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PLC Papers

Created For:

PiXL PLC 2017 Certification

Coordinates in four quadrants 2 Grade 3

Objective: Work with coordinates in all four quadrants.

Question 1

Write down the coordinates of: The red Angry bird ……….……. (A1) The green Pig ………..……(A1) The black bird …………..……… (A1)

(3) Question 2 Follow the following instructions using the graph on the next page.

a) Plot (3,2) and label it A

b) Plot B (3,-4)

c) Mark M the mid point of AB, and write down the coordinates ………. (A1)

d) Plot C (-1,2)

e) Name the type of triangle by joining ABC…………………. (A1)

f) What is the area of the triangle? …………………………. (A1)(M1)

(4)


(3)

Total marks / 10


Plotting straight line graphs 2 Grade 3

Objective: Plot graphs of straight-lines in the coordinate plane

Question 1

(a) Complete the table of values for y = 2x + 5

(2)

(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = -2 to x = 2

(2)

(Total: 4 marks)


Question 2

On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3

(3 marks)


Question 3

On the grid,

(a) draw the line x = 3

(b) draw the line y = −1

(c) draw the line y = x

(3 marks)

Total Mark /10


Position-to-term rules 2 Grade 3

Objective: Generate terms of a sequence from a position-to-term rule, including from patterns and diagrams.

Question 1.

The table shows some terms in a number sequence and their position in the sequence.

Position 1 2 3 4 5 6

Term 14 21 42

Fill in the missing terms in the sequence. (Total 2 marks)

Question 2.

Write down the first six terms of the sequence for each of these position-to-term rules.

(a) Position number add 8

…………………………………………………………………………….. (1)

(b) (3 × position number) subtract 2

…………………………………………………………………………….. (1)

(Total 2 marks)

Question 3.

The table shows the first five terms of a number sequence and their position in the sequence.

Position 1 2 3 4 5

Term 4 7 10 13 16

(a) Describe the position-to-term rule for this sequence.

….………………………………………………………………………………

…………………………………………………………………………………. (1)


(b) Write down the 10th term of the sequence.

.……………………………… (1)

(Total 2 marks)

Question 4.

Look at these shapes made from squares.

(a) Draw shape 4.

(1)

(b) Complete this table

Shape number 1 2 3 4 5

Number of squares 1 4

(1)

(c) How many squares are in the 7th shape?……………………………… (1)

(d) Complete this formula to describe the position-to-term rule.

Number of squares = ____ × shape number – 2 (1)

(Total 4 marks)

Total /10


Sequences and Rules 2 Grade 2

Objective: Generate terms of a sequence from a term-to-term rule, including from patterns and diagrams.

Question 1.

Write down the next two terms in each of the sequences below:

(a) 1.6, 2, 2.4, 2.8, ____, ____,… (1)

(b) 1, 3, 9, 27, ____, ____,… (1)

(Total 2 marks)

Question 2.

Describe the term-to-term rule for each of these sequences.

(a) 2.5, 3, 3.5, 4, 4.5, …

…………………………………………………………………………………………...

(1)

(b) 80, 40, 20, 10, 5, …

…………………………………………………………………………………………...

(1)

(Total 2 marks)

Question 3.

Use the first term and the term-to-term rule to generate the first five terms of this sequence.

First term is 12, term-to-term rule is subtract 0.3

…………………………………………………………………………...............................................

(Total 1 mark)


Question 4.

Write down the missing terms in this sequence.

___, 6, ___, -2, -6, …

(Total 2 marks)

Question 5.

Look at the sequence of patterns made from counters.

(a) Draw the next two patterns in the sequence.

(2)

(b) How many counters will be in pattern 6? …………………………………………..

(1)

Total /10


Sequences of square, triangular and cube numbers 2 Grade 3

Objective: Recognise and use sequences of square, triangular and cube numbers, and simple arithmetic sequences.

Question 1.

(a) Write down the next two terms of this arithmetic sequence.

8.6, 8.2, 7.8, 7.4, ___, ___,… (1)

(b) Work out the missing terms in this arithmetic sequence.

6, ___, 0, -3, ___, … (2)

(Total 3 marks)

Question 2.

This pattern of dots show the first three square numbers.

(a) Draw the pattern of dots for the 4th and 5th square number.

(2)

(b) How many dots are there in the 7th pattern?

…………………. (1)

(Total 3 marks)


Question 3.

Here are the first five terms of the triangular number sequence.

1, 3, 6, 10, 15, …

Find the next two terms of the sequence.

