Class 9 Math Masters: Conquer The Quiz Challenge!

1. If x + 5 = 10, then what is the value of x?

5

10

15

-5

To find the value of x in the equation x + 5 = 10, we need to isolate x by subtracting 5 from both sides of the equation. This gives us x + 5 - 5 = 10 - 5, which simplifies to x = 5. Therefore, the value of x that satisfies the equation is 5. This is a basic algebraic equation that demonstrates the principle of balancing equations to solve for an unknown variable.

Explanation

To find the value of x in the equation x + 5 = 10, we need to isolate x by subtracting 5 from both sides of the equation. This gives us x + 5 - 5 = 10 - 5, which simplifies to x = 5. Therefore, the value of x that satisfies the equation is 5. This is a basic algebraic equation that demonstrates the principle of balancing equations to solve for an unknown variable.

2. What is 3/20 as a decimal?

0.3

0.5

0.15

1.5

To convert the fraction 3/20 into a decimal, divide the numerator by the denominator. The calculation is performed by dividing 3 by 20. When you divide 3 by 20, you get 0.15. Therefore, the decimal equivalent of the fraction 3/20 is 0.15. This decimal value directly results from the division process, representing the proportion of 3 parts out of a total of 20 parts.

Explanation

To convert the fraction 3/20 into a decimal, divide the numerator by the denominator. The calculation is performed by dividing 3 by 20. When you divide 3 by 20, you get 0.15. Therefore, the decimal equivalent of the fraction 3/20 is 0.15. This decimal value directly results from the division process, representing the proportion of 3 parts out of a total of 20 parts.

3. What is the value of x in the equation 4(x+2)=24?

X=11/2

X=4

X=-4

X=16

To solve the equation 4(x+2)=24

Distribute the 4:

4x+8=24

Subtract 8 from both sides to isolate the term with x:

4x=16

Divide both sides by 4 to solve for x:

x=16/4

Therefore, the value of x is 4.

Explanation

To solve the equation 4(x+2)=24

Distribute the 4:

4x+8=24

Subtract 8 from both sides to isolate the term with x:

4x=16

Divide both sides by 4 to solve for x:

x=16/4

Therefore, the value of x is 4.

4. David and John share $455 in the ratio of 2:3, respectively. How much money does John get?

$182

$273

$91

$175

David and John share $455 in the ratio of 2:3. This means for every 2 units that David receives, John receives 3 units. To find out how much money each person gets, you first need to determine the total number of parts into which the money is divided:

Total parts = 2 (David) + 3 (John) = 5 parts

Now, calculate the value of one part:

Value of one part = Total money / Total parts = $455 / 5 = $91

Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:

Money John receives = 3 parts x $91/part = $273

Therefore, John receives $273.

Explanation

David and John share $455 in the ratio of 2:3. This means for every 2 units that David receives, John receives 3 units. To find out how much money each person gets, you first need to determine the total number of parts into which the money is divided:

Total parts = 2 (David) + 3 (John) = 5 parts

Now, calculate the value of one part:

Value of one part = Total money / Total parts = $455 / 5 = $91

Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:

Money John receives = 3 parts x $91/part = $273

Therefore, John receives $273.

5. The ratio of girls to boys in a school is 5:7. If there are 525 girls, how many boys are there?

375

625

735

325

The ratio of girls to boys in the school is 5:7. This means for every 5 girls, there are 7 boys. Given there are 525 girls, we first determine how many times the part of the ratio (5) fits into the actual number of girls (525).

Calculate the multiplier for the ratio:

525 (number of girls) / 5 (girl ratio part) = 105

Now, use this multiplier to find the number of boys:

Multiply the boy ratio part by the multiplier:

7 (boy ratio part) x 105 (multiplier) = 735

Therefore, there are 735 boys in the school.

Explanation

The ratio of girls to boys in the school is 5:7. This means for every 5 girls, there are 7 boys. Given there are 525 girls, we first determine how many times the part of the ratio (5) fits into the actual number of girls (525).

Calculate the multiplier for the ratio:

525 (number of girls) / 5 (girl ratio part) = 105

Now, use this multiplier to find the number of boys:

Multiply the boy ratio part by the multiplier:

7 (boy ratio part) x 105 (multiplier) = 735

Therefore, there are 735 boys in the school.

6. What is 0.67543 rounded to 2 significant figures?

0.68

0.7

0.67

0.70

To round the number 0.67543 to 2 significant figures:

Identify the first two significant figures, which are 6 and 7.
Look at the third digit, which is 5. Since 5 is greater than or equal to 5, you round up the second significant figure (7) to 8.

