asal education

 1. Which is greater than 4?

(a) 5,

(b) -5,

(c) -1/2,

(d) -25.


Solution:

5 greater than 4.

Answer: (a)

2. Which is the smallest?

(a) -1,

(b) -1/2,

(c) 0,

(d) 3.


Solution:

The smallest number is -1.

Answer: (a)



3. Combine terms: 12a + 26b -4b – 16a.

(a) 4a + 22b,

(b) -28a + 30b,

(c) -4a + 22b,

(d) 28a + 30b.


Solution:

12a + 26b -4b – 16a.

= 12a – 16a + 26b – 4b.

= -4a + 22b.

Answer: (c)



4. Simplify: (4 – 5) – (13 – 18 + 2).

(a) -1,

(b) –2,

(c) 1,

(d) 2.


Solution:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Answer: (d)



5. What is |-26|?

(a) -26,

(b) 26,

(c) 0,

(d) 1


Solution:

|-26|

= 26.

Answer: (b)

6. Multiply: (x – 4)(x + 5)

(a) x² + 5x - 20,

(b) x² - 4x - 20,

(c) x² - x - 20,

(d) x² + x - 20.



Solution:

(x – 4)(x + 5).

= x(x + 5) -4(x + 5).

= x² + 5x – 4x – 20.

= x² + x - 20.

Answer: (d)



7. Factor: 5x² – 15x – 20.

(a) 5(x-4)(x+1),

(b) -2(x-4)(x+5),

(c) -5(x+4)(x-1),

(d) 5(x+4)(x+1).


Solution:

5x² – 15x – 20.

= 5(x² – 3x – 4).

= 5(x² – 4x + x – 4).

= 5{x(x - 4) +1(x - 4)}.

= 5(x-4)(x+1).

Answer: (a).



8. Factor: 3y(x – 3) -2(x – 3).

(a) (x – 3)(x – 3),

(b) (x – 3)²,

(c) (x – 3)(3y – 2),

(d) 3y(x – 3).

Solution:

3y(x – 3) -2(x – 3).

= (x – 3)(3y – 2).

Answer: (c).



9. Solve for x: 2x – y = (3/4)x + 6.

(a) (y + 6)/5,

(b) 4(y + 6)/5,

(c) (y + 6),

(d) 4(y - 6)/5.


Solution:

2x – y = (3/4)x + 6.

or, 2x - (3/4)x = y + 6.

or, (8x -3x)/4 = y + 6.

or, 5x/4 = y + 6.

or, 5x = 4(y + 6).

or, 5x = 4y + 24.

or, x = (4y + 24)/5.

Therefore, x = 4(y + 6)/5.

Answer: (b).

10. Simplify:(4x² - 2x) - (-5x² - 8x).


Solution:

(4x² - 2x) - (-5x² - 8x)

= 4x² - 2x + 5x² + 8x.

= 4x² + 5x² - 2x + 8x.

= 9x² + 6x.

= 3x(3x + 2).



Answer: 3x(3x + 2)

11. Find the value of 3 + 2 • (8 – 3)

(a) 25,

(b) 13,

(c) 17,

(d) 24,

(e) 15.


Solution:

3 + 2 • (8 – 3)

= 3 + 2 (5)

= 3 + 2 × 5

= 3 + 10

= 13

Answer: (d)

12. Rice weighing 3³/₄ pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?


Solution:

3³/₄ ÷ 4 pounds.

= (4 × 3 + 3)/4 ÷ 4 pounds.

= 15/4 ÷ 4 pounds.

= 15/4 × 1/4 pounds.

= 15/16 pounds.

Now we know that, 1 pound = 16 ounces.

Therefore, 15/16 pounds = 15/16 × 16 ounces.

= 15 ounces.

Answer: 15 ounces.



13. Factor: 16w³ – u⁴w³


Solution:

16w³ – u⁴w³.

= w³(16 – u⁴).

= w³(4² - ((u²)²).

= w³(4 + u²)(4 - u²).

= w³(4 + u²)(2² - u²).

= w³(4 + u²)(2 + u)(2 - u).

Answer: w³(4 + u²)(2 + u)(2 - u).



14. Factor: 3x⁴y³ – 48y³.


Solution:

3x⁴y³– 48y³.

= 3y³(x⁴ – 16).

= 3y³[(x²)² - 4²].

= 3y³(x² + 4)(x² - 4).

= 3y³(x² + 4)(x² - 2²).

= 3y³(x² + 4)(x + 2)(x -2).

Answer: 3y³(x² + 4)(x + 2)(x -2)

15. What is the radius of a circle that has a circumference of 3.14 meters?


Solution:

Circumference of a circle = 2πr.

Given, circumference = 3.14 meters.

Therefore,

2πr = Circumference of a circle

or, 2πr = 3.14.

or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].

or, 6.28r = 3.14.

or, r = 3.14/6.28.

or, r = 0.5.

Answer: 0.5 meter.