Grade 10 : Mathematics - 3. Linear Equations (Set 2)

Question 1

At a school stationery shop, 2 pens and 3 notebooks cost $17, while 5 pens and 2 notebooks cost $26.

What is the individual cost of 1 pen?

Accepted Answer

B) $4

Answer

A) $3

Answer

C) $5

Answer

D) $6

Question 2

A motorboat travels 12 km downstream in 2 hours and covers 8 km upstream in 2 hours.

What is the speed of the motorboat in still water?

Accepted Answer

B) 5 km/h

Answer

A) 4 km/h

Answer

C) 6 km/h

Answer

D) 7 km/h

Question 3

A father's present age is three times his son's age. In 10 years, the father's age will be double his son's age.

What is the father's present age?

Accepted Answer

A) 30 years

Answer

B) 35 years

Answer

C) 40 years

Answer

D) 45 years

Question 4

The sum of two numbers is 45, and their difference is 13. What is the larger number?

Accepted Answer

C) 29

Answer

A) 26

Answer

B) 28

Answer

D) 31

Question 5

What condition must be satisfied for the pair of linear equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ to have a unique solution?

Accepted Answer

A) $\frac{a_1}{a_2} 
eq \frac{b_1}{b_2}$

Answer

B) $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$

Answer

C) $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Answer

D) $a_1 a_2 + b_1 b_2 = 0$

Question 6

For what value of $k$ will the system of equations $3x + 2y = 5$ and $6x + ky = 9$ represent parallel lines?

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 3

Answer

D) 6

Question 7

A city taxi charges a base fee plus a constant rate per kilometer. For a distance of 10 km, the total charge is $20. If the per-kilometer rate is $1.50, what is the base fee?

Determine the fixed base fee of the taxi service.

Accepted Answer

C) $5

Answer

A) $3

Answer

B) $4

Answer

D) $6

Question 8

Two supplementary angles differ by $34^\circ$. What is the measure of the smaller angle?

Accepted Answer

B) $73^\circ$

Answer

A) $63^\circ$

Answer

C) $83^\circ$

Answer

D) $107^\circ$

Question 9

The sum of the digits of a two-digit number is 9. Reversing the digits increases the number by 27. What is the original number?

Accepted Answer

B) 36

Answer

A) 27

Answer

C) 45

Answer

D) 63

Question 10

The length of a rectangular garden is 4 meters more than its width. If the perimeter of the garden is 32 meters, what is its length?

Accepted Answer

B) 10 m

Answer

A) 8 m

Answer

C) 12 m

Answer

D) 14 m

Question 11

Maya purchased 3 adult tickets and 2 child tickets for a movie for $46. Liam purchased 2 adult tickets and 4 child tickets for $44.

Find the cost of one adult ticket.

Accepted Answer

B) $12

Answer

A) $10

Answer

C) $14

Answer

D) $15

Question 12

Plan	Monthly Fixed Fee	Cost per Minute
Plan A	$12	$0.10
Plan B	$18	$0.06

At how many call minutes will both phone plans cost exactly the same amount?

Accepted Answer

C) 150 minutes

Answer

A) 100 minutes

Answer

B) 120 minutes

Answer

D) 180 minutes

Question 13

What is the intersection point $(x, y)$ of the two lines $x + y = 6$ and $x - y = 2$?

Accepted Answer

B) (4, 2)

Answer

A) (2, 4)

Answer

C) (3, 3)

Answer

D) (5, 1)

Question 14

Two numbers are in the ratio $3 : 4$. If 5 is added to each number, the ratio becomes $4 : 5$. What is the sum of the two numbers?

Accepted Answer

B) 35

Answer

A) 30

Answer

C) 40

Answer

D) 45

Question 15

How many solutions exist for the system of linear equations $2x + 3y = 7$ and $4x + 6y = 14$?

Accepted Answer

C) Infinitely many solutions

Answer

A) Unique solution

Answer

B) No solution

Answer

D) Exactly two solutions

Question 16

A balance scale has 4 identical metallic spheres and a 2 kg weight on the left pan, perfectly balancing 2 identical spheres and a 10 kg weight on the right pan.

What is the mass of one metallic sphere?

Accepted Answer

C) 4 kg

Answer

A) 2 kg

Answer

B) 3 kg

Answer

D) 5 kg

Question 17

If $x = 2, y = 3$ is a solution of the linear equation $3x + ky = 15$, what is the value of $k$?

Accepted Answer

B) 3

Answer

A) 2

Answer

C) 4

Answer

D) 5

Question 18

3 kg of apples and 2 kg of oranges cost $14. Meanwhile, 1 kg of apples and 4 kg of oranges cost $13.

What is the price of 1 kg of oranges?

Accepted Answer

B) $2.50

Answer

A) $2.00

Answer

C) $3.00

Answer

D) $3.50

Question 19

A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator, and it becomes $\frac{1}{4}$ when 8 is added to its denominator. What is the original fraction?

Accepted Answer

B) $\frac{5}{12}$

Answer

A) $\frac{4}{11}$

Answer

C) $\frac{7}{15}$

Answer

D) $\frac{3}{8}$

Question 20

Statement I: The pair of equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ represents two parallel lines.
Statement II: If $\frac{a_1}{a_2} = \frac{b_1}{b_2} eq \frac{c_1}{c_2}$, then the system of linear equations is inconsistent and has no solution.

Choose the correct option regarding Statement I and Statement II.

Accepted Answer

A) Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I.

Answer

B) Both Statement I and Statement II are true, but Statement II is not the correct explanation for Statement I.

Answer

C) Statement I is true, but Statement II is false.

Answer

D) Statement I is false, but Statement II is true.

Grade 10 : Mathematics - 3. Linear Equations (Set 2)