 JUNIOR MATHS

## Samples

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!

## Question 1

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 $$\#(A\cap B)$$?

(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) $$2$$

## Question 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 $$\#(A\cap B)$$?

(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) $$1$$

## Question 3

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 $$\#(A\cap B)$$?

(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) $$0$$

## Question 4

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 $$\#(A’)$$?

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

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

(c) $$5$$

(d) $$3$$

(e) $$2$$

## Question 5

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 $$(A\cap B)’$$.

(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!

## Question 1

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?

(a) $$7$$

(b) $$6$$

(c) $$7$$

(d) $$12$$

## Question 2

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?

(a) $$7$$

(b) $$6$$

(c) $$7$$

(d) $$12$$

## Question 3

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?

(a) $$7$$

(b) $$6$$

(c) $$6.5$$

(d) $$12$$

## Question 4

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?

(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!

## Question 1

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?

(c) and (d) only

## Question 2

Calculate the length $$x$$ in the following right-angled triangle.

$$5$$

## Question 3

Calculate the length $$x$$ in the following right-angled triangle.

$$3$$

## Question 4

Calculate the length $$x$$ in the following right-angled triangle.

$$17$$

## Question 5

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

$$3.6$$

## Question 6

Calculate the length $$x$$ in the following right-angled triangle.

$$5$$

## Question 7

Calculate the length $$x$$ in the following diagram, correct to one decimal place.

$$6.4$$

Linear Sequences (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!

## Question 1

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?

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

(b) $$7$$

(c) $$T_n=n$$

(d) $$300$$

## Question 2

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?

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

(b) $$23$$

(c) $$T_n=4n+3$$

(d) $$403$$

## Question 3

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 $$61$$?

(a) $$5,9,13$$

(b) $$121$$

(c) $$15$$th

## Question 4

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 $$32$$?

(a) $$2,7,12$$

(b) $$247$$

(c) $$7$$th

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 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?

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

(b) $$25$$

(c) $$T_n=n^2$$

(d) $$100$$

## Question 2

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?

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

(b) $$41$$

(c) $$T_n=n^2+2n+6$$

(d) $$446$$

## Question 3

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?

(a) $$3,7,13,21,31$$

(b) $$111$$

(c) $$2$$

## Question 4

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?

(a) $$6,13,26,45,70$$
(b) $$285$$
(c) $$6$$