Download Math 10 C: Trigonometry Practice Exam

Math 10C Factors and Products Practice Exam
Math 10 C: Factors and Products Practice Exam
Name: ___________________________
Period:
_____________________
Date: ___________________________
Teacher: _____________________
Show your work in the space beside each question. Diagrams shown are not drawn to scale.
Multiple Choice
1. Write the prime factorization of 4116.
a. 23  3  7 2
b. 2 2  3  7 3
c. 22  3  7 2
d. 2  32  7 3
2. Determine the greatest common factor of 84, 210, and 336.
a. 14
b. 1680
c. 21
d. 42
3. The constant in 3x 2  2 y 2  6 y  3x  7 is
a. 3
b. -7
c. -3
d. 6
4. The simplified form of
a.
b.
c.
d.
15m 4 n3
is
3mn3
5m5 n 6
5m 3 n
5m3n
5m3
5. Simplify 3x 2 (2 xy3 )
a. 6x3 y 3
b. 6x 2 y3
c. 6x 2 y 6
d. 6x3 y 5
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Math 10C Factors and Products Practice Exam
5x2y
6. When simplified
+
4
2
2
4
a. -2x y + 7x y
b. 5x2y2
c. -2x2y + 7xy2
d. -2x2y + 8xy2
8xy2 – 7x2y
–
xy2
equals
7. The expression (5x2 – 5xy – 7y2) – (4x2 + xy – 3y2) is equivalent to
a. x2 – 4xy – 10y2
b. x2 – 6xy – 10y2
c. x2 – 6xy – 4y2
d. x2 – 4xy – 4y2
8. The expression (5y2 – 13y + 17) – (6y2 + 4y – 13) + (y2 – 9y – 9) equals
a. y2 – 17y + 3
b. – y2 – 26y – 7
c. – 26y + 21
d. – 18y – 7
9. Expand and simplify:
a.
b.
c.
d.
10. Expand and simplify:
a.
b.
c.
d.
12 x3 y 4  8 x5 y 3  14 x3 y 5
.
2 x3 y 2
6 y 2  4 x 2 y  7 xy 3
6 xy 2  4 xy  7 xy 3
6 y 2  4 x2 y  7 y3
6 xy 2  4 xy  7 y3
11. Simplify
a.
b.
c.
d.
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Math 10C Factors and Products Practice Exam
12. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to
check.
a. y 2  3 y  12
b. y 2  8 y  15
c. y 2  12 y  5
d. y 2  14 y  3
13. Identify the greatest common factor of the terms in the trinomial 6s 3t 4  12s 4t 2  15s 2t 3
a. 6s 2t 2
b. 3s 2t 3
c. 3s 2t 2
d. 3s 3t 2
14. Factor: 3b 2  15b  18
a. 3(b  2)(b  3)
b. 3(b  2)(b  3)
c. 3(b  1)(b  6)
d. 3(b  1)(b  6)
15. Complete
a.
b.
c.
d.
Use the following Table for the three four questions.
=  x2
= + x2
=+x
= -x
16. Which multiplication sentence does this set of algebra tiles represent?
a.
b.
c.
d.
(2x + 2)(2x – 2)
(2x2 + 2)(2x2 + 2)
(2x2 + 2x)(2x2 + 2x)
(2x + 2)(2x + 2)
3
=+1
= -1
Math 10C Factors and Products Practice Exam
17. Which set of algebra tiles represents
a.
3x2+x+4
b.
c.
d.
18. Which diagram illustrates the product x (x - 1)
a)
b)
c)
d)
19. Expand and simplify (5m – 3n)2
a. 25m2 – 9n2
b. 25m2 – 15mn + 9n2
c. 25m2 – 30mn + 9n2
d. 25m2 + 9n2
20. Which polynomial, written in simplified form, represents the area of this rectangle?
8x – 4y
x + 5y
a.
b.
c.
d.
8x2 – 36xy – 20y2
8x2 + 22xy – 20y2
16x2 +72xy – 40y2
8x2 +36xy – 20y2
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Math 10C Factors and Products Practice Exam
21. Fi
is a perfect square.
a.
b.
c.
d.
9
36
49
196
22. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded
region
3x + 8
x +6
x –3
a.
b.
c.
d.
2x + 6
5x2 + 31x + 66
5x2 + 37x + 30
5x2 + 31x + 30
5x2 + 37x + 66
23. The value of the expression 2x2 + 6xy + y2 when x = -5 and y = 2
a. -6
b. 114
c. -106
d. 14
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Math 10C Factors and Products Practice Exam
Short Answer
Expand the following:
1. (3x+2)(x – 1)
2. (x – y + 1)(2x + y)
Factoring the following algebraically or pictorially. Show all work.
1. 3x2 + 66x – 144
2. 24x2 – 31xy + 10y2
3. 4x2 – 81
4. x4 – x2 – 30
5. 15x2y3 – 10xy2 + 20x3y3
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Math 10C Factors and Products Practice Exam
Written Response
1. The area of a rectangle is given by the expression x2 - 13x - 30.
a) Write this expression for the area of the rectangle as the product of two factors.
b) Determine a simplified expression for the perimeter of this rectangle.
2. Write and simplify an algebraic expression to represent the area of the figure shown below.
3x + 2
2x + 1
4x  3
x
3. Write an expression for the width of this rectangle.
2a
Area = 2a 2+ 12ab
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Math 10C Factors and Products Practice Exam
4. Find and correct the error(s) in this solution of factoring by decomposition.
5. Find a possible integer to replace
so that the trinomial
How many possible solutions are there?
