Question

year 9 numeracy (calculator allowed)

15 the table below lists the original price and the amount of discount of the same shirt at four different shops.

shirt sale
shop | original price | discount
a | $20 | 25%
b | $24 | \\(\frac{1}{3}\\)
c | $30 | 30%
d | $18 | $2 off

which shop has the lowest sale price for the shirt?
a
b
c
d

16 ruby designs a rectangular picture for her wall.
inside her rectangle, she adds three straight lines as shown.
what is the size of angle x?
degrees

Explanation:

Calculate sale prices for Shop A and Shop B

Using the Percentage Discount and Fractions knowledge points

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Calculate sale prices for Shop C and Shop D

Using the Percentage Discount knowledge point

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Comparing all prices, Shop A has the lowest sale price of \(\$15\).

Identify geometric relationships in Question 16

Using the Angle Relationships knowledge point
The diagram shows a horizontal line and a vertical line intersecting inside a rectangle, forming a right angle (\(90^\circ\)) indicated by the square symbol.
A straight line forms a straight angle of \(180^\circ\).
The vertical line is perpendicular to the horizontal line, meaning the angle on the left side of the vertical line above the horizontal line is also \(90^\circ\).

Solve for the unknown angle x

Using the Angle Relationships knowledge point
The diagonal line, the vertical line, and the horizontal line meet at a point.
The angle adjacent to the \(45^\circ\) angle on the straight horizontal line is a right angle (\(90^\circ\)).
The angle \(x\) and the \(45^\circ\) angle lie on a straight line (the diagonal line), or we can use the supplementary relationship along the straight line:

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Answer:

Question 15

• (A) Shop A (Correct answer)
• (B) Shop B
• (C) Shop C
• (D) Shop D

Question 16

What is the size of angle x?
<blank>45</blank> degrees