $$10\mbox{ cm}$$

(b) $$31.4\mbox{ cm}$$

(c) $$78.5\mbox{ cm}^2$$

## Question 2

A circle has an area of $$452.16\mbox{ m}^2$$.

Calculate the circle’s:

(b) diameter

(c) circumference

Use $$3.14$$ as an approximation for $$\pi$$.

(a) $$12\mbox{ m}$$

(b) $$24\mbox{ m}$$

(c) $$75.36\mbox{ m}$$

## Question 3

Consider the following sector of a circle.

Calculate:

(a) the arc length

(b) the perimeter of the sector

Use $$3.14$$ as an approximation for $$\pi$$.

(a) $$7.85\mbox{ cm}$$

(b) $$25.85\mbox{ cm}$$

## Question 4

The length of the arc of a sector of a circle is $$15\mbox{ cm}$$.

If the radius of the circle is $$20\mbox{ cm}$$, what is the angle within the sector correct to the nearest degree?

Use $$3.14$$ as an approximation for $$\pi$$.

$$43^{\circ}$$

## Question 5

A cube has a surface area of $$600\mbox{ cm}^2$$.

What is the cube’s volume?

$$100\mbox{ cm}^3$$

## Question 6

A cube has a surface area of $$486\mbox{ mm}^2$$.

What is the cube’s volume?

$$729\mbox{ mm}^2$$

## Question 7

Consider the following prism.

The height of the prism is $$4\mbox{ cm}$$.

Calculate the prism’s:

(a) cross-sectional area

(b) volume

(c) surface area

(a) $$12\mbox{ cm}^2$$

(b) $$720\mbox{ cm}^3$$

(c) $$504\mbox{ cm}^2$$

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) $$60\%$$

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}

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 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}

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.