11+ Bucks Free Interactive Guide Maths non-Verbal Reasoning Verbal Reasoning week 3
Welcome to week 3 of my free interactive 11+ Bucks course! This blog will be updated every week, just as if you were attending tuition. I am a professional 11+ tutor but I am sharing my weekly notes, tips, and clips from other free sites. I have carefully chosen clips that are relevant to you as you prepare for September 2018.
This week, I have a sample non-Verbal Reasoning paper written by the same exam board that sets the 11+ in Bucks. But first, some verbal reasoning.
(open in Chrome)
Move a Letter
In each question below, one letter from the word on the left must be moved into the word on the right to make two new words. The letters must not be re-arranged. Both new words must make sense. Write the two new words in the spaces provided.
(Example and questions 1- 6 taken from the Bucks 11+ sample paper)
Example CLIMB LOSE (move C) LIMB CLOSE
CHEAT WARS (__________) (_________ )
PAINT BRAIN (__________) (_________ )
FIRST PAWN (__________) (_________ )
CLOTH SORT (__________) (_________ )
SPORT LACES (__________) (_________ )
TRAMP PIER (__________) (_________ )
and some of mine
THEM HIS (__________) (_________ )
BOOKS HONE (__________) (__________)
TRAIN PEAL (___________) (__________)
PS: both must be real words, names aren’t allowed, and all spellings must be correct!
Warm Up. Clockwise and anti-clockwise are very important in non-Verbal Reasoning: Here’s a clip.
Play this one game (below) about angles.
It’s getting a bit more difficult now. Look at the clip below, and do the ‘revise’ and ‘test’ sections
Here is a Sample Paper from the 11+ Bucks (Buckinghamshire) exam board GL Assessment.
You may need: access to a printer,
a pen or pencil,
an analogue clock,
and a plughole and bathwater.
I will go through the sample paper section by section, giving insider tips. If you haven’t seen non-Verbal Reasoning before, and many of you haven’t, it will look very puzzling at first, even like nonsense. But there is sense to it, and with practice you will begin to see patterns and to solve the puzzles!
The following images are taken from the https://www.gl-assessment.co.uk/media/169656/nvr-1-familiarisation-test-booklet.pdf.
The tips are mine.
What is the rule of the example puzzle below?
Rule 1, the dot acquires an extra ring around it, the number going up by one in each box. This is to do with number.
Which, A B C D or E follows the rules of the puzzle and completes the sequence?
P1: The next puzzle Practice 1 (or P1) has two rules.
Rule 1, the number of arrows increases by one each time.
Rule 2, the direction of the arrow alternates, pointing downwards then upwards etc.
Which, A to E, follows these two rules and completes the sequence?
Rule 1 Rule 2
P2: In the next puzzle, Practice 2 (or P2)
Rule 1 is that the sequence of the pattern ‘jumps’ over one square, so the sequence jumps from 1, to 3, to 5, and the other sequence jumps from 2 to 4
Rule 2, the pattern for 1, 3, 5, shows that the six-sided shape (hexagon) is always the same but theshading of the diagonal lines inside the shape changes direction from diagonal to the left, to diagonal to the right.
Which out of A to E follows rules 1 and 2?
The following sequence has 3 rules.
Rule 1: positionof a shape is important (look at the example below, how the rectangle moves DOWN by 1/3 of the box. You can see it most clearly in boxes 2/3/4.) It returns to its original position.
Rule 2: the circle moves UP by 1/3 of the box.
There is also a 3rd rule: can you see what it is?
position (where a shape disappears, and in which direction it disappears. Does it disappear in a clockwise direction? Or anti-clockwise?)
shape is important, and the so is the number of sides a shape has: triangles, squares, pentagons, hexagons, septagons, (even your octogons, nonagons and decagons).
You also need to deal with stars, crosses, X, arrows, ovals, shapes that look like the letter Y, shapes that you will have to find names for yourself (as this will help,)
shapes that look like torpedos
shapes that look like keyholes
rotation 90 °, 45°, 180°, clockwise and anti-clockwise
Shapes can move clockwise or anti-clockwise around a square box, (though we are more accustomed to seeing them move around a circular shape like a clock)
Are all the arrows below going clockwise?
Trace you finger round in the direction of the arrow. Does it go the same way round as the fingers on a clock?
