Venn Diagrams (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 sets \(A=\{1,2,3,4,5\}\) and \(B=\{4,5,6,7\}\).

**(a)** Represent these sets on a Venn Diagram.

**(b)** List the elements of \(A\cup B\).

**(c)** List the elements of \(A\cap B\).

**(d)** What is \(\#A\)?

**(e)** What is \(\#B\)?

**(f)** What is \(\#(A\cup B)\)?

**(g)** What is \(\#(A\cap B)\)?

Answer

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

**(b)** \(\{1,2,3,4,5,6,7\}\)

**(c)** \(\{4,5\}\)

**(d)** \(5\)

**(e) **\(4\)

**(f) **\(7\)

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

Consider the sets \(A=\{3,6,9,12,15\}\) and \(B=\{5,10,15,20\}\).

**(a)** Represent these sets on a Venn Diagram.

**(b)** List the elements of \(A\cup B\).

**(c)** List the elements of \(A\cap B\).

**(d)** What is \(\#A\)?

**(e)** What is \(\#B\)?

**(f)** What is \(\#(A\cup B)\)?

**(g)** What is \(\#(A\cap B)\)?

Answer

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

**(b)** \(\{3,5,6,9,10,12,15,20\}\)

**(c)** \(\{15\}\)

**(d)** \(5\)

**(e) **\(4\)

**(f) **\(8\)

**(g) **\(1\)

Consider the sets \(A=\{1,3,5,7,9\}\) and \(B=\{2,4,6,8,10\}\).

**(a)** Represent these sets on a Venn Diagram.

**(b)** List the elements of \(A\cup B\).

**(c)** List the elements of \(A\cap B\).

**(d)** What is \(\#A\)?

**(e)** What is \(\#B\)?

**(f)** What is \(\#(A\cup B)\)?

**(g)** What is \(\#(A\cap B)\)?

Answer

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

**(b)** \(\{1,2,3,4,5,6,7,8,9,10\}\)

**(c)** \(\{\}\)

**(d)** \(5\)

**(e) **\(5\)

**(f) **\(10\)

**(g) **\(0\)

Consider the sets \(U=\{1,2,3,4,5\}\) and \(A=\{1,3,5\}\).

**(a)** Represent these sets on a Venn Diagram.

**(b)** List the elements of \(A’\).

**(c)** What is \(\#U\)?

**(d)** What is \(\#A\)?

**(e)** What is \(\#(A’)\)?

Answer

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

**(b)** \(\{2,4\}\)

**(c)** \(5\)

**(d)** \(3\)

**(e) **\(2\)

Consider the sets \(U=\{1,2,3,4,5,6, 7\}\), \(A=\{1,3,5\}\) and \(B=\{2,4,6\}\).

**(a)** Represent these sets on a Venn Diagram.

**(b)** List the elements of \(A’\).

**(c)** List the elements of \(B’\).

**(d)** List the elements of \((A\cup B)’\).

**(e)** List the elements of \((A\cap B)’\).

Answer

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

**(b)** \(\{2,4,6,7\}\)

**(c)** \(\{1,3,5,7\}\)

**(d)** \(\{7\}\)

**(e)**\(\{1,2,3,4,5,6,7\}\)

Mean, Mode & Median (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!**

Consider the following data set:

\begin{align}\{1, 2, 3, 4, 6, 6, 6, 7, 7, 8, 9, 10, 11, 12, 13 \}\end{align}

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

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

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

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

Answer

**(a)** \(7\)

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

**(c)** \(7\)

**(d)** \(12\)

Consider the following data set:

\begin{align}\{2,12,4,6,6,7,3,10,6,7,1,9,8,11,13 \}\end{align}

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

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

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

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

Answer

**(a)** \(7\)

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

**(c)** \(7\)

**(d)** \(12\)

Consider the following data set:

\begin{align}\{1,2, 3, 4, 6, 6, 6, 7, 8, 9, 10, 11, 12, 13 \}\end{align}

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

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

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

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

Answer

**(a)** \(7\)

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

**(c)** \(6.5\)

**(d)** \(12\)

Consider the following data set:

\begin{align}\{1,2, 3, 54, 55, 55, 57, 59 \}\end{align}

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

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

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

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

Answer

**(a)** \(35.75\)

**(b)** \(55\)

**(c)** \(54.5\)

**(d)** \(58\)

Pythagoras' Theorem (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!**

The three lengths (in centimetres) of different triangles are shown below.