Therefore, 0.67543 rounded to 2 significant figures is 0.68. This process ensures the number is represented accurately while maintaining the specified precision.

Explanation

To round the number 0.67543 to 2 significant figures:

Identify the first two significant figures, which are 6 and 7.
Look at the third digit, which is 5. Since 5 is greater than or equal to 5, you round up the second significant figure (7) to 8.

Therefore, 0.67543 rounded to 2 significant figures is 0.68. This process ensures the number is represented accurately while maintaining the specified precision.

7. What is the simplified form of 5ab - 7ba + 4ab=?

2ab

-2ab

16ab

None

First, recognize that ab and ba are equivalent (since multiplication is commutative). Therefore, we can combine the terms:

5ab−7ab+4ab

Now, combine like terms:

(5−7+4)ab

2ab

Thus, the simplified form of 5ab−7ba+4ab is 2ab.

Explanation

First, recognize that ab and ba are equivalent (since multiplication is commutative). Therefore, we can combine the terms:

5ab−7ab+4ab

Now, combine like terms:

(5−7+4)ab

2ab

Thus, the simplified form of 5ab−7ba+4ab is 2ab.

8. Given the equation x²+4x+3=0, what are the values of x?

2 or 3

-1 or -3

1 or 3

5 or -1

To solve the quadratic equation x^2 + 4x + 3 = 0, you can factorize it:

(x + 3)(x + 1) = 0

Setting each factor equal to zero gives:

x + 3 = 0

Solving for x, x = -3

x + 1 = 0

Solving for x, x = -1

Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.

Explanation

To solve the quadratic equation x^2 + 4x + 3 = 0, you can factorize it:

(x + 3)(x + 1) = 0

Setting each factor equal to zero gives:

x + 3 = 0

Solving for x, x = -3

x + 1 = 0

Solving for x, x = -1

Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.

9. What is 68/0.00001 expressed as an ordinary number?

6,800,000

680000

68000

0.00068

To solve:

68 ÷ 0.00001

= 68 × 100,000

= 6,800,000

68 ÷ 0.00001 = 68 ÷ (1 ÷ 100,000) = 68 × 100,000 = 6,800,000

Explanation

To solve:

68 ÷ 0.00001

= 68 × 100,000

= 6,800,000

68 ÷ 0.00001 = 68 ÷ (1 ÷ 100,000) = 68 × 100,000 = 6,800,000

10. What is the value of 4*4-2*(-3)+6= ?

17

28

-36

None

We follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):

First, multiply:

4 × 4 = 16

2 × (-3) = -6

Now, substitute these values into the expression:

16 - (-6) + 6

Subtracting a negative is the same as adding:

16 + 6 + 6 = 28

Explanation

We follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):

First, multiply:

4 × 4 = 16

2 × (-3) = -6

Now, substitute these values into the expression:

16 - (-6) + 6

Subtracting a negative is the same as adding:

16 + 6 + 6 = 28

11. What is the result when you reduce $80 by 11%?

$8.80

$71.20

$69

None

To find the amount remaining after reducing $80 by 11%, first calculate 11% of $80. Multiply 80 by 0.11 to get the reduction amount. This calculation gives 80 * 0.11 = $8.80. Now, subtract this amount from the original $80 to find the reduced total. The calculation is 80 - 8.80 = $71.20. Therefore, when you reduce $80 by 11%, you will get $71.20. This result is achieved by applying the percentage reduction to the original amount and subtracting the calculated value from the original total.

Explanation

To find the amount remaining after reducing $80 by 11%, first calculate 11% of $80. Multiply 80 by 0.11 to get the reduction amount. This calculation gives 80 * 0.11 = $8.80. Now, subtract this amount from the original $80 to find the reduced total. The calculation is 80 - 8.80 = $71.20. Therefore, when you reduce $80 by 11%, you will get $71.20. This result is achieved by applying the percentage reduction to the original amount and subtracting the calculated value from the original total.

12. If 2x+5y=18 and x=2, what is the value of 4x+5y?

20

19

22

21

First, substitute x=2 into the equation 2x+5y=18:

2(2)+5y=18

4+5y=18

Next, solve for 𝑦 by isolating y:

5y=18−4

5y=14

y=2.8

Now, substitute x=2 and y=2.8 into the expression 4x+5y:

4(2)+5(2.8)

8+14

22

Therefore, the value of 4x+5y is 22.

