Graphs and Data Representation

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Graphs and Data Representation — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionData visualizations and infographicsAssessment Practice

5 marks~8 minCriterion A

The diagram shows the graph of

f(x) = x^2 - 6x + k

for

0 \le x \le 6

, where

k

is a constant. The graph passes through the point

(1, 3)

Show that

k = 8

. [1]

Find the coordinates of the vertex of the graph. [2]

State the values of

m

for which

f(x) = m

has exactly one solution in the domain

0 \le x \le 6

, and justify your answer. [2]

Solutions

2QuestionData visualizations and infographicsAssessment Practice

6 marks~9 minCriterion C

A group of 60 students were asked to choose their favourite fruit. The results are shown below.

Fruit	Apple	Banana	Orange	Grape
Students	21	15	12	12

Show that the sector angle for Apple in a pie chart is

126°

. [1]

A student claims that the combined sector angle for Banana and Orange equals the sector angle for Apple. Determine whether this claim is correct, showing all working. [2]

Two students are chosen at random from the group, one after the other, without replacement. The probability that both students chose Apple is

\dfrac{7}{59}

. Justify whether this result suggests that Apple is a genuinely popular choice among the group, or whether it could reasonably be explained by chance. [3]

Solutions

3QuestionData visualizations and infographicsAssessment Practice

6 marks~9 minCriterion B

The diagram shows Figures 1 to 4 of a pattern made from small equilateral triangles.

Figure 1	1 shaded triangle	0 unshaded triangles.
Figure 2	2 shaded triangles	1 unshaded triangle.
Figure 3	3 shaded triangles	3 unshaded triangles.
Figure 4	4 shaded triangles	6 unshaded triangles.

The total number of small triangles in Figure

n

is denoted

T(n)

Write down the values of

T(1)

T(2)

T(3)

, and

T(4)

. [1]

Find a rule for

T(n)

in the form

T(n) = an^2 + bn

where

a

and

b

are constants to be determined. [3]

The number of unshaded triangles in Figure

n

is given by

U(n) = \frac{n^2 - n}{2}.

Using your rule from part (b), deduce a simplified expression for the number of shaded triangles

S(n)

in Figure

n

, and justify why

S(n)

must always equal

n

. [2]

Solutions

4QuestionData visualizations and infographicsAssessment Practice

7 marks~11 minCriterion D

The table below shows monthly sales (in thousands of dollars) for three products over six months.

Month	Jan	Feb	Mar	Apr	May	Jun
Product A	10	12	15	8	20	18
Product B	8	10	12	14	16	15
Product C	5	7	9	11	13	12

Calculate the total sales for Product C over the six months, and hence find the overall total sales across all products and all months. [2]

A rival company claims that Product C accounts for more than 27% of total sales over the six months. Deduce whether this claim is correct, showing all working. [2]

The company sets a target: in a seventh month, Product A must achieve sales high enough so that Product A's share of the new seven-month overall total exceeds 40%. Products B and C each sell 15 thousand dollars in month 7. Find the minimum integer value of Product A's month-7 sales (in thousands of dollars) that meets this target, and justify whether this target is a realistic expectation for Product A based on its six-month sales record. [3]

Solutions

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