Free Printable MATHEMATICS 10 INVENTORY EXAM 2022-2023

1.

What are the next three terms in the sequence 2, 9, 16, 23, 30, . . . ?

a)

37, 43, 50

b)

37, 44, 51

c)

37, 43, 50

d)

37, 44, 50

2.

What is the next term in the sequence $4,\ 4\frac{1}{4},\ 4\frac{1}{2},\ 4\frac{3}{4},\ ...$ ?

a)

$4\frac{4}{4}$

b)

5

c)

$5\frac{1}{4}$

d)

$5\frac{1}{2}$

3.

The next three terms in the sequence 49, 44, 39, 34, 29, … are

(a)

4.

Choose the next two terms of the sequence 1, 4, 9, 16, 25, …

a)

30

b)

36

c)

40

d)

49

5.

Which of the following are the next two terms in the sequence A, D, G, J, …?

a)

L, M

b)

M, N

c)

M, P

d)

O, P

6.

Which of the following are the next two terms of the sequence 0.5, 1.5, 4.5, 13.5, …?

a)

40.5, 80.5

b)

41.5, 123.5

c)

40.5, 121.5

d)

41.5, 120.5

7.

Choose the next two terms of the sequence 1, 8, 27, 64, 125, …

a)

216

b)

343

c)

512

d)

789

8.

What is the next term of the sequence 4, -12, 36, -108, …?

a)

300

b)

-324

c)

324

d)

-325

9.

What is the next term of the sequence $\frac{2}{3},\ \frac{1}{3},\ \frac{1}{6},\ \frac{1}{12},\ ...?$

a)

$\frac{1}{16}$

b)

$\frac{1}{24}$

c)

$\frac{1}{36}$

d)

$\frac{1}{48}$

10.

What is the next term of the sequence J, F, M, A, M, J, J, ...?

a)

A

b)

S

c)

O

d)

N

11.

Given $a_n=7n\ +\ 5,\$ what is its $15^{th}$ term?

a)

100

b)

105

c)

110

d)

115

12.

Given $a_n=2n\ -7,\$ what is its $29^{th}$ term?

a)

51

b)

55

c)

58

d)

61

13.

Given $𝑎_n=12-n,\$ what is its $50^{th}$ term?

a)

-40

b)

-38

c)

-36

d)

-34

14.

Given $a_n=n^2+3,$ find $a_{16}$ .

a)

256

b)

259

c)

302

d)

305

15.

Given $a_n=\ 2n^3,$ find $a_6$ and $a_8$ .

a)

432 and 1020

b)

430 and 1024

c)

432 and 1024

d)

430 and 1020

16.

What are the first five terms of the sequence

a_n=7n\ +\ 5

?

a)

12, 19, 26, 33, 40

b)

12, 19, 25, 33, 40

c)

13, 19, 26, 33, 40

d)

13, 19, 25, 33, 40

17.

Choose the first three terms of the sequence

a_n=2n-7

.

a)

-5

b)

-3

c)

-1

d)

1

18.

What are the third and fourth terms of the sequence

a_n=12-n

? Choose all correct answers.

a)

9

b)

8

c)

7

d)

6

19.

What are the first three terms of the sequence

a_n=n^2+3

?

a)

4, 7, 12

b)

4, 8, 16

c)

4, 9, 16

d)

4, 12, 36

20.

What are the second and third terms of the sequence

a_n=2n^3

?

a)

16 and 54

b)

16 and 18

c)

12 and 54

d)

12 and 18

21.

What is the common difference of the given arithmetic sequence:

–2, 5, 12, 19, 26, . . . ?

a)

–2

b)

3

c)

5

d)

7

22.

Which of the following is the common difference of the given arithmetic sequence:

16, 8, 0, –8, –16, . . . ?

a)

-9

b)

-8

c)

-7

d)

-6

23.

Which of the following sequence is an arithmetic sequence?

a)

5, 12, 21, 32, 45, . . .

b)

3, 6, 12, 24, 48, . . .

c)

–8, –5, –2, 1, 4, . . .

d)

12, 7, 11, 6, 10, 5, . . .

24.