**(a)** \(1,2,3\)

**(b)** \(2,5,10\)

**(c)** \(7,24,25\)

**(d)** \(9,40,41\)

Which of these triangles are right-angled?

Answer

**(c)** and **(d)** only

Calculate the length \(x\) in the following right-angled triangle.

Answer

\(5\)

Calculate the length \(x\) in the following right-angled triangle.

Answer

\(3\)

Calculate the length \(x\) in the following right-angled triangle.

Answer

\(17\)

Calculate the length \(x\) in the following right-angled triangle, correct to one decimal place.

Answer

\(3.6\)

Calculate the length \(x\) in the following right-angled triangle.

Answer

\(5\)

Calculate the length \(x\) in the following diagram, correct to one decimal place.

Answer

\(6.4\)

Linear Sequences (OL)

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

Consider the following sequence:

\begin{align}1,2,3,4,5,6…\end{align}

**(a)** Show that this sequence is linear.

**(b)** What is the next term in this sequence?

**(c)** What is the general term for this sequence?

**(d)** What is the \(300\)th term in this sequence?

Answer

**(a)** The difference between successive terms is a constant value of \(1\).

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

**(c)** \(T_n=n\)

**(d)** \(300\)

Consider the following sequence:

\begin{align}7,11,15,19…\end{align}

**(a)** Show that this sequence is linear.

**(b)** What is the next term in this sequence?

**(c)** What is the general term for this sequence?

**(d)** What is the \(100\)th term in this sequence?

Answer

**(a)** The difference between successive terms is a constant value of \(4\).

**(b)** \(23\)

**(c)** \(T_n=4n+3\)

**(d)** \(403\)

The general term of a sequence is given by:

\begin{align}T_n=4n+1\end{align}

**(a)** What are the first three terms of this sequence?

**(b)** What is \(30\)th term of this sequence?

**(c)** Which term of the sequence is \(61\)?

Answer

**(a)** \(5,9,13\)

**(b)** \(121\)

**(c)** \(15\)th

The general term of a sequence is given by:

\begin{align}T_n=5n-3\end{align}

**(a)** What are the first three terms of this sequence?

**(b)** What is \(50\)th term of this sequence?

**(c)** Which term of the sequence is \(32\)?

Answer

**(a)** \(2,7,12\)

**(b)** \(247\)

**(c)** \(7\)th

Quadratic Sequences (HL)

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

Consider the following sequence:

\begin{align}1,4,9,16,…\end{align}

**(a)** Show that this sequence is quadratic.

**(b)** What is the next term in this sequence?

**(c)** What is the general term for this sequence?

**(d)** What is the \(10\)th term in this sequence?

Answer

**(a)** The second difference is a constant value of \(2\).

**(b)** \(25\)

**(c)** \(T_n=n^2\)

**(d)** \(100\)

Consider the following sequence:

\begin{align}9,14,21,30,…\end{align}

**(a)** Show that this sequence is quadratic.

**(b)** What is the next term in this sequence?

**(c)** What is the general term for this sequence?

**(d)** What is the \(20\)th term in this sequence?

Answer

**(a)** The second difference is a constant value of \(2\).

**(b)** \(41\)

**(c)** \(T_n=n^2+2n+6\)

**(d)** \(446\)

The general term of a sequence is given by:

\begin{align}T_n=n^2+n+1\end{align}

**(a)** What are the first five terms of this sequence?

**(b)** What is \(10\)th term of this sequence?

**(c)** What is the second difference of this sequence?

Answer

**(a)** \(3,7,13,21,31\)

**(b)** \(111\)

**(c)** \(2\)

The general term of a sequence is given by:

\begin{align}T_n=3n^2-2n+5\end{align}

**(a)** What are the first five terms of this sequence?

**(b)** What is \(10\)th term of this sequence?

**(c)** What is the second difference of this sequence?

Answer

**(a)** \(6,13,26,45,70\)

**(b)** \(285\)

**(c) **\(6\)

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