Free Printable GRADE 10 MATH QUIZ

1.

State your complete name in capital letters. (Ex. KHANAKAN, BANDAR A.)

4 lines

2.

A sequence consists of the following terms, $a_{1\ }=\ 1,\ a_{2\ }=\ 3,\ a_{3\ }=\ 5$ , and it follows a general form $a_{n\ }=\ 2n-1$ . What is the 4th term?

a)

6

b)

7

c)

8

d)

9

3.

Given that the 74th term of an arithmetic sequence is 80, and the 84th term is 110, what is the 10th term?

a)

-142

b)

-112

c)

36

d)

58

4.

Which of the following is a key characteristic that helps differentiate a geometric sequence from an arithmetic sequence?

a)

The first term is always equal to one.

b)

The common ratio between terms is constant.

c)

The common difference between terms is constant.

d)

The terms of the sequence do not follow any specific pattern.

5.

A runner is training for a marathon. During the first week, he ran 10 miles, and then each succeeding week, he increase his distance by 2 miles. If he continues this pattern for 8 weeks, how many miles will he has to run during these 8 weeks?

a)

24 miles

b)

64 miles

c)

106 miles

d)

136 miles

6.

Which of the following statements is/are true given that $a_{1\ }=\ 2,\ d=2,$ and r = 1.5?
I. The 7th term of the arithmetic sequence is greater than the 6th term of the geometric sequence.
II. The 7th term of the arithmetic sequence is equal to the 6th term of the geometric sequence.
III. The 7th term of the arithmetic sequence is less than the 6th term of the geometric sequence.

a)

I only

b)

II only

c)

III only

d)

I and II only

7.

Which of the following is an arithmetic sequence?

a)

1, 1, 1, 1, 1, 1, 1, ...

b)

1, 1, 2, 3, 5, 8, 13, ...

c)

2, 4, 8, 16, 32, 64, ...

d)

3, 6, 9, 12, 16, 20, 24, ...

8.

What is the sum of the first 20 terms of the arithmetic series if the first term is 3 and the 20th term is 79?

a)

760

b)

790

c)

820

d)

850

9.

Which of the following are the two geometric means between 13.5 and 364.5?

a)

25.5 and 94.5

b)

30.5 and 112.5

c)

40.5 and 121.5

d)

42.5 and 134.5

10.

Which of the following illustrates a geometric sequence?

a)

1, 2, 3, 4, 5, 6

b)

2, 4, 6, 8, 10, 12

c)

2, 6, 18, 54, 162, 486

d)

3, 6, 18, 72, 360, 2160

11.

What is f(2) if $f\left(x\right)\ =\ x^{2\ }-4x+3$ ?

a)

-3

b)

-1

c)

0

d)

1

12.

Which of the following is an example of a polynomial function?

a)

$y\ =\sqrt{\ x\ }+2$

b)

$\frac{x}{x^2+2x\ -3}=y$

c)

$e^{x\ }=7$

d)

$\frac{1}{2}x^{2\ }-3x+1=0$

13.

Given that (x-c) is a factor of f(x), which of the following statements is/are NOT true?
I. (x-c) is divisible by f(x)
II. f(x) is divisible by (x-c).
III. The remainder when f(x) is divided by x-c is 0.

a)

I only

b)

II only

c)

III only

d)

II and III only

14.

When dividing a polynomial using synthetic division, which of the following is TRUE about the divisor?

a)

It must be a quadratic polynomial.

b)

It can be a binomial or a trinomial.

c)

It must be a binomial of the form (x-a).

d)

Synthetic division cannot be used for polynomial division.

15.

Which of the following sequence is an example of a Fibonacci sequence?

a)

1, 2, 4, 8, 16, 32,

b)

0, 1, 1, 2, 3, 5

c)

3, 6, 9, 12, 15, 18

d)

2, 4, 8, 16, 31, 32

16.

Which of the following rules should be used to determine the nth term of the sequence 3, 9, 27, ... $a_n$

a)

$3n^3$

b)

$3^n$

c)

$3\ +\left(n-1\right)^3$

d)

$3+\left(n+1\right)^3$

17.