Trace your finger or pencil in the direction of the arrow. Does it go round the same way as the clock, or in the opposite direction?
The first set of arrows were all going clockwise, and the second set were all going anti-clockwise, but they may not have looked like it. That is why you have to TRACE IT.
When a shape moves around a box 90° (clockwise) it goes from corner to corner like this.
All those arrows are pointing clockwise too.
When a shape moves around a box 45°, it goes from the side to the corner, to the side to the corner, and so on.
We can also have on shape moving clockwise by 90° and another shape moving anti-clockwise by 45°. Look at the square first. Then the circle.
The arrow in the shape below (imagine it is the finger on a square clock) moves from the mid-line of the box, to the corner of the box, to mid-line of the next box, so it is moving 45°, (anti-clockwise)
But the arrow in the sequence below goes from the line of the box, to the next line, and the next line, so the arrow is moving 90° (anti-clockwise)
If you print and cut out the boxes and put them on top of each other you can see this for yourself: measure the angle if you have a protactor.
If the arrow moved from corner to corner, it would also be moving 90°
order of shapes may be important: square, circle, triangle
size is important. Does the shape get bigger, smaller? C = big shape, D = small shape.
layering (Only the top shape will be fully visible. If a shape obscures some of another shape, it means it is on top of that shape. Put 4 different coloured cards on top of each other – you can see one card obscures the card underneath (the part that overlaps the card underneath). This can go on for several layers.
You may want to print off the sample exam paper and use that. We are only going through section of the sample paper 1 here. Please keep the rest of the paper as you will need it in later weeks of this blog. Please do not look closely at the rest of the paper as there are very few example of free-to-use gl assessment papers, in fact this is the only one I have found so far. It is better for you to put it somewhere safe until I go through section 2 with you on this blog.
Look at shapes on left, then pick one from A to E that ‘fits’ the pattern and goes in the empty box
Clues: Direction (clockwise or anti-clockwise) and Shape are the clues for question 1 Always cross off the ones you can eliminate with a quick stroke of a pencil.
Clue: Position is your clue for question 2
Clues: Order (the order the different shapes go in) andDirection (up or down)
Clues: Number and Shading combined are your clues for question 4
Clues: Position (up/down) and Shading (white/black) are you clues for question 5
Clues: Rotation and shading are your clues for question 6
Clues: Rotation and shading are your clues for question 7
If the picture is very complex and it is all too much to take in at once, like the picture above, focus on one part first, like the bottom left hand square, eliminate the wrong answers, then look at another part of the drawing, say the bottom right hand square, and eliminate what you can, until you are left with one. That is your answer.
Clues: Number (of sides) and Rotation are your clues for question 8
When turning something in you mind, focus on one part of it so that you don’t get lost and confused.
Clues: Rotation (clockwise and anti-clockwise)andShading
Clues: Position, Shading and Counting help with q10.
Tip: when the first one, (or the second one,) is blank do the sequence from right to left
Clues: Position/transformation, Shape combined, the black dot is tricky
Clues: Pointing: up, down, up, which direction do things point in? and Shading.
Clue: Rotation of outer shape. Inner shape moves as well, but independently.
Draw these as you imagine each one will look upright, then compare it to the picture to see if you got it right. If you didn’t draw the image on the picture, then turn it 90 degrees, and see how it really looks.
Clues: Shading, Line Types and Position are what counts in question 14
Clues: Number, Position and Rotation for question 15
Clues: Number, Shading, Position
Remember: when the first one is blank do the sequence from right to left
Clues: Shading, Rotation,
Clues: Rotation, Shading
Clues; Number, Position
Clues: Shading, Position
Did you remember to do the sequence from right to left on Q18?
If you found the rule fairly easily to find, if you could ‘just see it,’ you have good spatial reasoning skills and you will find that often you can ‘just see’ the answer. Some of us have to work at it, thinking it through in terms of number, size, shape, shading, direction, rotation, number of degrees of rotation.
Here are the right answers to the questions above. Do not waste them. If you got the answer wrong, or if you guessed, it is essential you read the explanation to learn ‘how they think’ and be on step closer to getting it right next time. If you got the answer right, you can learn from reading the explanations also.
