QCAA Practice Questions for Unit 3 & 4 General Maths External Assessment

Question 6

Is the three-mean smoothed temperature for Wednesday approximately 26? (2 marks)

Question 7

Is the five-mean smoothed temperature approximately 30? (2 marks)

Question 8

Is the seven-mean smoothed temperature for Thursday approximately 23? (2 marks)

Question 9

Find the arc length that subtends an angle of magnitude 105° at the centre of a circle of radius 25 cm. (3 marks)

Question 10

Find the size of the angle subtended at the centre of a circle of radius length 30 cm by an arc length of: (4 marks)

(a) 50cm

(b) 25cm

Question 11

A chord of length 6 cm is drawn in a circle of radius 7cm. Find the length of the minor arc cut off by the chord. (3 marks)

Question 12

An island in the pacific is 10 hours behind GMT. (3 marks)

(a) What is the longitude of the island?

(b) What is the time in London when it is 4 a.m. on the island?

(c) What is the time on the island when it is 5:30 a.m. in London?

Question 13

The longitude of Hanoi is 105°E, while the longitude of Cape Howe is 150°E. When the time in Hanoi is 2:30 p.m., what is the time at: (3 marks)

(a) Cape Lowe?

(b) London?

Question 14

How many terms from this recurrence relation F0 = 150, Fn+1 = 0.6Fn − 12 are positive? (2 marks)

Question 15

How many terms from this recurrence relation Y0 = –45, Yn+1 = 0.8Yn + 2 are negative? (2 marks)

Question 16

A reducing-balance loan can be modelled by A0 = 2500, An+1 = 1.08 × An − 600 (5 marks)

(a) What is the value of the repayment each compounding period?

(b) Use calculator recursion to determine how much is still owed on the loan after three repayments have been made.

(c) How much interest has been paid after three repayments?

Question 17

A reducing-balance loan can be modelled by A0 = 5000, An+1 = 1.01 × An – 860 (5 marks)

(a) What is the value of the repayment each compounding period?

(b) Determine how much is still owed on the loan after five repayments have been made.

(c) How much interest has been paid after five repayments?

Question 18

Given an annuity A0 = 5000, An+1 = 1.01 × An – 1030: (5 marks)

(a) Explain how we can tell this annuity is in withdrawal phase.

(b) What is the payment that is withdrawn from this annuity each compounding period?

(c) Determine the amount left in the annuity after three payments have been received.

(d) How much interest has been earned after three payments have been received?

Question 19

Draw a graph that has: (4 marks)

(a) Three vertices, two of which have an odd degree

(b) Four vertices and five edges, one of which is a loop

(c) Six vertices, one of which is isolated, and eight edges

(d) Six vertices, two of which have an odd degree, and which contain at least one subgraph that is a triangle.

Question 20

There are four different human blood types: O, A, B and AB. Blood can be donated from one human to another using the following rules:

• Type O can donate blood to any type
• Type AB can receive blood from any type
• Each type can donate blood to its own type
• Each type can receive blood from its own type

Construct a graph to show this. (6 marks)

Solutions to QCAA General Maths EA Practice Questions

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