Free Printable 7 Topic Assessment Form A

1.

Select all the expressions that could represent the volume of a box, which is a fourth degree polynomial in variables x and y.

a)

3x²y² + 6x² – 7xy – 14x

b)

10xy + 12x + 2xy² – y² – 5y – 6

c)

–6 + 7xy + 9x² + 2x³y

d)

2x³y + 5x²y – xy – 6y

e)

3x⁴y⁴ – 3x²y + 17xy² – 10y

2.

Emily collects and trades rocks. She starts with 8x² rocks, for some number x, and then buys 7x⁴. She then trades away x⁵, then gives away 9x, and finally sells another 5 rocks. Write an expression for the number of rocks Emily now has in standard form.

a)

–9x + 8x² + 7x⁴ – 5 – x⁵

b)

8x² – 5 + 7x⁴ – 9x – x⁵

c)

–x⁵ + 7x⁴ + 8x² – 9x – 5

d)

–5 – 9x + 8x² + 7x⁴ – x⁵

3.

Simplify (5x³ + 7x – 8) + (2x³ – 5x² – x).

a)

7x³ – 5x² + 6x – 8

b)

3x³ + 5x² + 8x – 8

c)

7x³ + 5x² + 6x – 8

d)

7x³ – 5x² + 8x – 8

4.

Simplify (–7x + 5) – (2x² – 8x + 6).

a)

–2x² + x – 1

b)

–9x² + 8x – 1

c)

–5x² + 8x – 1

d)

–2x² – 15x – 1

5.

The product of –8y²(2y² + 7y – 5) is

a)

–16y⁴ – 56y³ + 40y².

b)

16y⁴ + 56y³ – 40y².

c)

–6y⁴ – y³ – 13y².

6.

What is the product of (6x² + 8)(3x² – 5x + 7)?

a)

A. 18x⁴ – 30x³ + 66x² – 40x + 56

b)

B. 18x⁴ – 30x³ + 42x² – 40x + 56

c)

C. 18x⁴ – 30x³ + 66x² – 5x + 56

d)

D. 18x⁴ – 30x³ + 66x² – 5x + 7

7.

Find the product of (1.5w + 4)(w + 4).

a)

1.5w² + 10w + 16

b)

1.5w² + 8w + 16

c)

1.5w² + 4w + 16

d)

1.5w² + 8w + 8

8.

Find the product of (6y – 2)².

a)

36y² – 24y + 4

b)

36y² + 24y – 4

c)

36y² + 4

d)

12y² – 16y + 4

9.

The product of (4x – 7)(4x + 7) is

a)

16x² – 21x – 49.

b)

16x² – 21x + 49.

c)

16x² – 49.

d)

16x² – 7.

10.

A square picture has a 1-in. frame around it. If the area of the frame alone is 36 in.², what is the area of the picture?

a)

64

b)

49

c)

36

d)

81

11.

What is the greatest common factor of the terms of the polynomial $-16y^4 + 12y^2 - 4y$ ?

a)

–4y

b)

$-2y^2$

c)

4y

d)

–8y

12.

The product of the areas of two rectangular rugs is 84 m^2. If each of the dimensions is a prime number, what are the four dimensions?

a)

2, 3, 3, 7

b)

3, 3, 4, 7

c)

2, 2, 3, 3

d)

2, 2, 3, 7

13.

Factor out the greatest common factor from the terms of the polynomial $2x^3 – 5x^2 + 25$ .

a)

$x^2(2x – 5) + 25$

b)

Already fully factored

c)

$5x(x^2 – x + 5)$

d)

$2x^3 – 5x(x^2 – 5)$

14.

Teslim is designing a cover for a book. He wants to have a rectangular grid with $x^2 - 10x + 21$ squares in it, for some positive whole number x. What are the possible side lengths for the grid?

a)

(x – 3) and (x – 7)

b)

(x – 3) and (x + 7)

c)

No whole number side lengths

d)

(x + 3) and (x + 7)

15.

The floor area of a rectangular room is represented by $x^2 + 3xy - 10y^2$ . What could the length and width be?

a)

(x + 2y) and (x – 5y)

b)

(x – 2y) and (x + 5y)

c)

x(x + 3y) and (3x – 10y)

d)

cannot be determined

16.

Factor by grouping: 6y^2 + 19y + 15.

a)

(2y + 3)(3y + 5)

b)

(2y + 5)(3y + 3)

c)

(6y + 3)(y + 5)

d)

(2y + 1)(3y + 15)

17.

The volume of a box in the shape of a rectangular prism is 15y^2 + 10y – 40. What could be the dimensions of the box?

a)

5, (y + 4) and (3y – 2)

b)

(5y – 10) and (3y + 4)

c)

5, (y – 2) and (3y + 4)

d)

5, (y + 2) and (3y – 4)

18.

The expression x^2 – 12x + 36 represents the area of a rectangular chalkboard. What is the factored form of the expression? If each factor represents the height and width of the chalkboard, what is the most specific description of its shape?

a)

$(x – 6)^2$ ; square

b)

(x – 6)(x + 6); rectangle

c)

$(x + 6)^2$ ; square

d)

$(x – 12)^2$ ; square

19.

Factor the perfect square trinomial 16y^2 – 24y + 9.

a)

$(8y – 3)^2$

b)

$(4y – 3)^2$

c)

(2y – 3)(8y – 3)

d)

(y – 3)(16y – 3)

20.

Factor the expression $25x^2 - 16$ .

a)

(5x + 4)(5x – 4)

b)

(25x + 16)(25x – 16)

c)

(5x + 16)(5x – 16)

d)

(25x + 4)(x – 4)

21.

A cone with height h and radius r has volume V = $(1/3)\pi r^2 h$ . If h is 9 in., and V is equal to $3\pi x^2 + 42\pi x + 147\pi$ in.^3, what is the cone’s radius r in terms of x?

a)

x + 7

b)

x + 3

c)

x - 7

d)

$x^2 + 7$

7 Topic Assessment Form A

Total questions: 21

Worksheet time: 11mins

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