Answers to Section 1 (Video with drawn explanations to follow.)
These will be meaningless unless you look at the graphic of the question as you read the answer (scroll up and down). It is essential that you SEE the solutions.
- B, Rule 1, because the circular line lengthens. Rule 2, it lengthens clockwise
- B, Rule 1, because the circular shape moves from one corner to the next in the pentagonal shape. Rule 2, it moves anti-clockwise.
- D, Rule 1, the shape, (I think of it as an anchor) flips 180 degrees in each box. Eliminate B and E. Rule 2, the black dot is always next to the straight line. Eliminate A. Rule 3, the curved line is replaced with a white circle, then the second curved line is replaced with a second white circle, and then the white dots get replaced by two curved lines again. So the picture in the next box must follow the sequence black line, black dot, and the curved line be replaced with a white dot. Only D works.
- B, Rule 1, the shape shaded black always disappears in the next box
- D, Rule 1, the oblong shape moves 1/3 of the way down the box. Rule 2, when it reaches the bottom of one box, it goes back to the top of the next box. So it can’t be option B or E. Rule 3, the dot alternates shading from black to white, and we are due a white dot. So, it can’t be option A. That leaves C or D. Rule 4, the dot also moves 1/3 of the square, but it goes UP the box, and it is due to be on the bottom, so it can’t be option C. That leaves option D.
- A, Rule 1, the shape (I think of it as something familiar, in this instance I think of it as buttons on a bag because that helps me visualise it) moves 45 degrees anti-clockwise. It is due in the top right hand corner so it can’t be B, C or D. That leaves A or E. Rule 2, the black dot moves one place to the right, so the black dot is due in the middle. The answer is A.
- D, There is too much to take in all at once so I focus on one small part of it to find Rule 1, each box gains two new semi-circles, with the white turning black, and the black turning white. Rule 2, the semi-circle in the bottom right hand corner of box 4, is black, so I know the next one has to be white, so I can eliminate A and C. I am now left with B, D and E. Rule 3, the semi-circle in the bottom left hand corner of box 4 is black so the next one has to be white, so out of the ones I have left, I can eliminate C. That leaves me with D and E. Rule 4, the semi-circle in the top left hand corner of box 4 is white, so the next one has to be black, so it can’t be E, and it must be D.
- D Rule 1, the pattern is hexagon, pentagon, hexagon, pentagon, so a hexagon has to be next, but all the options are hexagons so that doesn’t help. Rule 2, The entire hexagon in boxes 1 and 3 rotates 90 degrees clockwise (I can tell by focusing on the shaded tip of it) so I can cross off B and E. Rule 3, The little leaf shape on the inside of the hexagon is always one corner to the left of the shaded triangle, so it has to be D.
- C Rule 1: The arrow rotates 45 degrees, so it has to be A, B, C or E. I can eliminate D. Rule 2, the line appears by the circle, then by the arrowhead, then disappears. It is due by the arrowhead so it can’t be A or B, which leaves C or E. Rule 3, The black and white half of the circle switch shading in each box, so it has to be C.
- D Rule 1, the Y shape alternates between up and down, (it turns 180 degrees) and it is due to be upside-down in the blank box. It has to be B or D. I can cross of A, C and E. Rule 2, the lines at the bottom of the shape in boxes 4 and 5 increase in number from 1 line to 2 lines, so perhaps the sequence is 1, 2, 3 lines. There is a gap in-between the 1 line and the 3 lines, so I think there may a two line option in the shapes I have left. There is: it’s D, but I’m not entirely sure. (Just to be on the safe side, there is also something going on with the shading of the box. Rule 3, the circle on the upside down Y is always white, and the box is always black, so I can eliminate B. That confirms it, it’s D.
- E I found this one very tricky. It took me a long time, so I left it and came back to it when I had done the others. I suggest you do the same if you get really stuck on one. (Have a guess, mark it G, and come back to it at the end.) The solution is to do with Position. Rule 1, the triangle moves diagonally up to the right of each box, then goes back to its original position, so that eliminates A. Rule 2, the circle does the same, so that eliminates D. I am left with B, C and E. Rule 3, the black dot moves diagonally from the bottom right corner, to the middle, to the top left corner. There is a slight optical illusion in that it looks like it is moving from bottom left to top right, but that is not the case if you think it through carefully. The answer is option E.