…………….. and …………..

(Total 2 marks)

Question 4.

Write down the missing terms in this cube numbers sequence.

1, ___, 27, 64, ___, …

(Total 2 marks)

Total /10


Using formulae 2 Grade 3

Objective: Understand and use mathematical formulae

Question 1

You can use this rule to work out the number of minutes to cook a piece of beef.

MULTIPLY THE WEIGHT, IN KG, BY 40 THEN ADD 20

The weight of a piece of beef is 2.5KG

Use the rule to work out the number of minutes it will take to cook this piece of beef.

………………………………..

(3 marks)

Question 2

David uses this rule to work out his pay.

This week David worked for 14 hours. His rate of pay was £6.50.

(a) Use this rule to work out his pay.

……………………………..

(2 marks)


Last week David’s pay was £105. He worked for 15 hours.

(b) Work out David’s rate of pay per hour last week.

……………………………..

(2 marks)

Question 3

John uses this formula to work out his overtime pay.

John’s overtime rate was £8.30 per hour. He worked 9 hours overtime.

(a) Work out his overtime pay.

…………………………….. (2 marks)

John used this formula to work out his total pay.

John’s basic pay was £245.

(b) Work out his total pay?

…………………………….. (1 mark)

Total /10

PLC Papers

Created For:


Coordinates in four quadrants 2 Grade 3 Solutions

Objective: Work with coordinates in all four quadrants.

Question 1

Write down the coordinates of: The red Angry bird …(-2,4)……. (A1) The green Pig ……(-3,-1)……(A1) The black bird …..(4,3)……… (A1)

(3) Question 2 Follow the following instructions using the graph on the next page.

a) Plot (3,2) and label it A

b) Plot B (3,-4)

c) Mark M the mid point of AB, and write down the coordinates M (3,-1) (A1)

d) Plot C (-1,2)

e) Name the type of triangle by joining ABC…… Right angled (A1)…….

f) What is the area of the triangle? ……12 units2

(A1)(M1)……….

(4)


(A3) 4 coordinates A, B, C correctly positioned.

(3)

Total marks / 10


Plotting straight line graphs 2 Grade 3 SOLUTIONS

Objective: Plot graphs of straight-lines in the coordinate plane

Question 1

(a) Complete the table of values for y = 2x + 5

(2)

(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = -2 to x = 2

(2)

(Total: 4 marks)

3

B2 for all 3 values correct in table

B1 for 2 values correct

M1 ft for plotting at least 2

correct points

A1 for correct line from x = -2 to

x = 2

7 9


Question 2

On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3

(3 marks)

M1 for at least 2 correct attempts to find

points

M1 ft for plotting at least 2 correct points

A1 for correct line from x = -1 to x = 3

OR

M2 for at least 2 correct points and no

incorrect points plotted

A1 for correct line from x=-1 to x=3


Question 3

On the grid,

(a) draw the line x = 3

(b) draw the line y = −1

(c) draw the line y = x

(3 marks)

Total Mark /10

x = 3 A1

y = -1 A1

y = x A1


Position-to-term rules 2 Grade 3 Solutions

Objective: Generate terms of a sequence from a position-to-term rule, including from patterns and diagrams.

Question 1.

The table shows some terms in a number sequence and their position in the sequence.

Position 1 2 3 4 5 6

Term 7 14 21 28 35 42

Position number multiplies by 7 (A1 – two correct) (A2 – three correct)

Fill in the missing terms in the sequence. (Total 2 marks)

Question 2.

Write down the first six terms of the sequence for each of these position-to-term rules.

(a) Position number add 8

9, 10, 11, 12, 13, 14, … (A1)

…………………………………………………………………………….. (1)

(b) (3 × position number) subtract 2

1, 4, 7, 10, 13, 16, … (A1)

…………………………………………………………………………….. (1)

(Total 2 marks)


Question 3.

The table shows the first five terms of a number sequence and their position in the sequence.

Position 1 2 3 4 5

Term 4 7 10 13 16

(a) Describe the position-to-term rule for this sequence.

The position-to-term rule is multiply the position number by three and then add one.

Or 3 × position number + 1 (A1)

….………………………………………………………………………………

…………………………………………………………………………………. (1)

(b) Write down the 10th term of the sequence.

3 × 10 + 1 31 (A1)

.……………………………… (1)

(Total 2 marks)

Question 4.

Look at these shapes made from squares.

(a) Draw shape 4.

