Grind 6A & 6B: Decimals (Common)

**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!**

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)** \(7\)

Answer

**(a)** \(1{,}000\)

**(b)** \(200\)

**(c)** \(30\)

**(d)** \(4\)

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

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

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

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)** \(1{,}000{,}000\)?

Answer

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

**(b)** \(5\)

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

**(d)** \(2\)

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)** \(\dfrac{5}{1{,}000}\)

Answer

**(a)** \(0.3\)

**(b)** \(0.12\)

**(c)** \(0.04\)

**(d)** \(0.346\)

**(e)** \(0.027\)

**(f)** \(0.005\)

Calculate the following without using a calculator:

**(a)** \(4.56+1.23\)

**(b)** \(3.14159+0.12\)

**(c)** \(3.1+0.053\)

Answer

**(a)** \(5.79\)

**(b)** \(3.26159\)

**(c)** \(3.153\)

Calculate the following without using a calculator:

**(a)** \(4.56-1.23\)

**(b)** \(3.14159-0.12\)

**(c)** \(3.1-0.053\)

Answer

**(a)** \(3.33\)

**(b)** \(3.02159\)

**(c)** \(3.047\)

Calculate the following without using a calculator:

**(a)** \(1.23+2.034+3.0045\)

**(b)** \(98.7-7.65-0.543\)

Answer

**(a)** \(6.268\)

**(b)** \(90.507\)

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 \(1{,}000\)

Answer

**(a)** \(31.4159\)

**(b)** \(314.159\)

**(c)** \(3{,}141.59\)

Calculate the following without using a calculator:

**(a)** \(3\times 4\)

**(b)** \(0.3\times 4\)

**(c)** \(3\times 0.4\)

**(d)** \(0.3\times 0.4\)

Answer

**(a)** \(12\)

**(b)** \(1.2\)

**(c)** \(1.2\)

**(d)** \(0.12\)

Calculate the following without using a calculator:

**(a)** \(1.2\times 3.6\)

**(b)** \(17.5\times 5.1\)

Answer

**(a)** \(4.32\)

**(b)** \(89.25\)

Calculate the following without using a calculator:

**(a)** \(1.46\times 5.3\)

**(b)** \(11.34\times 26.58\)

Answer

**(a)** \(7.738\)

**(b)** \(301.4172\)

Grind 6C: Area & Volume (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!**

Calculate the area of the following triangle.

Answer

\(22\mbox{ cm}^2\)

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

What is the width of the triangle?

Answer

\(10\mbox{ cm}\)

Calculate the area of the shaded region.

Answer

\(400\mbox{ cm}^2\)

Calculate the area of the following parallelogram.

Answer

\(24\mbox{ cm}^2\)

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

What is the parallelogram’s height?

Answer

\(9.5\mbox{ cm}\)

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

Calculate the cube’s:

**(a)** volume

**(b)** surface area

Answer

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

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

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

Calculate the cube’s:

**(a)** volume

**(b)** surface area

Answer

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

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

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

Answer

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

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

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

Answer

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

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

Grind 6D: Circles & Prisms (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!**

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 \(\pi\).

Answer

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

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

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

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

Calculate the circle’s:

**(a)** radius

**(b)** diameter

**(c)** circumference

Use \(3.14\) as an approximation for \(\pi\).

Answer

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

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

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

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 \(\pi\).

Answer

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

**(b) **\(25.85\mbox{ cm}\)

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 \(\pi\).

Answer

\(43^{\circ}\)

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

What is the cube’s volume?

Answer

\(100\mbox{ cm}^3\)

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

What is the cube’s volume?

Answer

\(729\mbox{ mm}^2\)

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

Answer

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

**(b) **\(720\mbox{ cm}^3\)

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

Grind 5E: Stem & Leaf Plots (OL)

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

Grind 6F: Stem & Leaf Plots (HL)

**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}

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.

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