Grade 11 maths placement test

Mathematics Department

Grade 11 Placement Test

Name ______________________________

Instructions:

Answer all the questions in the spaces provided.

Show all your working.

Section A ? No calculators allowed Section B ? Calculators allowed

Unless otherwise stated in the question, all numerical answers must be given exactly or to three significant figures.

Questions marked with (HL) show higher level questions.

Formulas - quadratic formula: = !!? !!!!!"

!!

sin rule: !"# ! = !"# ! = !!" !

!

!

!

cos rule: ! = ! + ! - 2 cos or cos = !!!!!!!!

!!"

Section A ? no calculator allowed 1) a) Simplify the following: 3f + 2 ? 4f ? 1

b) Multiply out the bracket: 3(x + 4)

c) Solve the equation:

!!!! = 4

!

.............................. ..............................

d) Make x the subject of the equation: s = v(x ? d)

..............................

2) Evaluate:

!

a) 36!

!

b) 8!

c) 5!! !!

3) Evaluate, with = 16 and = 8.

!

!?!!

.............................. .............................. .............................. .............................. ..............................

4) Simplify:

!

2 ! ? 9! !

..............................

5) Eight students in Mr. O'Neil's Physical Education class did pushups and situps. Their results are shown in the following table.

Student number of pushups (x) number of situps (y)

1 2 3 4 5 6 78 24 18 32 51 35 42 45 25 32 28 38 40 30 52 48 52

The graph below shows the results for the first seven students.

y

60

50

number of 40

situps (y) 30

20

10

O 10 20 30 40 50 60 x number of pushups (x)

a) Plot the results for the eighth student on the graph.

b) If = 34 and = 40, draw a line of best fit on the graph.

c) A student can do 60 pushups. How many situps can the student be expected to do?

........................ situps

6) A is the point (0, 4).

=

3 2

a) Find the coordinates of B.

B = (...............,...............) C is the point (3, 4). BD is a diagonal of the parallelogram ABCD. b) Express as a column vector.

=

1 -3

c) Calculate the length of AE.

..............................

..............................

7) 320 students took a test. The cumulative frequency graph gives information about their marks.

a) Work out an estimate for the interquartile range of their marks. ..............................marks

b) If 75% of the students passed the test, what was the pass mark? ..............................marks

 ................
................

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