Explanation

First, substitute x=2 into the equation 2x+5y=18:

2(2)+5y=18

4+5y=18

Next, solve for 𝑦 by isolating y:

5y=18−4

5y=14

y=2.8

Now, substitute x=2 and y=2.8 into the expression 4x+5y:

4(2)+5(2.8)

8+14

22

Therefore, the value of 4x+5y is 22.

13. Change 36 km/h to meters per second:

20

10

36

None

Convert kilometers to meters: 1 kilometer (km) = 1000 meters (m). So, 36 km = 36 * 1000 = 36000 meters.

Convert hours to seconds: 1 hour = 60 minutes, and 1 minute = 60 seconds. So, 1 hour = 60 * 60 = 3600 seconds.

Divide the distance in meters by the time in seconds: 36000 meters / 3600 seconds = 10 meters/second.

Explanation

Convert kilometers to meters: 1 kilometer (km) = 1000 meters (m). So, 36 km = 36 * 1000 = 36000 meters.

Convert hours to seconds: 1 hour = 60 minutes, and 1 minute = 60 seconds. So, 1 hour = 60 * 60 = 3600 seconds.

Divide the distance in meters by the time in seconds: 36000 meters / 3600 seconds = 10 meters/second.

14. If x-12y = 0, what is y/x?

1/6

12

1/12

None

To find the ratio of y/x from the equation x-12y = 0, first rearrange the equation to solve for y in terms of x. By moving all terms involving y to one side and all other terms to the opposite side, we get x = 12y. Now, divide both sides of this equation by x to isolate y/x on one side. This gives us y/x = 1/12. Hence, the value of y/x equals 1/12. This is calculated by dividing the coefficient of y by the coefficient of x in the rearranged equation.

Explanation

To find the ratio of y/x from the equation x-12y = 0, first rearrange the equation to solve for y in terms of x. By moving all terms involving y to one side and all other terms to the opposite side, we get x = 12y. Now, divide both sides of this equation by x to isolate y/x on one side. This gives us y/x = 1/12. Hence, the value of y/x equals 1/12. This is calculated by dividing the coefficient of y by the coefficient of x in the rearranged equation.

15. Factor the quadratic expression: x²+x-30:

(x+5)(x-6)

(x-5)(x+6)

(x-6)(x-5)

None

The given quadratic expression, x^2 + x - 30, can be factorized as (x - 5)(x + 6). This can be determined by finding two numbers that multiply to give -30 and add up to 1, which are -5 and 6 in this case. Therefore, the correct answer is (x - 5)(x + 6).

Explanation

The given quadratic expression, x^2 + x - 30, can be factorized as (x - 5)(x + 6). This can be determined by finding two numbers that multiply to give -30 and add up to 1, which are -5 and 6 in this case. Therefore, the correct answer is (x - 5)(x + 6).

16. What is the next number in the sequence: 3, 7, 15, 31, ?

47

63

72

58

The given sequence is increasing, and each number is obtained by doubling the previous number and then adding 1.

Starting with 3:

3 * 2 + 1 = 7

7 * 2 + 1 = 15

15 * 2 + 1 = 31

To find the next number, we apply the same pattern:

31 * 2 + 1 = 63

So, the next number in the sequence is 63.

Explanation

The given sequence is increasing, and each number is obtained by doubling the previous number and then adding 1.

Starting with 3:

3 * 2 + 1 = 7

7 * 2 + 1 = 15

15 * 2 + 1 = 31

To find the next number, we apply the same pattern:

31 * 2 + 1 = 63

So, the next number in the sequence is 63.

17. The sum of three consecutive even numbers is 222. What are the numbers?

73,74,75

74,74,74

72,74,76

None

Let the three consecutive even numbers be

𝑥, x+2, and x+4.

Their sum is given by:

x+(x+2)+(x+4)=222

Combine like terms:

3x+6=222

Subtract 6 from both sides:

3x=216

Divide both sides by 3:

x=72

Therefore, the three consecutive even numbers are:

x=72

x+2=74

x+4=76

So, the numbers are 72, 74, and 76.

Explanation

Let the three consecutive even numbers be

𝑥, x+2, and x+4.

Their sum is given by:

x+(x+2)+(x+4)=222

Combine like terms:

3x+6=222

Subtract 6 from both sides:

3x=216

Divide both sides by 3:

x=72

Therefore, the three consecutive even numbers are:

x=72

x+2=74

x+4=76

So, the numbers are 72, 74, and 76.