Which of the following sequence is NOT an arithmetic?

a)

25, 13, 1, –11, –23, . . .

b)

9, 15, 21, 27, 33, . . .

c)

–12, –4, 4, 12, 20, 28, . . .

d)

–4, 5, 18, 35, 56, 81, . . .

25.

What is the common difference of the given arithmetic sequence:

–26, –17, –8, 1, 10, 19, . . .?

a)

–9

b)

–10

c)

9

d)

10

26.

Type AS if the given sequence is an arithmetic and NAS if it not an arithmetic sequence:

6, 18, 20, 42, 54, . . .

(a)

27.

Type AS if the given sequence is an arithmetic and NAS if it not an arithmetic sequence:

–13, –7, –2, 2, 5, 7, . . .

(a)

28.

Type AS if the given sequence is an arithmetic and NAS if it not an arithmetic sequence:

8, –7, –22, –37, –52, –67

(a)

29.

What is the common difference of the given arithmetic sequence: –20, –9, 2, 13, 24, 35, . . .?

(a)

30.

What is the common difference of the given arithmetic sequence: 9, –4, –17, –30, –43, –56, . . .?

(a)

31.

Find the common ratio of the geometric sequence
$2,\ \frac{1}{2},\ \frac{1}{8},\ \frac{1}{32},\ ...$

a)

$\frac{1}{3}$

b)

$\frac{1}{12}$

c)

$\frac{1}{16}$

d)

$\frac{1}{4}$

32.

Is the sequence 148, 1488, 14888, 148888, ... a geometric sequence?

a)

Yes, it is a geometric sequence.

b)

No, it is not a geometric sequence.

33.

What is the next term in the geometric sequence

0.75, 3, 12, 48, ... ?

a)

96

b)

144

c)

192

d)

240

34.

In a geometric sequence, the 4th term is -12 and the 5th term is -24. Find the common ratio.

a)

2

b)

-2

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

35.

Find the next three terms of the sequence

31104, 5184, 864, ___, ___, ___.

a)

104, 44, 24

b)

124, 44, 14

c)

144, 24, 4

d)

164, 54, 34

36.

A sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio (r).

a)

Arithmetic Sequence

b)

Geometric Sequence

c)

Harmonic Sequence

d)

Fibonacci Sequence

37.

In the geometric sequence

2, 6, 18, n, 162, ..., what is the value of n?

a)

54

b)

90

c)

24

d)

36

38.

Which of the following is a geometric sequence?

a)

1, 4, 7, 10, ...

b)

1, 2, 6, 24, ...

c)

1, 1, 2, 3, ...

d)

1, 3, 9, 27, ...

39.

which sequence has a common ratio of -2?

a)

4, 8, 16, 32

b)

4, -8, 16, -32

c)

32, 16, 8, 4

d)

-32, 16, -8, 4

40.

If the first term of a geometric sequence is 6 and its common ratio is 2, the next three terms are:

a)

12, 24, 48

b)

8, 10, 12

c)

4, 2, 0

d)

3, 6, 9

41.

Which of the following is a polynomial?

a)

$4x^5-3x^4+2x^3-x^2+\ x\ +\ 2x^{\frac{1}{2}}+\ 6$

b)

$6x^3+2x^2+\ 5\ +\ 3x^{-2}$

c)

$\frac{2}{3}x^5-x^{2\ }+\ 2\sqrt{2}$

d)

$5x^7+3x^6-4\sqrt{x}-\ 7$

42.

If the side of a square is (3x + 4y - z) cm, what is its area?

a)

$\left(9x^{2\ }+\ 16y^2+\ z^2\right)cm^2$

b)

$\left(9x^2+\ 16y^2+\ z^{2\ }+6x\ +\ 8y\ -\ 2z\right)\ cm^2$

c)

$\left(9x^2+\ 16y^2-z^2+24xy\ -\ 8yz\ -\ 6xz\right)cm^2$

d)

$\left(9x^2+16y^2+z^2+\ 24xy\ -\ 8yz-6xz\right)cm^2$

43.

