Free Printable Midterm Quality Assessment Exam – Math 8 (Converted to MCQ/MSQ)

1.

Which expression is not a monomial?

a)

$-3x^2yz$

b)

$2x^3y$

c)

$\dfrac{x^2}{y}$

d)

$x^2y$

2.

Which monomial is not like term with the monomial $2xy^2$ ?

a)

$-2xy^2$

b)

$2xy^2$

c)

$2x^2y$

d)

$3xy^2$

3.

Among the following, which expression is not a polynomial?

a)

$x+2\sqrt{xy}$

b)

$12x^2y$

c)

$\sqrt{5}$

d)

$x^2y+3xy+1$

4.

The expansion of $(x+1)^2$ is:

a)

$x^2-2x+1$

b)

$x^2+2x+1$

c)

$x^2-3x+2$

d)

$x^2+x+1$

5.

The factorization (expansion) of $x^2-2^2$ is:

a)

$x+2$

b)

$(x+2)^2$

c)

$(x-2)(x+2)$

d)

$(x-2)^2$

6.

In quadrilateral ABCD with angle measures $\widehat{A}=50^\circ,\ \widehat{B}=120^\circ,\ \widehat{C}=120^\circ$ , what is the measure of angle D?

a)

$50^\circ$

b)

$60^\circ$

c)

$70^\circ$

d)

$80^\circ$

7.

Find the false statement.

a)

A rectangle with four right angles is a square.

b)

A rectangle with perpendicular diagonals is a square.

c)

A rectangle whose one diagonal bisects an angle is a square.

d)

A rectangle with two adjacent equal sides is a square.

8.

Choose the correct answer. Which quadrilateral has perpendicular diagonals?

a)

Rhombus

b)

Square

c)

Rectangle

d)

Both A and B

9.

A parallelogram that has one right angle is a:

a)

Rhombus

b)

Rectangle

c)

Right trapezoid

d)

Square

10.

A rectangle with perpendicular diagonals is a:

a)

Right trapezoid

b)

Rhombus

c)

Square

d)

Rectangle

11.

Given polynomials $A=3x^2y+x^2+y^2+xy-3x^2y$ , $B=-3xy$ , and $C=A+B$ . Determine which statements are true.

a)

The degree of $B$ is 2.

b)

After simplification, $A=x^2+xy+y^2$ .

c)

After simplification, $C=x^2+y^2$ .

d)

$C$ evaluated at $x=25, y=26$ equals $-1$ .

e)

$C$ equals $(x-y)^2$ .

12.

Compute the value of $B=x^2-2xy+y^2$ at $x=1$ and $y=2$ .

a)

0

b)

1

c)

2

d)

3

13.

Perform the multiplication: $4x^3y\cdot(-2xy^2)$ .

a)

$-8x^4y^3$

b)

$-8x^3y^2$

c)

$-6x^4y^3$

d)

$8x^4y^3$

14.

Expand and simplify: $3xy\,(5x^2+2xy-4y^2)$ .

a)

$15x^3y+6x^2y^2-12xy^3$

b)

$15x^3y+6xy^2-4y^2$

c)

$5x^3y+2x^2y^2-4xy^2$

d)

$15x^3y-6x^2y^2+12xy^3$

15.

Compute the quotient: $\dfrac{15x^5y^2z}{3x^2z}$ .

a)

$5x^3y^2$

b)

$5x^2y^2z$

c)

$12x^3y$

d)

$3x^3y^2$

16.

Given $M=-2x^2+3xy-5y^2$ and $N=3x^2-2xy+2y^2$ , compute $M+N$ .

a)

$x^2+xy-3y^2$

b)

$x^2+y^2$

c)

$-x^2+xy-3y^2$

d)

$x^2-xy-3y^2$

17.

Compute $(10x^4y^5-15x^3y^4+7x^2y^3):(5xy)$ .

a)

$2x^3y^4-3x^2y^3+\tfrac{7}{5}xy^2$

b)

$2x^3y^4-3xy^3+7xy^2$

c)

$2x^2y^5-3x^2y^3+\tfrac{7}{5}xy^2$

d)

$2x^3y^5-3x^2y^4+\tfrac{7}{5}xy^3$

18.

Simplify $(2x-y)(4x^2+2xy+y^2)-8x^3$ .

a)

$-y^3$

b)

$y^3$

c)

$8x^3-y^3$

d)

$-8x^3-y^3$

19.

In parallelogram ABCD with $AB>BC$ . Let E and K be the midpoints of CD and AB, respectively. Which statement is correct?

a)

Quadrilateral AECK is a parallelogram.

b)

Lines AC, DB, and EK are concurrent.

c)

Neither statement is correct.

d)

Both statements A and B are correct.

