4 Pedro makes cards.

(a) He makes cards at a rate of 9 cards every 20 minutes.

Work out the number of cards he makes in 8 hours [2]

(b) Each card costs 12 cents to make.

Pedro sells each card for 50 cents.

Work out his percentage profit on each card % [2]

5 Nuwa is buying a phone.

One website sells the phone for 953 Yuan.

A different website sells the same phone for $141.

The exchange rate is 1 Yuan = $0.152 .

Calculate the difference between these phone prices.

Give your answer in dollars, correct to the nearest cent.

$ [2] , ,

6 One morning, a dentist has appointments for 10 patients.

The stem-and-leaf diagram shows the waiting time for 8 of these patients. 0 1 4 1 0 2 9 2 1 5 5

Key: 1 | 0 represents 10 minutes

The times for the two other patients, P and Q, are not shown in the stem-and-leaf diagram.

The mean waiting time of all 10 patients that morning is 16 minutes.

The range of waiting times is 26 minutes.

Patient P waits longer than patient Q.

Find the waiting time for each of patient P and patient Q.

Patient P min

Patient Q min

[4]

7 The diagram shows a parallelogram. NOT TO SCALE x m 6.51 m

The parallelogram has the same perimeter as a circle with radius 4 m.

(a) Show that . m x 6 06

, correct to 2 decimal places.

[4]

(b) NOT TO SCALE 6.51 m 36° 6.06 m

The floor of a room is in the shape of this parallelogram.

It costs $18 per square metre to tile the floor.

Calculate the total cost of tiling the floor.

$ [4] , ,

8 A B y x – 6 – 5 – 4 – 3 – 2 – 1 – 3 – 2 – 1 5 4 7 6 3 2 1 0 1 2 3 4 5 6 – 4 – 5

(a) On the diagram, draw the image of

(i) shape A after a translation by the vector 1 7

e o [2]

(ii) shape A after a reflection in the line y x 1

• . [3]

(b) Describe fully the single transformation that maps shape A onto shape B [3] , ,

9 The diagram shows the speed–time graph for part of a car journey.

NOT TO SCALE 0 0 15 25 60 80 Speed (km / h) Time (minutes)

Find the total distance travelled in the 25 minutes km [3] 10 Find the nth term of each sequence.

(a) 17, 9, 1, – 7, -15, f

[2]

(b) 3, 12, 27, 48, 75, f

[2] , ,

2 Solve.

x 8 17 27

=

x = [2]

11 The table shows some values for y x x 2 3 3

• .

Where appropriate, values of y are given correct to 2 decimal places. x -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y -1 4 3.88 3 2.13 2 7

(a) Complete the table. [2]

(b) Draw the graph of y x x 2 3 3

• for x 2 2 G G

. y x – 2 – 1 – 1 1 2 3 4 5 6 7 1 0 2

[4]

(c) By drawing a suitable straight line on the grid, solve the equation . x x 2 5 1 0 3 - +

.

x = or x = or x = [4] , ,

12 A C D E O y° x° 65° 52° B NOT TO SCALE

A, B and C lie on a circle centre O.

DE is a tangent to the circle at C.

Angle ABC = 52° and angle BCE = 65°.

(a) Find the value of x.

Give a geometrical reason for your answer. x = because [2]

(b) Find the value of y.

y = [2]

13 Simplify.

m m 2 7 8 3 +

[2] 14 (a) Carlos invests $24 000 at a rate of 3.2% per year compound interest.

Calculate the value of his investment at the end of 4 years.

$ [2]

(b) Carlos buys a painting for $x.

He sells the painting for $40 870.

He makes a profit of 34%.

Calculate the value of his profit.

$ [3]

(c) Carlos also buys a car with a value of $32 500.

The value of the car decreases exponentially by 23% each year.

Find a formula for the value, $V, of the car at the end of n years [3] , ,

3 Write down the order of rotational symmetry of a regular decagon [1]

1 Write the ratio 60 grams : 3 kilograms in the form n 1| .

1 | [2] , ,

15 A D 140° C B 180 m 300 m 112 m NOT TO SCALE

The diagram shows a field, ABCD, in the shape of a quadrilateral.

BD is a straight path across the field.

(a) Calculate BC.

BC = m [3]

(b) Calculate angle DBC.

Angle DBC = [3]

(c) The total area of the field, ABCD, is 35 900 m2.

Work out the length of the shortest distance from D to AB m [4] , ,

16 The histogram shows information about the masses of some coconuts.

The masses are classified into four categories A, B, C and D. 0.9 1.0 1.1 1.2 1.3 Mass (kg) Frequency density 1.4 1.5 1.6 50 0 100 150 200 A B C D

(a) Show that there are 10 coconuts in category D.

[1]

(b) Two of the coconuts from those in category C and category D are chosen at random.

Find the probability that both are from category D [3]

(c) Calculate an estimate of the mean mass of the coconuts kg [4] , ,

17 Expand and simplify.

( )( )( ) x x x 2 2 3 4

[3] , ,

18 C B A O a b NOT TO SCALE

In the diagram, OA is parallel to CB.

OA | CB = 4 | 3

OA a

and OB b

.

(a) Find AB in terms of a and b.

AB = [1]

(b) M is the midpoint of OC.

Find M A in terms of a and b.

Give your answer in its simplest form.

M A = [3]