Which statement best describes the rational root theorem?
The rational root theorem states that ---.

a)

all roots of a polynomial must be a rational number.

b)

a polynomial with integer coefficients has roots that are either integers or irrational numbers.

c)

a polynomial with integer coefficients has roots that are either integers or complex conjugates.

d)

if a polynomial has a rational root, it must be a ratio of the factors of the constant and the leading coefficient.

18.

Which of the following is a factor of $x^{2\ }+5x-36?$

a)

x+4

b)

x+9

c)

x-9

d)

x-12

19.

If $x^2+8x-20$ is divided by x-2, what is the quotient?

a)

x+6

b)

x+8

c)

x+10

d)

x+12

20.

In 2021, a town had a population of 5,000 residents. Assuming a consistent 20% increase in population every 5 years, what would be the projected population of the town in the year 2041?

a)

10, 368

b)

15, 136

c)

20, 284

d)

25, 186

21.

To create a sinking fund that will provide capital to purchase some new equipment, a company deposits Php 500,000 into an account on January 1 every year for 5 years. If the account earns 12% interest, compounded annually, how much is the sinking fund immediately after the 5th deposit is made?

a)

Php 1,426,762

b)

Php 2,672,234

c)

Php 3,176,424

d)

Php 4,156,482

22.

The area of the circle can be solved using the formula $A\ =\ \pi\ r^2$ . Given that the radius of the circle is 4 in, and a central angle was formed which is a right angle, what is the area of the shaded region?

a)

$16\pi\ in^2$

b)

$8\pi\ in^2$

c)

$4\pi\ in^2$

d)

$2\pi\ in^2$

23.

Two chords, AB and CD of the same circle are equidistant from its center. Which of the following statements is true?

a)

The chords are equal in length.

b)

The chords have a common endpoint.

c)

The midpoint of the chord divides the radius into two equal parts.

d)

The distance of the center from the end point of the chord is half the length of the chord.

24.

The number of tablets sold by a shop can be modeled by the expression N(t) = 7t+25 and the price of the table is modeled by an expression $P\left(t\right)\ =\ 3t^{2\ }+3t\ +36$ where t is the number of months in a year. If we use this model, what is the total amount of revenue generated by the shop at the end of the year?

a)

49,356

b)

54,936

c)

58,640

d)

59,642

25.

What is the value of A in the polynomial $f\left(x\right)\ =\ x^3-Ax\ +8$ if -2 is one of its zeroes?

a)

0

b)

1

c)

2

d)

3

26.

Which of the following statements is true about the central angle and its intercepted arc?

a)

The degree measure of the central angle is always half of the degree of the degree measure of its intercepted arc.

b)

The measure of the intercepted arc is directly proportional to the measure of the central angle.

c)

The measure of the intercepted arc is always double the measure of the central angle.

d)

The arc length is equal to the product of the central angle and its radius.

27.

A carpenter will construct a room with a length represented by (a+4) meters, its width is represented by (2a-3) meters, and its height by (3a-10) meters. What is the value of a if the volume of the room is 80 cubic meters?

a)

2

b)

4

c)

6

d)

10

28.

The length of chord AB of a circle is 12 cm. If the diameter of the circle is 20 cm, what is the distance of chord AB from the center of the circle?

a)

4 cm

b)

8 cm

c)

12 cm

d)

16 cm

29.

N and M are points in the number line. Which of the following is the correct way of finding the distance between N and M?

a)

N - M

b)

M + N

c)

|N - M|

d)

|M+N|

30.

Suppose that one endpoint of segment AB is A(20,19) and its midpoint is M(17, -1). What is AB?

a)

$6\ \sqrt{\ 201}$

b)

$4\sqrt{\ 137}$

c)

$3\sqrt{\ 329}$

d)

$2\ \sqrt{\ 409}$

31.