20.

A rectangular field has length $5x+3y$ meters and width $5x-3y$ meters. A walkway 3 meters wide is built around the inside of the field; the remaining area is planted with grass. For $x=12$ and $y=3$ , what is the total cost to plant the grass if the price is 50000 đồng per square meter?

a)

$105\,000\,000$ đồng

b)

$126\,000\,000$ đồng

c)

$141\,750\,000$ đồng

d)

$157\,500\,000$ đồng

21.

Which of the following expressions is not a monomial?

a)

$-3x^2yz$

b)

$2x^3y$

c)

x

d)

$x^2 / y$

22.

Select all expressions that are not like terms with the monomial $3x^2y^2$ .

a)

$3xy^2$

b)

$x^3y^2$

c)

$5x^2y^2$

d)

$-2x^2y^2$

23.

Among the following expressions, which one is not a polynomial?

a)

$2x^2y$

b)

x + 2√(xy)

c)

√5

d)

$x^2y + 3xy + 1$

24.

The result of expanding $(x − 2)^2$ is

a)

$x^2 - 2x + 1$

b)

$x^2 + 2x + 1$

c)

$x^2 - 2x + 4$

d)

$x^2 - 4x + 4$

25.

The factorization of $x^2 - 3^2$ is

a)

$(x + 3)^2$

b)

(x − 3)(x + 3)

c)

(x − 9)(x + 9)

d)

$(x - 3)^2$

26.

In quadrilateral ABCD, given Â = 60°, B̂ = 130°, and Ĉ̂ = 120°, what is the measure of angle D̂?

a)

50°

b)

60°

c)

70°

d)

80°

27.

Find the false statement about rectangles.

a)

A rectangle with two adjacent equal sides is a square.

b)

A rectangle whose diagonals are perpendicular is a square.

c)

A rectangle in which a diagonal bisects an angle is a square.

d)

Any rectangle with four right angles is a square.

28.

Choose the correct answer. Which quadrilateral has perpendicular diagonals?

a)

Rhombus

b)

Square

c)

Rectangle

d)

Both A and B

29.

A parallelogram with one right angle is

a)

a square

b)

a rectangle

c)

a right trapezoid

d)

a rhombus

30.

A rectangle with perpendicular diagonals is

a)

a right trapezoid

b)

a rhombus

c)

a square

d)

a rectangle

31.

Given polynomials A = $4x^2y + x^2 + y^2 + xy - 4x^2y$ , B = $-3xy$ , and C = $A + B$ . Statement: The degree of polynomial A is 2. Choose True or False.

a)

True

b)

False

32.

Given polynomials A = $4x^2y + x^2 + y^2 + xy - 4x^2y$ , B = $-3xy$ , and C = A + B. Statement: After simplifying, A = $x^2 + xy + y^2$ . Choose True or False.

a)

True

b)

False

33.

Given polynomials A = $4x^2y + x^2 + y^2 + xy - 4x^2y$ , B = $-3xy$ , and C = A + B. Statement: After simplifying, C = $x^2 + y^2$ . Choose True or False.

a)

True

b)

False

34.

Given polynomials A = $4x^2y + x^2 + y^2 + xy - 4x^2y$ , B = $-3xy$ , and C = $A + B$ . Statement: The value of C at x = 24 and y = 25 is −1. Choose True or False.

a)

True

b)

False

35.

Find the value of $B = x^2 - 2xy + y^2$ at x = 2 and y = 1.

a)

0

b)

1

c)

2

d)

3

36.

Compute $4x^3y \cdot (−2xyz^2)$ . Choose the correct result.

a)

$−8x^4y^2z^2$

b)

$-8x^5yz^2$

c)

$-2x^3y^2z^2$

d)

$8x^4y^2z^2$

37.

Compute 3xy ⋅ (5x^2 + 2xy − 4y^2). Choose the correct result.

a)

$15x^3y + 6x^2y^2 − 12xy^3$

b)

$15x^2y + 6xy^2 − 12y^3$

c)

$5x^3y + 2x^2y^2 − 4xy^3$

d)

$15x^3y + 6xy^2 − 12y^3$

38.

Compute (15x^5y^2z) : (3x^2z). Choose the correct result.

a)

$5x^3y^2$

b)

$5x^2y^2z$

c)

$12x^3y^2z^2$

d)

$3x^3y^2$

39.

Given M = $−2x^2 + 3xy − 5y^2$ and N = $3x^2 − 2xy + 2y^2$ , find M + N.

a)

$x^2 + xy - 3y^2$

b)

$x^2 - xy - 3y^2$

c)

$x^2 + 5xy - 3y^2$

d)

$x^2 + xy + 3y^2$

40.

