Ratio & Basic Proportion: WJEC GCSE Numeracy Intermediate June 2023 Unit 1 Q8

Numeracy Intermediate June 2023 Unit 1 Q8

WJECIntermediateCurrent spec7 marksRatio & Basic Proportion Scatter Diagrams & Correlation

8. The scatter diagram shows the length and width of some television remote handsets.

(a) Two of the remotes have the same width.
Write down the width and lengths of these remotes. [2]

Width …………… cm

Lengths are …………… cm and …………… cm.

(b) Consider the remote with a width of 4·5 cm.
Write down the ratio of the width of this remote to its length.
Give your answer in its simplest form. [2]

(d) Draw a line of best fit on the scatter diagram. [1]

(e) Is it certain that another television remote with length 18·5 cm will have a width in the range 3 cm to 4 cm?

Yes ☐ No ☐

You must give a reason for your answer. [1]

Scheme	Marks	Comments
Width 3.9 cm AND Lengths 17.7 cm and 18.5 cm	B2	Accept lengths given in either order, 17.7 cm and 18.5 cm or 18.5 cm and 17.7 cm B1 for any 2 correct measurements

Scheme	Marks	Comments
9 : 35	B2	Mark final answer Must be expressed as a ratio for B1 or B2 B1 for sight of 4(.)5 : 17(.)5 or equivalent, or 35 : 9

Scheme	Marks	Comments
(Strong) negative (correlation)	B1	CAO

Mark scheme (d)

Scheme	Marks	Comments
Suitable line of best fit drawn	B1	The straight line (accept intention if a ruler is not used) must have points above and below it, generally this is 3 above and 4 below The line must be of sufficient length, to illustrate trend for at least 5 points The trend shows that there are points above and below the line at each end of the line Allow, e.g. the line of best fit following the ‘trend’ from top left corner provided 3 points are above the line with 2 points above the line, one point ‘on’ the line and 4 points below the line with 3 points above the line, 2 ‘on’ the line and 2 points below the line Do not accept, e.g. a line from the bottom right corner with 3 points above the line and 3 or 4 points ‘on’ the line from top corner with 4 points ‘on’ the line a line joining the first point to the last point a ‘corner to corner’ line line NOT drawn to follow the clear ‘trend’ joining ‘point to point’ a line of insufficient length, trend only shown for fewer than 5 points Note: ‘on’ the line includes a point just touching the line, no gap between the point and the line

Scheme

Marks

Comments

Suitable line of best fit drawn

The straight line (accept intention if a ruler is not used) must have points above and below it, generally this is 3 above and 4 below
The line must be of sufficient length, to illustrate trend for at least 5 points
The trend shows that there are points above and below the line at each end of the line

Allow, e.g. the line of best fit following the ‘trend’

from top left corner provided 3 points are above the line
with 2 points above the line, one point ‘on’ the line and 4 points below the line
with 3 points above the line, 2 ‘on’ the line and 2 points below the line

Do not accept, e.g.

a line from the bottom right corner
with 3 points above the line and 3 or 4 points ‘on’ the line
from top corner with 4 points ‘on’ the line
a line joining the first point to the last point
a ‘corner to corner’ line
line NOT drawn to follow the clear ‘trend’
joining ‘point to point’
a line of insufficient length, trend only shown for fewer than 5 points

Note: ‘on’ the line includes a point just touching the line, no gap between the point and the line

Mark scheme (e)

Scheme	Marks	Comments
‘No’ indicated or implied with an explanation, e.g. ‘not certain to fit the trend’, ‘only a small sample of remotes measured’	E1	Allow ‘No’ with, e.g. ‘can be all different sizes of remotes’, ‘width does not depend on the length of the remote’, ‘width could be anywhere in the range 1 to 6 cm’, ‘not all remotes are the same width’, ‘insufficient data’, ‘may not fit the pattern’ Do not accept ‘No’ with, e.g. ‘no way of knowing’ (without a reason), ‘because you can’t be certain’ (without a reason)