- D Rule 1, upright T shape is due, so I can eliminate A, B, and C. I am left with D and E. Rule 2, the black shape is moving, but it hasn’t moved at all in E, which is exactly the same as the shape in the 3rd box. I am left with D. To check, I look for another rule, Rule 3, the black shading moves down 1/3 in each new shape, so it must be in a different position in shape 3. So it can’t be E, (that would take 4 moves, not 3).
- E Rule 1, the keyhole shape rotates 90 degrees, from line to line, going anti-clockwise. I can eliminate A, C, D. I am left with B and E. Rule 2, The circle alternates between white and black, and I am due a white, but both of the options I have left have white circles. Rule 3, the crooked line goes from the bottom left of the shape, to the bottom right of the next shape, (if I draw all the shapes upright). It is due to go to the bottom right, but B goes to the bottom left. I can eliminate B. The answer is E.
- D Rule 1, background lines alternate between horizontal and vertical. Horizontal lines are due, so I can eliminate A, B and C. I am left with D and E. Rule 2, a diamond shape is due, but both options I have left are diamond shapes. Rule 3, the black shading moves one place anti-clockwise, so I can rule out E. The answer is D.
- D, 1 circle disappears in each box, in an anti-clockwise direction. I should be left with one circle in the bottom right hand corner of box 4. I can eliminate A, C, and E. I am left with B and D. Rule 2, the arrow rotates 90 degrees clockwise so it is due to point South. I can eliminate B. I am left with D. The answer is D.
- E, Do this going from right to left. Rule 1, the number of oblong shapes goes 1, 2, 3, 2. Could it be that it goes 1, 2, 3, 2, 1? The only option in the answers is a 1, so it must be that. It doesn’t get me any closer to getting the right answer though. Rule 2, the shading of the circle goes black, white, black, white, so a black is due. That eliminates B and C. I am left with A, D and E. There has just been a circle in the middle so I can eliminate D. I am left with options A and E. Rule circle appears in column 2 (from right of box to left), 1, 3, 2, so a circle in column 1 is due. That eliminates A. I am left with E. The answer is E.
- C, Rule 1, graphic (I think it looks like a tie) needs to have black shading, so I can eliminate D. I am left with A, B, C and E. Rule 2, the top of the shape, which is black on the left, white on the right, can’t be A. I am left with B, C and E. Rule 3, the inner leaf shape has to be underneath the black triangle, so I can eliminate E. I am left with B and C. I now have a 50/50 chance of getting it right.
- C, (from right to left,) Rule 1, bottom of shape is in bottom right corner of box, then middle of base, then bottom left hand corner, so I know the shape is moving 45 degrees anti-clockwise, so the shape is due bottom left of the box, pointing diagonally. I am left with A, C or E. I can eliminate B and D. Rule 2, black becomes white and white becomes black, so we are due white/black in that corner, so I can eliminate A and E. I am left with C. C is the answer.
- C, I got to Rule 4 before I found one that mattered. Rule 4, on the left side we have 2 circles and 1 on the right, then three on the left side and 2 on the right, then 1 on the left side and three on the right, then two on the left and one on the right- which is where we started out – so could it be that three on the left and two on the right follows again? This answer is there, and it is the only rule that leaves us with only 1 answer. C is the answer.
- D, Rule 1, lose one black shape going anti-clockwise, so I need to have one black half-a-square remaining in the bottom left hand corner of the box. I can eliminate A and C. I am left with B, D and E. Rule 2, the black triangular shape switches from the outermost side of the inner square to the innermost side. In option B, the black triangular shape has not moved, so I can eliminate it. I am left with D and E. Number of inner squares reduces 9, 6, 4, _, 1. That sequence doesn’t mean much until I take into account that the jump from 9 to 6 is 3, the jump from 6-4 is 2, and the jump from 4-2 is 2, and the jump from 2-1 is 1. So the ‘jumps’ go down 3, 2, 1. I have found the final rule. The answer is D.
If you found the non-Verbal Reasoning difficult, carry on, as it gets easier
as you get used to it.
If you found the non-Verbal Reasoning impossible, you need to take step back and start working at age 9-10 level.
Here is a book I recommend:
You can come back to the higher level in a few months time.