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Oct. 8, 2013
Math 10 Pre IB – Test #2B
NAME:_____________________________
Ch. 1 and 2: Number Sets, Venn Diagrams, Expanding & Factoring
Part A: Multiple Choice – Circle the letter of the correct answer. (10 pts)
1. A' B' is the same as:
(a) A' B
(b) A  B '
(c) A' B'
(d) ( A  B)'
2. Which of the following statements is FALSE?
(a)  16.33  Q
1
(b)   Q
3
(c) Q  Z
(d) N  Z
3. The diagrams below represent a class of children. G is the set of girls and F is the set of children who
like football. Decide which diagram has shading that represents the set of boys that dislike football.
(a)
(b)
(c)
(d)
4. Sixty students were surveyed about which sports they like to watch on TV. The results are shown in
the Venn diagram.
How many students watch football
or hockey?
(a)13
(b) 37
(c) 43
(d) 56
5. Which number set is represented by:
(a) x | 5  x  0
(b) x | 5  x  0
(c) x | 5  x  0, x  Z 
(d) x | 5  x  0, x  Z 
6. Which multiplication sentence does this set of algebra tiles
represent?
(a) (2 x 2  2)( 2 x 2  2)
(b) (2 x  2)( 2 x  2)
(c) (2 x 2  2 x)( 2 x 2  2 x)
(d) (2 x  2)( 2 x  2)
7. Expand and simplify: (6 p  3)(6 p  7)  (7 p  4)( p  2)
(a) 29 p 2  6 p  13
(b) 29 p 2  42 p  13 (c) 29 p 2  42 p  29 (d) 29 p 2  6 p  29
8. 5 x 4 y 2  6 x 3 y 2 can simplify to:
(b) 5 x 4 y 2  6 x 3 y 2
(a) 11x 7 y 2
(c) 30 x 7 y 4
(d) x 3 y 2 (5 x  6)
9. Find an integer to replace □ so that this trinomial is a perfect square:
(a) 18
(b) 72
(c) 648
64x2 – □ xy + 81y2
(d) 144
10. 25 x 2  9 y 2 can be factored into:
(a) (5 x  3 y )(5 x  3 y )
(b) (25 x 2  9 y 2 ) 2
(c) (5 x  3 y )(5 x  3 y )
Part B: Answer the following questions in the spaces provided.
1. (3 pts) In a survey of a high school classroom of 30
people, it was determined that 18 people like vanilla ice
cream, and 17 people like chocolate ice cream. 6 people
didn’t like either flavour.
(a) Draw and label a Venn diagram to model this situation.
(b) How many students like either vanilla or chocolate ice
cream?
(d) cannot be factored
2. (7 pts) Given:
U  x 1  x  15, x  Z 
A = {even numbers}
and A and B are subsets of U such that:
B = {factors of 12}
(a) Complete the Venn diagram to show the relationship between the sets U, A, and B.
A
B
(b) Find:
(i) A  B
______________________________
(ii) A  B
______________________________

(iii)  A  B 
______________________________
(iv) n A  B
______________________________
(c) Shade the part of the diagram that represents  A
' B' .
3. (7 pts) All the members of a group of 40 teenagers belong to at least one club.
There are 3 clubs, chess, drama and art.






11 of the teenagers belong to only the art club.
6 of the teenagers belong to all 3 clubs.
3 of the teenagers belong to the chess and art clubs but
not to the drama club.
28 of the teenagers belong to the art club.
3 of the teenagers belong only to the chess club.
5 of the teenagers belong only to the drama club.
(a) How many of the group do chess and drama but not art?
(b) How many of the group belong to the chess club?
(c) How many of the group participate in at least 2 clubs?
4. (10 pts) Expand and simplify each of the following:
(a) ( x  5)( x  8)
(b) 3x(4 x 2  2 x  7)
(c) (3x  5)( 2 x  4)
(d) ( x  5) 2
(e) ( x  3)( x  2) 2
(f) ( x  8)( x  2)  (4 x  1)( 2 x  3)
(g) (3x  2) 4
4. (12 pts) Factorise completely:
(a) 25a 2  b 2
(b) x 2  x  56
(c) 4 x 2  11x  6
(d) 4a 2  20a  24
(e) 32 x 3  18 x 2
(f) ( x  3) 2  5( x  3)
(g) 10 x  25  x 2
(h) 15k 3  20k 2  3k  4