If the sum of (3x⁵ - 6x² + 8x + 5) and (3x⁴ + 7x³ - 7x² - 9x + 12) is subtracted from (3x⁵ + 8x⁴ - 8x + 15), the difference is...

a)

$5x^4+7x^{3\ }-\ 13x^{2\ }-\ 9x\ +\ 32$

b)

$5x^4+\ 7x^{3\ }-\ 13x^{2\ }-\ 7x\ -\ 2$

c)

$5x^4-7x^3+13x^2-7x\ -\ 2$

d)

$5x^4-\ 7x^{3\ }+\ 13x^{2\ }-\ 9x\ +\ 32$

44.

What expression must be subtracted from 3x⁴ - 2x³ + 6x² + 8x - 5 to get x⁴ + 6x³ - x² + 16x - 12?

a)

$2x^{4\ }-\ 6x^{3\ }+\ 10x^{2\ }+\ 8x\ -\ 7$

b)

$2x^{4\ }-\ 8x^{3\ }+\ 7x^{2\ }-\ 8x\ +\ 7$

c)

$2x^{4\ }+\ 6x^{3\ }+\ 13x^{2\ }+\ 16x\ -\ 12$

d)

$2x^{4\ }+\ 6x^{3\ }-\ x^{2\ }+\ 16x\ -\ 12$

45.

Find the surface area of a box whose side is (x + y + 7) cm.

a)

$\left(6x^{2\ }+\ 6y^2+\ 294\right)cm^2$

b)

$\left(6x^{2\ }+\ 6y^{2\ }+\ 6xy\ +\ 42x\ +\ 42\ y\ +\ 294\right)cm^2$

c)

$\left(6x^{2\ }+\ 6y^2+12xy\ +\ 84\ x\ +\ 84\ y\ +\ 294\right)cm^2$

d)

$\left(x^{2\ }+\ y^2+\ 2xy\ +\ 14x\ +\ 14y\ +\ 49\right)cm^2$

46.

Find the product: (m + n - 9)(m + n + 9)

a)

$m^2+n^2-81$

b)

$m^2+2mn+n^{2\ }-\ 81$

c)

$m^2+n^2-18mn\ -\ 81$

d)

$m^2+\ n^2+18mn\ -\ 81$

47.

Solve for x: $x^3+6x^2-13x\ -\ 42=0$

a)

$-7,\ 3,\ 2$

b)

$7,-3,\ 2$

c)

$7,\ 3,\ -2$

d)

$-\ 7,\ \ 3,\ -2$

48.

Determine the degree of the polynomial x⁵ - 2x⁴ - 7x³ + 6.

a)

$3$

b)

$4$

c)

$5$

d)

$6$

49.

The length of a rectangle is (x⁴ + 3X³ - 7X² + 12X - 10) cm and its width is (x³ - 3x² + 15) cm. Find the perimeter of the rectangle.

a)

$\left(x^4\ +\ 8x^{3\ }-23x^{2\ }+\ 24x\ +\ 10\right)cm$

b)

$\left(x^4+8x^3-23x^2+24x\ -10\right)cm$

c)

$\left(2x^4+8x^{3\ }-23x^2+24x\ +\ 10\right)cm$

d)

$\left(2x^4+8x^3-23x^2+24x-10\right)cm$

50.

Determine the difference of (8x³ - 3x² + 4x - 5) and (5x³ + 2x² - 6x + 7).

a)

$3x^3+x^2\ -10x\ -\ 2$

b)

$3x^3+x^2\ +10x\ +\ 2$

c)

$3x^3-5x^2\ +10x\ -12$

d)

$3x^3+5x^2\ +10x\ +12$

51.

The perimeter of a rectangle is (8x³ + 6x² + 4x + 6) cm. Determine the length of the rectangle if its width is (3x² + 7x - 6) cm.

a)

$\left(5x^3+6x^2\ -3x\ +\ 12\right)cm$

b)

$\left(8x^3\ -10x\ +\ 18\right)cm$

c)

$\left(8x^3+18x-18\right)cm$

d)

$\left(8x^3+\ 3x^2-3x\ +\ 12\right)cm$

52.

Which of the following is a factor of x⁴ - 29x² + 100?

a)

$x+10$

b)

$x-4$

c)

$x+4$

d)

$x-5$

53.

