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Math 10 NRF
Exam Review
Mrs. DesMeules
Chapter 3 Exam Review
For questions 1 and 2, choose the correct answer: A, B, C, or D
1. The greatest common factor of 36, 20, and 40 is:
A. 360
B. 4
C. 2
D. 1
2. Which polynomial is a perfect square trinomial?
A. 9x2 + 49
B. 9x2 + 16x + 49
2
C. 9x – 49
D. 9x2 –42x + 49
3. a) Determine the cube root of 5832.
b) Determine the square root of 256.
c) Determine the least common multiple of the roots in parts a and b.
4. a) Complete this diagram by sketching
the tiles that represent the product.
Write the multiplication sentence
the diagram represents.
b) Complete this rectangle diagram.
Write the multiplication sentence
the diagram represents.
c) How can you check that the multiplication sentences in parts a and b are correct?
5. Expand and simplify.
a) (4r + 6)(3r – 6)
b) (2x – y)(x2 – 6xy – y2)
c) (3a + 2b)(a – b) – (2a + b)(2a – 3b)
6. Factor each polynomial. Verify by multiplying the factors.
a) 8a2b – 4ab2
b) 8h2 – 18k2
c) 16f2 + 8f + 1
d) 6m2 – m – 2
2
2
e) 10x – 29xy + 10y f) r2 – 2r – 15
7. Find and correct the error in this factorization: 3a2 – 7a – 6 = (3a – 2)(a + 3)
8. A right rectangular prism has dimensions r by 3r + 1 by 2r + 2.
a) Write and simplify a polynomial for the surface area
of the prism.
b) The prism is cut in half along the broken line shown.
Write and simplify a polynomial for the surface area
of each smaller prism.
c) Factor each trinomial in parts a and b.
Why is the surface area in part a not two times
the surface area in part b?
Chapter 4 Exam Review
For questions 1 and 2, choose the correct answer: A, B, C, or D
1. Which length is an irrational number?
A.
B.
C.
D.
2. Which expression is equal to
A.
a 1b
ab 1
B.
ab 1
a 1b
a2
?
b2
a 2b
C. 2
ab
D.
ab 2
a 2b
3. a) Which number has been incorrectly located?
Identify the number and mark its correct location.
b) Where would you locate
3
30 ? Justify your answer.
4. Evaluate without using a calculator. Explain what you did.
a)
4
38
b)
3
c) 0.012
1000
2
1
1
1
 

 
5. A student simplified  3c 2 d 2   2d 2 c 2  as follows:

 

2
1
 2 0  32  1 0  32 
 2 12   2  12 
 3c d   2d c  =  3 c d  2 d c 




 

3
3
 
 

=  9d 2  2c 2 



= 18cd 3
18c
= 3
d
Identify the errors in this solution, then write a correct solution.
6. Rewrite 8

1
3
as a radical, then evaluate the radical.
7. Simplify. Which exponent laws did you use?
a)
 1 34 
x y 
 x 3 y 2 