(A1) (1)

(b) Complete this table

Shape number 1 2 3 4 5

Number of squares 1 4 7 10 13


(A1) (1)

(c) How many squares are in the 7th shape?……………19 (A1) (1)

(d) Complete this formula to describe the position-to-term rule.

Number of squares = ___3_ × shape number – 2 (A1) (1)

(Total 4 marks)

Total /10


Sequences and Rules 2 Grade 2 Solutions

Objective: Generate terms of a sequence from a term-to-term rule, including from patterns and diagrams.

Question 1.

Write down the next two terms in each of the sequences below:

(a) 1.6, 2, 2.4, 2.8, 3.2, 3.6,…

(A1) sequence is adding 0.4 (1)

1, 3, 9, 27, 81, 243, …

(A1) sequence is multiplying 3 (1)

(Total 2 marks)

Question 2.

Describe the term-to-term rule for each of these sequences.

(a) 2.5, 3, 3.5, 4, 4.5, …

The term to term rule is add 0.5 to the previous term. (A1)

…………………………………………………………………………………………...

(1)

(b) 80, 40, 20, 10, 5, …

The term to term rule is divide the previous term by 2. (A1)

(Accept halve the previous term)

…………………………………………………………………………………………...

(1)

(Total 2 marks)

Question 3.

Use the first term and the term-to-term rule to generate the first five terms of this sequence.


First term is 12, term-to-term rule is subtract 0.3

12, 11.7, 11.4, 11.1, 10.8 (A1)

…………………………………………………………………………...............................................

(Total 1 mark)

Question 4.

Write down the missing terms in this sequence.

10, 6, 2, -2, -6, … (A1, A1)

(Total 2 marks)

Question 5.

Look at the sequence of patterns made from counters.

(a) Draw the next two patterns in the sequence.

(A1, A1) 2)

(b) How many counters will be in pattern 6? 13………………………………… (A1,)

(1)


Total /10


Sequences of square, triangular and cube numbers 2 Grade 3 Solutions

Objective: Recognise and use sequences of square, triangular and cube numbers, and simple arithmetic sequences.

Question 1.

(a) Write down the next two terms of this arithmetic sequence.

8.6, 8.2, 7.8, 7.4, 7, 6.6,…

sequence is subtracting 0.4 (A1) (1)

(b) Work out the missing terms in this arithmetic sequence.

6, 3, 0, -3, -6, … (A1,A1) (2)

(Total 3 marks)

Question 2.

This pattern of dots show the first three square numbers.

(a) Draw the pattern of dots for the 4th and 5th square number.

(A1,A1)

(2)

(b) How many dots are there in the 7th pattern? 49 … (A1)

…………………. (1)


(Total 3 marks)

Question 3.

Here are the first five terms of the triangular number sequence.

1, 3, 6, 10, 15, …

Find the next two terms of the sequence. 21, 28 …

Add 2, 3, 4, 5, 6, 7, etc (A1,A1)

…………….. and …………..

(Total 2 marks)

Question 4.

Write down the missing terms in this cube numbers sequence.

1, 8, 27, 64, 125, …

Cube numbers 23 and 53 (A1,A1)

(Total 2 marks)

Total /10


Using formulae 2 Grade 3 Solutions

Objective: Understand and use mathematical formulae

Question 1

You can use this rule to work out the number of minutes to cook a piece of beef.

MULTIPLY THE WEIGHT, IN KG, BY 40 THEN ADD 20

The weight of a piece of beef is 2.5KG

Use the rule to work out the number of minutes it will take to cook this piece of beef.

12020405.2 =+×

120

………………………………..

(3 marks)

Question 2

David uses this rule to work out his pay.

This week David worked for 14 hours. His rate of pay was £6.50.

(a) Use this rule to work out his pay.

9150.614 =×=Pay

91 ……………………………..

(2 marks)

Last week David’s pay was £105. He worked for 15 hours.

(b) Work out David’s rate of pay per hour last week.


7£15

105

==

=ursNumberofho

PayRateofpay

7£ ……………………………..

(2 marks)

Question 3

John uses this formula to work out his overtime pay.

John’s overtime rate was £8.30 per hour. He worked 9 hours overtime.

(a) Work out his overtime pay.

70.74930.8 =×=yOvertimePa

70.74£

…………………………….. (2 marks)

John used this formula to work out his total pay.

John’s basic pay was £245.

(b) Work out his total pay?

70.31970.74245 =+=TotalPay

70.319

…………………………….. (1 mark)

Total /10

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