18. Given the equation y²+ 4=20, what are the values of y?

4 only

-4 only

4 or -4

16

To solve the equation y^2 + 4 = 20, first subtract 4 from both sides:

y^2 + 4 - 4 = 20 - 4

This simplifies to:

y^2 = 16

Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:

y = sqrt(16)

This gives:

y = 4 and y = -4

Therefore, y equals both 4 and -4.

Explanation

To solve the equation y^2 + 4 = 20, first subtract 4 from both sides:

y^2 + 4 - 4 = 20 - 4

This simplifies to:

y^2 = 16

Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:

y = sqrt(16)

This gives:

y = 4 and y = -4

Therefore, y equals both 4 and -4.

19. The gradient of the line y = 4 -2x is:

4

2

-2

None

The gradient of a line represents its steepness or slope. In the given equation, y = 4 - 2x, the coefficient of x (-2) represents the slope of the line. Since the coefficient is negative, the line has a negative slope. Therefore, the gradient of the line y = 4 - 2x is -2.

Explanation

The gradient of a line represents its steepness or slope. In the given equation, y = 4 - 2x, the coefficient of x (-2) represents the slope of the line. Since the coefficient is negative, the line has a negative slope. Therefore, the gradient of the line y = 4 - 2x is -2.

20. The gradient of the line joining (-4,-1) and (4,2) is:

-3/8

3/8

0

8/3

The gradient of a line is determined by the change in y divided by the change in x between two points on the line. In this case, the change in y is 2 - (-1) = 3 and the change in x is 4 - (-4) = 8. Therefore, the gradient is 3/8.

Explanation

The gradient of a line is determined by the change in y divided by the change in x between two points on the line. In this case, the change in y is 2 - (-1) = 3 and the change in x is 4 - (-4) = 8. Therefore, the gradient is 3/8.

21. The price of an item increases by 20% and then decreases by 20%. What is the net effect on the price?

Increased by 4%

Decreased by 4%

Increased by 0%

Increased by 40%

Let's assume the original price of the item is $100.

Price after increase: After a 20% increase, the price becomes $100 + ($100 * 20/100) = $120.

Price after decrease: After a 20% decrease, the price becomes $120 - ($120 * 20/100) = $96.

Net change: The net change in price is $96 - $100 = -$4.

Percentage change: The percentage change is (-$4 / $100) * 100% = -4%.

Therefore, the net effect on the price is a decrease of 4%.

Explanation

Let's assume the original price of the item is $100.

Price after increase: After a 20% increase, the price becomes $100 + ($100 * 20/100) = $120.

Price after decrease: After a 20% decrease, the price becomes $120 - ($120 * 20/100) = $96.

Net change: The net change in price is $96 - $100 = -$4.

Percentage change: The percentage change is (-$4 / $100) * 100% = -4%.

Therefore, the net effect on the price is a decrease of 4%.

22. If 2x-3y +4x-7y=0, then what is the value of y/x?

3/5

5/3

5/11

-3/5

Explanation

23. If 30% of a number is 18, what is 150% of that number?

54

60

90

150

First, find the whole number: If 30% of the number is 18, then 10% is 6 (18 / 3 = 6). Therefore, 100% of the number is 60 (6 x 10 = 60).

To find 150%, calculate 50% of the number, which is 30 (60 / 2 = 30). Add this to the original number: 60 + 30 = 90.

Explanation

First, find the whole number: If 30% of the number is 18, then 10% is 6 (18 / 3 = 6). Therefore, 100% of the number is 60 (6 x 10 = 60).

To find 150%, calculate 50% of the number, which is 30 (60 / 2 = 30). Add this to the original number: 60 + 30 = 90.

24. What is the gradient of the line x+3y=9?

3

1/3

-1/3

None

To find the gradient (or slope) of the line, we need to rearrange the equation into slope-intercept form, which is y = mx + c, where m is the gradient.

Rearrange the equation: x + 3y = 9 3y = -x + 9 y = (-1/3)x + 3

Identify the gradient: Now the equation is in slope-intercept form, and we can see that the gradient (m) is -1/3.

Explanation

To find the gradient (or slope) of the line, we need to rearrange the equation into slope-intercept form, which is y = mx + c, where m is the gradient.

Rearrange the equation: x + 3y = 9 3y = -x + 9 y = (-1/3)x + 3

Identify the gradient: Now the equation is in slope-intercept form, and we can see that the gradient (m) is -1/3.