4
1
3
2
b) ( x 2 x 2 y 1 ) 2 ( y 6 ) 3
3
d)  
4
 
4
Chapter 5 Exam Review
For questions 1 and 2, choose the correct answer: A, B, C, or D
1. How many of these equations represent a linear function?
y = –5x + 8
g(x) = 2
2
y=x –5
x = –1
A. 1
B. 2
C. 3
D. 4
2. For the function f(x) = 2x – 3, what is the value of x when f(x) = 15?
A. 27
B. 6
C. 9
D. –9
3. For each relation represented below:
i) State whether it is a function and how you know.
ii) If the relation is a function:
State its domain and range.
Represent the function a different way.
State whether it is a linear function and how you know.
iii) If the relation is a linear function:
Identify the dependent and independent variables.
Determine the rate of change.
a)
b)
a
b
1
3
3
6
5
9
7
12
c) {(0, 2), (2, 4), (4, 6), (0, –2), (2, –4), (4, –6)}
4. This table of values shows how the profit from the sale of T-shirts relates to
the number of T-shirts sold.
Number of
T-Shirts Sold, n
0
1
2
3
4
5
6
Profit ($), P
–20
–15
–10
–5
0
5
10
a) What does a negative profit indicate?
b) Graph the data. Did you connect the points? Explain.
c) Determine the domain and range. Could you extend the graph? Identify and explain any
restrictions on the domain and range.
d) Determine the rate of change for this function. What does it represent?
e) Suppose the table is extended.
i) What is the profit on the sale of 64 T-shirts?
ii) How many T-shirts must be sold to make a profit of $325?
Chapter 6 Exam Review
For questions 1 and 2, choose the correct answer: A, B, C, or D
1. What is the slope of this line?
A. –2
B. 
1
2
C.
1
2
D. 2
2. Which equation is not equivalent to the others?
3
A. y – 8 =  (x + 8)
2
3
B. y =  x + 4
2
C. 3x + 2y – 8 = 0
3
D. y + 2 =  (x – 4)
2
3. a) Determine the slope of each line.
i) a line that passes through A(–4, 7) and B(6, 3)
ii) a line described by the equation 5x – 2y + 7 = 0
b) Are the lines in part a parallel, perpendicular, or neither? Justify your answer.
4. Graph each equation. Describe the strategies you used.
3
a) y – 2 = –2(x + 3) b) 2x – 5y + 10 = 0
c) y = x – 2
5
5. a) Write an equation for each graph. Describe your strategy.
i)
ii)
b) Write each equation in part a in general form.
c) Use a point on the line to verify each equation.
6. a) Write an equation for the line that passes through E(4, –3) and is parallel to the line
5
y + 1 = (x – 4). Write the equation in general form.
7
b) Write an equation for a line with x-intercept –3 and y-intercept 5.
Explain your strategy.
7. Josie started a part-time job when she was 16. Each month, she put a fixed amount into her
savings account. After 4 months, Josie had $770 in her savings account. After one year,
she had $1450 in her savings account.
a) Write an equation to describe this relation. Write your equation in slope-intercept form.
b) How much money will Josie have after 2 years?
c) How long will it be until Josie has $4000 in her savings account?
Chapter 6 extended Review: Distance of a line and Midpoint
8. . Determine th coordinates of the midpoint, M, of line segment CD.
9. Determine the coordinates of the midpoint of the line segment with each pair of
endpoints.
a) A (7, 4), B(1, 3)
b) C(-3, 4), D(6, 0)
c) E (-5, 0), F(8, -3)
d) G(0,0), H(-4, 5)
10. Calculate the length of the line segment VW
11. Determine the length of the line segment with each pair of endpoints.
a) J(5, 9), K(5, -4)
b) M(-2,7), N(6, 7)
c) P(-4, -3), Q(-4, 11)
d) R(-1, 0), S(8, 0)
Chapter 7 Exam Review
For questions 1 and 2, choose the correct answer: A, B, C, or D
1. Which statement below is false for this linear system?
3x – 4y = –9.5

y

2 x   2
2
A. If you multiply equation  by 8, then add the new equation to equation ,
you can eliminate y.
B. The system has one solution because the slopes of the lines are different.
C. If you replace equation  with 4x – y = –4, the new system will have the same solution
as the original system.
D. The solution of the linear system is: (2, –0.5)
2. Which system has exactly one solution?
A. y = –4x – 2
y = –4x + 5
1
1
C. x  y  2
3
2
1
5
x y
6
2
B. 6x – 3y = –1
–2x + y = 4
`
D. y = 3x – 2
y = 3x + 2
3. Solve each linear system. Explain what you did for part c.
a) –3x – 6y = 9
b) 3x – 4y = 13
2x + 2y = –4
5x + 3y = 12
c)
1
1
5
x y
2
3
12
5
1
1
x y
6
2
6
4. Given the linear equation 4x – 2y = –4, write another linear equation that will form a linear
system with each number of solutions. Explain what you did.
a) exactly one solution
b) no solution
c) infinite solutions
5. a) Write a linear system to model this situation:
In Claire’s school, 41 of the 80 grade 10 students were not born in Canada. Sixty
percent of the boys and 40% of the girls in grade 10 were not born in Canada.
b) Solve this related problem: How many boys and how many girls are in grade 10?
Explain what you did.
6. A gift shop sold hand-made moccasins. One order of 4 pairs of children’s moccasins and
3 pairs of women’s moccasins cost $244.65. Another order of 2 pairs of children’s
moccasins and 4 pairs of women’s moccasins cost $229.70.
a) Write a linear system to model this situation.
b) Solve this related problem: What is the cost for a pair of each type of moccasin?