Spec_11_Test_2_2018_FINAL.docx
Tick your teacherMiss ChengDr. PearceMs RimandoMiss SindelTick your teacherMiss ChengDr. PearceMs RimandoMiss SindelPERTH MODERN SCHOOL
YR11 MATHEMATICS SPECIALIST – 2018
TEST 2 – Counting (8%)
NAME: ____________________________________ DATE: Wednesday 4/4/2018
[To achieve full marks and to allow assessment of outcomes, working and reasoning should be shown.]
[A maximum of 2 marks will be deducted for incorrect rounding, units, etc.]
This is a Calculator Assumed Assessment Mark_________/37
Reading: 5 minutes Working: 40 minutes
A committee of four students are to be formed from five boy candidates and six girl candidates. How many ways that this can be done if [6 marks = 1, 2, 3]
there is no restriction.
it contains same number of students from both genders.
it contains at least one student from each gender.
[7 marks = 4, 3]
(a) Find the value for m if 9Cm = 4 × 7Cm – 1.
(b) Prove that .
Fifty-three students’ names are printed on a list. Explain the reason why at least three names begin with the same letter. [2 marks]
Three-digit numbers are constructed using digits 0, 1, 2, 3, 4, 5. Each digit is used at most once. How many such numbers are [6 marks = 2, 2, 2]
constructed?
Even numbers?
Multiples of 5?
A bag contains 17 identical cubes except for their colour, with four coloured orange, six coloured blue and seven coloured white. [6 marks = 2, 2, 2]
(a) How many different arrangements of coloured cubes are possible when three cubes are drawn from the bag and placed in a line? [2 mark]
(b) How many different combinations of coloured cubes are possible when three cubes are drawn from the bag? [2 marks]
(c) Determine the least number of cubes that should be removed from the bag to ensure that the resulting selection contains at least three cubes of one colour. Justify your answer. [2 marks]
[6 marks = 2, 4]
A triangle PQR has sides QP=a, QR=b. Determine the vector where is the midpoint of side.
Two forces are applied to a body. One has magnitude 200 N and acts due south. Another has magnitude 240 N and acts on a bearing of 65º. Draw a diagram to demonstrate this scenario and find the magnitude and resultant of the two forces. [4 marks]
Fifteen dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we pick from these 15 that do not form an equilateral triangle? [3 marks]