8
can be factored.
Math 10C Factors and Products Practice Exam
Factors and Products Practice Exam Answer Section
MULTIPLE CHOICE
1. B
4116 = 2 2  3  7 3
11. C
12 x3 y 4  8 x5 y 3  14 x3 y 5
2 x3 y 2
2. D
Greatest common factor is 42
Factors of 84 – 1, 2, 3, 4, 6, 7, 12, 14,
21, 28, 42, 84
Factors of 210 – 1, 2, 3, 5, 6, 7, 10, 14,
15, 21, 30, 35, 42, 70, 105, 210
Factors of 336 – 1, 2, 3, 4, 6, 7, 8, 12,
14, 16, 21, 24, 28, 42, 48, 56, 84, 112,
168, 336
3. B
The constant is the term with no
variable.
So the constant is -7
4. D
5. A
6. C
7. C
(5y2 – 13y + 17) – (6y2 + 4y – 13) + (y2 – 9y – 9)
(5y2 – 13y + 17) + (-6y2 - 4y + 13) + (y2 – 9y – 9)
5y2 – 13y + 17 - 6y2 - 4y + 13 + y2 – 9y – 9
-26y + 21
8. C
(5x2 – 5xy – 7y2) – (4x2 + xy – 3y2)
(5x2 – 5xy – 7y2) + (-4x2 - xy + 3y2)
x2 – 6xy – 4y2
9. A
p2 – 7p + 3p – 21 = p2 – 4p – 21
10. A
28 – 4r – 7r + r2 = 28 – 11r + r2
9
12 x3 y 4 8x5 y3 14 x3 y 5
 3 2  3 2 3 2
2x y
2x y
2x y
2
2
3
 6 y  4x y  7 y
12. B
y2+8y+15 3x5= 15
3+5 = 8
13. C
14. D
-3(b2-5b-6)
-3(b + 1)(b – 6)
15. B
16. D
17. C
18. B
19. C
(5m – 3n)2 =(5m – 3n)(5m – 3n)
= 25m2 – 15mn – 15mn + 9n2
= 25m2 – 30mn + 9n2
20. D
(8x – 4y)(x+5y)
= 8x2 + 40xy – 4xy – 20y2
= 8x2 + 36xy – 20y2
21. C
If 2 first term last term = middle
term, then it is a perfect square.
2 first term 9 = 42
2 3
6
first term =42
first term = 42
first term = 7
Therefore first term is 49
Math 10C Factors and Products Practice Exam
23. A
2(-5)2 + 6(-5)(2) + (2)2
22. A
(3x  8)(2 x  6)  ( x  6)( x  3)
(6 x 2  18 x  16 x  48)  ( x 2  3 x  6 x  18)
(6 x 2  34 x  48)  ( x 2  3x  18)
(6 x 2  34 x  48)  ( x 2  3x  18)
5 x 2  31x  66
SHORT ANSWER
Expand Solutions:
1. 3x2 – x – 2
2. 2x2 – xy – y2 + 2x + y
(x – y + 1)(2x + y)
= 2x2 + xy – 2xy – y2 + 2x + y
= 2x2 – xy – y2 + 2x + y
Factor Solutions:
1. 3(x + 24)(x - 2)
3(x2 + 22x – 48)
__x__ = -48
__+__ = 22
24, and -2
3(x – 24)(x + 2)
2. (8x – 5y)(3x – 2)
__x__ = 240
__+__ = -31
-15 and -16
24x2 – 15xy – 16xy + 10y2
3x(8x – 5y) – 2(8x – 5y)
(8x – 5y)(3x – 2)
3. (2x – 9)(2x + 9)
4. (x2 – 6)(x2 + 5)
__x__ = -30
__+__ = -1
-6 and 5
5. 5xy2(3xy – 2 + 4x2y)
10
= 2(25) – 60 + 4
= 50 – 60 + 4 = -6
Math 10C Factors and Products Practice Exam
WRITTEN RESPONSE
1. a) factor to find the dimensions:
(x – 15)(x + 2)
b) perimeter = l + l + w + w
= (x – 15) + (x – 15) + (x + 2) + (x + 2)
= 4x – 26
OR
perimeter = 2l + 2w
= 2(x – 15)+ 2(x + 2)
= 2x – 30 + 2x + 4
= 4x – 26
2. 8x2 + 3x + 2
3x + 2
2x + 1
4x  3
(3x+2) – x = 2x+ 2
(4x – 3) – (2x + 1) = 2x - 4
x
(3x + 2)(2x+1) + (x)(2x – 4)
6x2 + 3x + 4x + 2 + 2x2 – 4x
8x2 + 3x + 2
OR
(x)(4x – 3) + (2x + 2)(2x + 1)
4x2 – 3x + 4x2 + 2x + 4x + 2
8x2 + 3x + 2
OR
(3x + 2)(4x – 3) – (2x+2)(2x – 4)
12x2 – 9x + 8x – 6 – (4x2 – 8x + 4x – 8)
12x2 – 9x + 8x – 6 – 4x2 + 8x – 4x + 8
8x2 + 3x + 2
3. Width is a + 6b
2a 2  12ab 2a 2 12ab

=
= a  6b
2a
2a
2a
4.
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Math 10C Factors and Products Practice Exam
5.
__ x __ = □
__ + __ = 1
Ways to Sum to 1:
0 and 1
-1 and 2
-2 and 3
-3 and 4
-4 and 5
Product:
0
-2
-6
-12
-20 etc
□
Possible solutions for : 0, 2, -6, - 12, etc.
Total Number of solutions = infinite
12