Drawing & Using Graphs: WJEC GCSE Higher June 2018 Unit 1 Q16

Higher June 2018 Unit 1 Q16

WJECHigherCurrent spec5 marksDrawing & Using Graphs

16.

(a) Draw the graph of the curve \(y = 2^x\) for values of \(x\) from –2 to 2.
Use the graph paper below. [3]

Unscaled graph paper with x- and y-axes crossing at the origin O

(b) Use your graph to find the value of \(2^{1{\cdot}4}\). [1]

Mark scheme (a)

Scheme

Marks

Comments

\(x\)	–2	–1	0	1	2
\(y\)	\(\frac{1}{4}\)	\(\frac{1}{2}\)	1	2	4

Any 3 correct pairs of coordinates (need not be for integer values of x.) Must include one negative value of x.

Suitable choice of uniform scales through the origin, \(x\) from – 2 to 2 and \(y\) from 0 to 4, AND plotting at least 3 points correctly.

FT their evaluations of \(y\) if shown (provided they do not produce a straight line).
Must include one negative value of x.
Tolerance for accuracy ± \(\frac{1}{2}\) a small square.

Joining with a curve.

CAO. Exponential curve which passes through (-2, \(\frac{1}{4}\)), (0, 1) and (2, 4).
Must not intercept x axis anywhere, including beyond the required range of x values.
Tolerance for accuracy ± \(\frac{1}{2}\) a small square.

If no table or evaluations of coordinates are given (for at least 3 pairs of values, including one negative value of x), then
B1 B1 may be implied by C1
or
if C0, B1 B1 may be implied by 3 correctly plotted points for y = 2^x (including one negative value of x).

Mark scheme (b)

Scheme	Marks	Comments
Reading from their graph for \(x = 1{\cdot}4\) \((y \approx 2{\cdot}6)\)	B1	FT ‘their curve’. (No FT for a straight line.) Tolerance for accuracy ± \(\frac{1}{2}\) a small square.

Mark scheme (c)

Scheme	Marks	Comments
Reading from their graph for \(y = 1{\cdot}4\) \((x \approx 0{\cdot}5)\)	B1	Accept an embedded answer. FT ‘their curve’. (No FT for a straight line.) Must include all relevant readings if ‘their graph’ is not one-to-one. Tolerance for accuracy ± \(\frac{1}{2}\) a small square.