Compute (10x^4y^5 − 15x^3y^4 + 7x^2y^3) : (5xy). Choose the correct result.

a)

$2x^3y^4 - 3x^2y^3 + (7/5)xy^2$

b)

$2x^3y^4 - 3x^2y^3 + 7xy^2$

c)

$2x^4y^6 - 3x^3y^5 + (7/5)x^2y^4$

d)

$2x^3y^5 - 3x^2y^4 + \frac{7}{5}xy^3$

41.

Simplify $(2x - y)(4x^2 + 2xy + y^2) - 8x^3$ .

a)

$-y^3$

b)

$8x^3 - y^3$

c)

$−8x^3 − y^3$

d)

$4x^3 - y^3$

42.

In parallelogram ABCD with AB > BC, points E and K are the midpoints of CD and AB, respectively. What type of quadrilateral is AECK?

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Trapezoid

43.

In parallelogram ABCD with AB > BC, points E and K are the midpoints of CD and AB, respectively. Which set of lines are concurrent (intersecting at one point)?

a)

AC, BD, EK

b)

AB, CD, EK

c)

AD, BC, EK

d)

AE, CK, BD

44.

A rectangular stadium has length $5x + 3y$ meters and width $5x - 3y$ meters. A 3-meter-wide walkway is built around the inside border of the stadium; the remaining central region is to be planted with grass. With $x = 12$ and $y = 3$ and the cost of planting 1 $m^2$ of grass being 50,000 VND, what is the total cost of planting the grassed area?

a)

50,000,000 VND

b)

120,000,000 VND

c)

141,750,000 VND

d)

283,500,000 VND

45.

Multiply $4x^3y imes -2xyz^2$ and choose the correctly simplified result.

a)

$-8x^4y^2z^2$

b)

$-8x^5yz^2$

c)

$-8x^3y^2z$

d)

$8x^4y^2z^2$

46.

Expand $3xy(5x^2 + 2xy - 4y^2)$ and select the correct expression.

a)

$15x^3y + 6x^2y^2 − 12xy^3$

b)

$15x^2y + 6x^3y^2 − 12xy^2$

c)

$15x^3y + 6xy^2 − 12x^2y^3$

d)

$15x^3y - 6x^2y^2 - 12xy^3$

47.

Simplify $15x^5y^2z ÷ 3x^2z$ .

a)

$5x^3y^2$

b)

$5x^2y^3$

c)

$12x^3y^2z$

d)

$5x^3y^2z^2$

48.

Compute $10x^4y^5 - 15x^3y^4 + 7x^2y^3$ ÷ $5xy$ and choose the correctly simplified result.

a)

$2x^3y^4 - 3x^2y^3 + \frac{7}{5}xy^2$

b)

$2x^4y^5 - 3x^3y^4 + \frac{7}{5}x^2y^3$

c)

$2x^3y^4 - 3x^2y^3 + 7xy^2$

d)

$2x^3y^3 - 3x^2y^2 + \frac{7}{5}xy$

49.

Simplify $(2x - y)(4x^2 + 2xy + y^2) - 8x^3 - y^3 - 8x^2$ and select the correct result.

a)

$-y^3$

b)

0

c)

$−8x^3 − y^3$

d)

$y^3 - 8x^2$

50.

Based on the shown diagram of the quadrilateral, which trio of points are collinear?

a)

E, O, K

b)

A, B, C

c)

D, E, C

d)

N, O, K

51.

According to the worksheet, the length of the grassy area is given by which expression (in meters)?

a)

5x + 3y − 6

b)

5x − 3y − 6

c)

5x + 3y + 6

d)

3x + 5y − 6

52.

According to the worksheet, the width of the grassy area is given by which expression (in meters)?

a)

5x − 3y − 6

b)

5x + 3y − 6

c)

5x − 3y + 6

d)

3x − 5y − 6

53.

Select the correct expanded expression for the area: (5x + 3y − 6)(5x − 3y − 6).

a)

$25x^2 − 60x + 36 − 9y^2$

b)

$25x^2 − 60x − 36 − 9y^2$

c)

$25x^2 + 60x + 36 − 9y^2$

d)

$25x^2 - 60x + 36 + 9y^2$

54.

When x = 12 and y = 3, what is the area of the grassy section (in m^2) computed from the given expression?

a)

2835

b)

2853

c)

2385

d)

2538

55.

What is the total calculated amount of money according to the worksheet?

a)

141,750,000 đồng

b)

141,500,000 đồng

c)

141,075,000 đồng

d)

141,250,000 đồng

Midterm Quality Assessment Exam – Math 8 (Converted to MCQ/MSQ)

Total questions: 55

Worksheet time: 28mins

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