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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