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Mathematics Test

Authored by Adeyemi Adekunle

Mathematics

12th Grade

Used 1+ times

Mathematics Test
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15 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Solve the following simultaneous equations : 3x + 2y = 13 and x - 2y = -1

x = 3

y = 2

x = 2

y = 3

x = 4

y = -1

x = -3

y = -2

Answer explanation

To solve the equations, substitute x from the second equation into the first. From x - 2y = -1, we get x = 2y - 1. Substituting into 3(2y - 1) + 2y = 13 gives y = 2. Then, x = 3. Thus, the solution is x = 3, y = 2.

2.

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

solve the simultaneous equations

3x - y - 10 = 0 and x2 + y2 = 100

(x,y) = (0,-10) or (6,8)

(x,y) = (-10,0) or (8,6)

(x,y) = (0,10) or (-6,8)

(x,y) = (6,-10) or (8,0)

Answer explanation

To solve the equations, substitute y from the first equation into the second. This gives x^2 + (3x - 10)^2 = 100. Solving this results in x = 0 or x = 6. Substituting back gives (0,-10) and (6,8), matching the correct choice.

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

600 tickets to a village fair were sold. Adult tickets were sold for $5 and child tickets were sold $3. A total $2500 was made from ticket sales. work out the number of adult ticket and number of child tickets sold

250 adult tickets and 350 child tickets

300 adult tickets and 300 child tickets

350 adult tickets and 250 child tickets

400 adult tickets and 200 child tickets

Answer explanation

Let A be adult tickets and C be child tickets. We have A + C = 600 and 5A + 3C = 2500. Solving these equations gives A = 350 and C = 250, confirming the correct choice is 350 adult tickets and 250 child tickets.

4.

FILL IN THE BLANK QUESTION

5 mins • 1 pt

A two-digit number is such that the products of its digits is 18. when 63 is subtracted from the number, the digits interchange their places. Find the number

Answer explanation

Let the two-digit number be 10a + b, where a and b are the digits. The conditions give us: ab = 18 and (10a + b) - 63 = 10b + a. Solving these, we find a = 9 and b = 2, so the number is 92.

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Answer explanation

To solve \(\frac{3x-4}{2}\ge\frac{x+1}{4}-1\), first simplify the right side to get \(\frac{x-3}{4}\). Then, multiply through by 4 to eliminate the fractions, leading to \(6x - 8 \ge x - 3\). Solving gives \(x \ge 1\), so the correct answer is \(x \ge 1\).

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Answer explanation

To solve \( \frac{x-2}{x+5} > 2 \), we rearrange to \( \frac{x-2}{x+5} - 2 > 0 \) leading to \( \frac{x-12}{x+5} > 0 \). The critical points are \( x = 12 \) and \( x = -5 \). Testing intervals shows \( x \in (-12, 5) \) is valid.

7.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

x = 2/3, y = 3/4

x = 1, y = 1

x = 1/2, y = 1/2

x = 0, y = 0

Answer explanation

To solve for x and y, rewrite the equation as 15^{3x-2} = 6.25 / 6^{1-2y}. Solving gives x = 2/3 and y = 3/4, which satisfies the condition that (3x-2) is a natural number. Thus, the correct answer is x = 2/3, y = 3/4.

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