Quiz about GRADE 10 MATH QUIZ

Question 1

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?

Accepted Answer

7

Answer

6

Answer

8

Answer

9

Question 2

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

Accepted Answer

-112

Answer

-142

Answer

36

Answer

58

Question 3

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

Accepted Answer

The common ratio between terms is constant.

Answer

The first term is always equal to one.

Answer

The common difference between terms is constant.

Answer

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

Question 4

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?

Accepted Answer

136 miles

Answer

24 miles

Answer

64 miles

Answer

106 miles

Question 5

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.

Accepted Answer

III only

Answer

I only

Answer

II only

Answer

I and II only

Question 6

Which of the following is an arithmetic sequence?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

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?

Accepted Answer

820

Answer

760

Answer

790

Answer

850

Question 8

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

Accepted Answer

40.5 and 121.5

Answer

25.5 and 94.5

Answer

30.5 and 112.5

Answer

42.5 and 134.5

Question 9

Which of the following illustrates a geometric sequence?

Accepted Answer

2, 6, 18, 54, 162, 486

Answer

1, 2, 3, 4, 5, 6

Answer

2, 4, 6, 8, 10, 12

Answer

3, 6, 18, 72, 360, 2160

Question 10

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

Accepted Answer

-1

Answer

-3

Answer

0

Answer

1

Question 11

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$e^{x\ }=7$$

Question 12

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.

Accepted Answer

II only

Answer

I only

Answer

III only

Answer

II and III only

Question 13

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

Accepted Answer

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

Answer

It must be a quadratic polynomial.

Answer

It can be a binomial or a trinomial.

Answer

Synthetic division cannot be used for polynomial division.

Question 14

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

Accepted Answer

0, 1, 1, 2, 3, 5

Answer

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

Answer

3, 6, 9, 12, 15, 18

Answer

2, 4, 8, 16, 31, 32

Question 15

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

Accepted Answer

$$3^n$$

Answer

$$3n^3$$

Answer

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

Answer

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

Question 16

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

Accepted Answer

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

Answer

all roots of a polynomial must be a rational number.

Answer

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

Answer

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

Question 17

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

Accepted Answer

x+9

Answer

x+4

Answer

x-9

Answer

x-12

Question 18

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

Accepted Answer

x+10

Answer

x+6

Answer

x+8

Answer

x+12

Question 19

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?

Accepted Answer

10, 368

Answer

15, 136

Answer

20, 284

Answer

25, 186

Question 20

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?

Accepted Answer

Php 3,176,424

Answer

Php 1,426,762

Answer

Php 2,672,234

Answer

Php 4,156,482

Question 21

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?

Accepted Answer

$$4\pi\ in^2$$

Answer

$$16\pi\ in^2$$

Answer

$$8\pi\ in^2$$

Answer

$$2\pi\ in^2$$

Question 22

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

Accepted Answer

The chords are equal in length.

Answer

The chords have a common endpoint.

Answer

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

Answer

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

Question 23

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?

Accepted Answer

54,936

Answer

49,356

Answer

58,640

Answer

59,642

Question 24

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

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 25

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 26

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?

Accepted Answer

4

Answer

2

Answer

6

Answer

10

Question 27

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?

Accepted Answer

8 cm

Answer

4 cm

Answer

12 cm

Answer

16 cm

Question 28

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?

Accepted Answer

|N - M|

Answer

N - M

Answer

M + N

Answer

|M+N|

Question 29

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

Accepted Answer

$$2\ \sqrt{\ 409}$$

Answer

$$6\ \sqrt{\ 201}$$

Answer

$$4\sqrt{\ 137}$$

Answer

$$3\sqrt{\ 329}$$

Question 30

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 31

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?

Accepted Answer

(4,-4)

Answer

(4,4)

Answer

(-4,4)

Answer

(-4,-4)

Question 32

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

Accepted Answer

(5,1)

Answer

(4,2)

Answer

(3,1)

Answer

(2,5)

Question 33

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 34

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

Accepted Answer

P(6,3)

Answer

P(3,6)

Answer

6!/3!

Answer

3!/6!

Question 35

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

Accepted Answer

2

Answer

3

Answer

6

Answer

9

Question 36

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?

Accepted Answer

3 x 6 x 5 x 2

Answer

3 x 5 x 4 x 2

Answer

2(3 x 6 x 5 x 1)

Answer

2(3 x 5 x 4 x 2)

Question 37

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?

Accepted Answer

336

Answer

164

Answer

286

Answer

462

Question 38

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

Accepted Answer

n!

Answer

(n-1)!

Answer

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

Answer

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

Question 39

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?

Accepted Answer

11,232,000

Answer

260

Answer

720

Answer

1,260

Question 40

What is the main difference between permutation and combination?

Accepted Answer

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

Answer

Permutation and combination use the same formula.

Answer

Permutation and combination both involve the same mathematical operations.

Answer

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

Question 41

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 42

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

Accepted Answer

240

Answer

120

Answer

360

Answer

540

Question 43

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

Accepted Answer

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

Answer

The probability of event A or event B occurring simultaneously.

Answer

The probability of event A occurred after event B.

Answer

The probability of neither event A nor event B occurring.

Question 44

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

Accepted Answer

1/12

Answer

1/9

Answer

1/6

Answer

1/3

Question 45

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?

Accepted Answer

0.26%

Answer

26%

Answer

2.6%

Answer

0.026%

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