If (x + 1) and (x + 3) are two factors of x³ - x² - 17x - 15, find the other one.

a)

$x-5$

b)

$x+5$

c)

$x+1$

d)

$x-12$

54.

Find the cubic polynomial equation with roots -2, 2, and 4.

a)

$x^3+4x^2-4x\ +\ 16\ =\ 0$

b)

$x^3-4x^2-x\ +\ 16\ =0$

c)

$10x^3-x^2-x+16\ =\ 0$

d)

$x^3-4x^2-4x\ +\ 16\ =\ 0$

55.

How many positive real roots does x⁴ - x³ - 11x² + 9x + 18 = 0?

a)

$1$

b)

$2$

c)

$3$

d)

$4$

56.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

57.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

58.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

59.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

60.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

61.

What the remainder after x³ - 2x² - 5x + 6 is divided by x - 4

(a)

62.

What the remainder after x³ - 2x² - 5x + 6 is divided by x - 3

(a)

63.

What the remainder after x³ - 2x² - 5x + 6 is divided by x + 2

(a)

64.

What the remainder after x³ - 2x² - 5x + 6 is divided by x - 1

(a)

65.

What the remainder after x² - x - 6 is divided by x + 3

(a)

66.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

67.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

68.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

69.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

70.

Which of the following is a completely factored polynomial?

a)

f(x)=2x⁴-3x³+8x-6

b)

f(x)=x²(x-1)(x+3)

c)

f(x)=x(x²-16)

d)

f(x)=(2x+1)(x²-3x-18)

71.

Which best describes the multiplicity of a root?

a)

It is the number of times the corresponding factor is repeated

b)

It is the highest degree of the polynomial

c)

It is the number of times x is multiplied by itself

d)

It is the number of x-intercepts on a graph

72.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

73.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

74.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

75.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

76.

Determine the leading coefficient in the function:

f(x) = 4x² + x - 8x³ + 6x⁷ - 1

(a)

77.

What type of polynomial function is f(x) = x?

(a)

78.

Determine the degree of f(x) = 10.

(a)

79.

Circle is a polygon

a)

yes

b)

No

80.

Segment EF is

a)

diameter

b)

radius

c)

chord

d)

sector

81.

Segment DF is

a)

diameter

b)

radius

c)

chord

d)

sector

82.

One-half of the diameter

a)

chord

b)

diameter

c)

radius

d)

sector

83.

Longest chord

a)

chord

b)

diameter

c)

radius

d)

sector

84.

Diameter is a chord.

a)

yes

b)

no

85.

Line GH is

a)

chord

b)

diameter

c)

secant

d)

tangent

86.

Line GE is

a)

chord

b)

diameter

c)

secant

d)

tangent

87.

A segment connecting two points

on the circle

a)

chord

b)

diameter

c)

secant

d)

tangent

88.

What do you call a shaded portion?

a)

tangent

b)

diameter

c)

secant

d)

sector

89.

What is the diameter of the circle?

a)

3

b)

6

c)

9

d)

12

90.

What is the radius of the circle?

a)

2cm

b)

5cm

c)

10cm

d)

20cm

91.

a)

Secant

b)

Diameter

c)

Radius

d)

Chord

92.

A given point directly in the middle of a circle.

a)

Radius

b)

Diameter

c)

Center

d)

Point

93.

The radius is....

a)

a line that crosses through the center and touches each edge

b)

the center point of a circle

c)

a line from the center point to the edge of the circle

d)

an element in science

94.

What does "circumference" mean?

a)

Space a circle takes up

b)

Distance around a circle

c)

Line from one side of a circle to another

d)

Line from center of circle to side

95.

Which of the following names a radius?

a)

segment AC

b)

segment DB

c)

segment AB

d)

segement BC

96.

Which of the following names a diameter?

a)

segment AC

b)

segment DB

c)

segment AB

d)

segment BC

97.

A line segment on the interior of a circle with endpoints on the circle

a)

Radius

b)

Diameter

c)

Secant

d)

Chord

98.

What is CB?

a)

diameter

b)

center

c)

circumference

d)

radius

MATHEMATICS 10 INVENTORY EXAM 2022-2023

Total questions: 98

Worksheet time: 2hrs 54mins

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