LEVEL 4      Using rules

(a)     The rule in a number sequence is add 8          Use this rule to write the missing numbers in the sequence.

1 mark

(b)     The rule in a different number sequence is double, then add 1          Use this rule to write the missing numbers in the sequence.

2 marks Q2.          Sequence          A sequence of numbers starts at the number 12. The numbers increase by 4 each time. 

12   16   20   24   28 ...          The sequence keeps going forever.

(a)     Will the number 39 be in the sequence? Tick ( ) Yes or No.

          Yes                    No          Explain your answer.

   

1 mark

(b)     Will the number 100 be in the sequence? Tick ( ) Yes or No.

          Yes                    No          Explain your answer.

   1 mark

 Q3.          Throwing dice          Some pupils throw two fair six-sided dice. Each dice is numbered 1 to 6

One dice is blue. The other dice is red. Anna’s dice show blue 5, red 3Her total score is 8. The cross on the grid shows her throw.

(a)     Carl’s total score is 6What numbers could Carl’s dice show?

          Put crosses on the gird to show all the different pairs of numbers Carl’s dice could show.

2 marks(b)     The pupils play a game.

 Winning rule: Win a point if the number on the blue dice is

the same as the number on the red dice. 

          Put crosses on the grid to show all the different winning throws.

2 marks

(c)     The pupils play a different game. The grid shows all the different winning throws.

          Complete the sentence below to show the winning rule.

 Winning rule: Win a point if the number on the blue dice is

......................................................................1 mark

 Level 5Q1.          Spiral          The grid shows the first eight lines of a spiral pattern.          The spiral pattern starts at the point marked .

(a)     Continue the spiral by drawing the next four lines on the grid below.

1 mark(b)     The table shows the length of each line.

 line number length

1 12 13 24 25 36 37 48 49 5

          The rule for finding the length of odd numbered lines is:

          What is the length of line number 23?

.............................. 1 mark

(c)     Fill in the box to show the rule for finding the length of even numbered lines.

1 mark(d)     What is the length of line number 18?

.............................1 mark

 Q2.          These patterns are made with matchsticks.

          Every pattern is made with an odd number of matchsticks.The rule for finding the number of matchsticks in a pattern is:

 2 times the number of triangles,

add 1

(a)     Jason wants to make the pattern with 9 triangles.Use the rule to find how many matchsticks he will need.

.............................. matchsticks1 mark

(b)     M = number of matchsticksT = number of triangles

          Use symbols to write down the rule connecting M and T.

1 mark

(c)     The rule for finding the number of triangles in a pattern is: 

The number of matchsticks take away 1,then divide by 2.

          Bethan uses 11 matchsticks to make a pattern.          Use the rule to find how many triangles she has in her pattern.

.............................. triangles1 mark

(d)     Misa uses 35 matchsticks to make a pattern.          Use the rule to find how many triangles she has in her pattern.

.............................. triangles1 mark

 

 

Level 6Q1.          Straight line graph          The graph shows the straight line with equation y = 3x – 4

(a)     A point on the line y = 3x – 4 has an x-coordinate of 50          What is the y-coordinate of this point?

  ..............................1 mark

(b)     A point on the line y = 3x – 4 has a y-coordinate of 50          What is the x-coordinate of this point?

  ..............................1 mark

(c)     Is the point ( –10, –34 ) on the line y = 3x – 4? 

  Yes    No

          Show how you know.

  

1 mark Q2.          Making patterns          Uri makes a sequence of shapes using square tiles.

The number of square tiles in shape number n is 

2n + 1

Uri makes a different sequence of shapes.In this sequence of shapes, the number of square tiles in shape number n is

 

3n + 1

Draw what the first 3 shapes might look like.

2 marks Q3.          Equations          Each point on the straight line x + y = 12 has

an x coordinate and a y coordinate that add together to make 12          Draw the straight line x + y = 12

1 mark 

Q4.          Equations of lines(a)     You can write the equation y = x + 4 in different ways.

Circle the correct ways below.

                x + y 4                   x 4 + y                   y – x 4y + 4 x                     x y – 4

2 marks

(b)     The equation of the line AB is y x + 4

Write an equation that describes line CD

1 mark 

 Q5.          Sequences          For each sequence below, tick ( ) the correct box to show if it is increasing,

decreasing or neither.

                                                      increasing          decreasing       neither

                                                                                     

                                                                               

                                                                                     

                                                                                      2 marks

 

 

Q6.          Selma is investigating the number of pins needed to pin squares o f paper to a wall display.

        First she tried 4 pins in each square Then she tried 3 pins.         Then she tried 2 pins

          She drew graphs to show her results.

          Selma has 16 pins.(a)     Use the correct graph to find the number of squares she can pin up with 4 pins in each

square. .............................. squares 1 mark

          How many squares can she pin up with 3 pins in each square?

.............................. squares 1 mark

(b)     The line through the points for p = 3s + 1 climbs more steeply than the lines through the points for p = 2s + 1 and p = s + 1.Which part of the equation p = 3s + 1 tells you how steep the line is?

1 mark

(c)     On the grid opposite, plot three points to show the graph for 8 pins in each square.

                              2 marks

(d)     What is the equation of this graph?

1 mark