What is the standard form of the equation of the circle $x^2+y^{2\ }-4x-6y-12\ =0$ ?

a)

$\left(x-2\right)^2+\left(y-3\right)^2=4^2$

b)

$\left(x-2\right)^2+\left(y-3\right)^2=5^2$

c)

$\left(x+2\right)^2+\left(y+3\right)^2=4^2$

d)

$\left(x+2\right)^2+\left(y+3\right)^2=5^2$

32.

The circle is tangent to both the x- and the y-axes. If the radius is 4 units and is located at the fourth quadrant, what is the center of the circle?

a)

(4,4)

b)

(-4,4)

c)

(-4,-4)

d)

(4,-4)

33.

What is the midpoint of A(2,6) and B(8, -4)?

a)

(5,1)

b)

(4,2)

c)

(3,1)

d)

(2,5)

34.

Which of the following represents the center-raidus form of the equation of the circle given the center (h,k) and radius r?

a)

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$

b)

$\left(x+h\right)^2+\left(y+k\right)^2=r^2$

c)

$\left(x-h\right)^2+\left(y+k\right)^2=r^2$

d)

$\left(x+h\right)^2+\left(y-k\right)^2=r^2$

35.

Which of the following expressions correctly represents the permutation of selecting 3 objects from a set of 6 distinct objects?

a)

P(6,3)

b)

P(3,6)

c)

6!/3!

d)

3!/6!

36.

Jason, Jeffrey and Karoll are to be seated on a circular table. In how many ways can they be seated?

a)

2

b)

3

c)

6

d)

9

37.

Which of the following expressions is best to use in finding the number of different arrangements, each consisting of four different letters, can be formed from the letters of the word "personal" if each arrangement is to begin and end with a vowel?

a)

3 x 5 x 4 x 2

b)

3 x 6 x 5 x 2

c)

2(3 x 6 x 5 x 1)

d)

2(3 x 5 x 4 x 2)

38.

How many committees of five can be formed from eight grade 8 and four grade 7 students if each committee consists of three grade 8 and 2 grade 7 students?

a)

164

b)

286

c)

336

d)

462

39.

Which of the following is the same as $1\cdot2\cdot3\cdot4\cdot...\cdot\left(n-1\right)\cdot n?$

a)

n!

b)

(n-1)!

c)

$\frac{n}{\left(n-r\right)!}$

d)

$\frac{n}{\left(n-r\right)!r!}$

40.

A lock combination can be opened using a series of three letters from the alphabet and three digits from 0 to 9. If repetition of the letters in the combination is not allowed, in how many ways can a combination be changed?

a)

260

b)

720

c)

1,260

d)

11,232,000

41.

What is the main difference between permutation and combination?

a)

Permutation and combination use the same formula.

b)

Permutation and combination both involve the same mathematical operations.

c)

Permutation is used in probability calculations, while combination is used in statistical analysis.

d)

Permutation invovles the arrangement of objects, while combination involves the selection of objects without regard to the order.

42.

A committee with 2 members is to be formed from a student council with 10 members. Which of the followint is the corrrect formula in finding the number of ways the committee be formed?

a)

$\left(n-1\right)!$

b)

$\frac{n!}{\left(n-r\right)!}$

c)

$\frac{n!}{\left(n-r\right)!r!}$

d)

$\frac{n!}{n_1!n_2!}$

43.

In how many ways can seven people sit around a circle if two of them must always sit together?

a)

120

b)

240

c)

360

d)

540

44.

What does $P\left(A\cup\ B\right)$ mean?

a)

The probability of event A or event B or both occurring.

b)

The probability of event A or event B occurring simultaneously.

c)

The probability of event A occurred after event B.

d)

The probability of neither event A nor event B occurring.

45.

Suppose two fair dice are rolled, what is the probability that a sum of 2 or 3 turns up?

a)

1/12

b)

1/9

c)

1/6

d)

1/3

46.

What is the probability of drawing four spades in succession from a deck of 52 playing cards if after each card is drawn, it is not replaced in the deck?

a)

26%

b)

2.6%

c)

0.26%

d)

0.026%

GRADE 10 MATH QUIZ

Total questions: 46

Worksheet time: 46mins

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