All grade answer math problems are solved here from different topics. A large number of objective answer math problems are solved here to help the students quickly to test their knowledge and skills on different topics.

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

Solution:

(4x2 - 2x) - (-5x2 - 8x)

= 4x2 - 2x + 5x2 + 8x.

= 4x2 + 5x2 - 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

2. Simplify: (-7x2 - 3x) - (4x2 - x)

Solution:

(-7x2 - 3x) - (4x2 - x)

= -7x2 - 3x - 4x2 + x

= -7x2 - 4x2 - 3x + x

= -11x2 – 2x

= -x(11x + 2)

3. Simplify: (-5x2 - 8x + 7) - (5x2 - 4)

Solution:

(-5x2 - 8x + 7) - (5x2 - 4)

= -5x2 - 8x + 7 - 5x2 + 4

= -5x2 - 5x2 - 8x + 7 + 4

= -10x2 – 8x + 11

Answer: -10x2 – 8x + 11

4. Simplify: (4x2 + 5x) + (x2 - 5x + 1)

Solution:

(4x2 + 5x) + (x2 - 5x + 1)

= 4x2 + 5x + x2 - 5x + 1

= 4x2 + x2+ 5x - 5x + 1

= 5x2 + 0 + 1

= 5x2 + 1

5. Simplify: (-6x + 3) - (-x2 + 5x)

Solution:

(-6x + 3) - (-x2 + 5x)

= -6x + 3 + x2 - 5x

= -6x - 5x + x2 + 3

= x2 – 11x + 3

Answer: x2 – 11x + 3

6. Simplify: (-9x - 5) - (-9x2 + x - 5)

Solution:

(-9x - 5) - (-9x2 + x - 5)

= -9x - 5 + 9x2 - x + 5

= 9x2 - 9x – x – 5 + 5

= 9x2 – 10x

= x(9x – 10)

7. Simplify: (2x - 4) - (6x + 6)

Solution:

(2x - 4) - (6x + 6)

= 2x - 4 - 6x – 6

= 2x – 6x – 4 – 6

= -4x – 10

= -2(2x + 5)

8. Simplify:(8+4x)/4x

Solution:

(8+4x)/4x

= 4(2 + x)/4x

[Cancel 4 from the numerator and denominator]

= (2 + x)/x

9. Decide whether the lines are parallel, perpendicular or neither.

x + 4y = 7 and 4x – y = 3

Solution:

x + 4y = 7

4y = -x + 7

y = (-1/4) x + 7

Slope of the equation x + 4y = 7 is -1/4.

Again, 4x – y = 3

y = 4x – 3

Slope of the equation 4x – y = 3 is 4.

Since multiplying both the slope of the equation = -1/4 × 4 = -1

Therefore, the given two equations are perpendicular to each other.

10. Simplify: 3x – 5 + 23x – 9

Solution:

3x – 5 + 23x – 9

= 3x + 23x – 5 – 9

= 26x – 14

= 2(13x – 7)

11. A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?

Solution:

The speed of the plane in still air = x miles/hour

The speed of the wind is 23 mph

Speed with the wind = (x + 23) mph

Speed against the wind = (x – 23) mph

Time = Distance/ Speed

According to the problem,

420/(x + 23) = 350/(x – 23)

420(x – 23) = 350(x + 23)

420x – 9660 = 350x + 805

420x – 350x = 8050 + 9660

70x = 17710

x = 17710/70

x = 253

Therefore, the speed of the plane in still air = 253 mph.

12. Use the discriminant to determine the number of real roots the equation has. 3x2 – 5x + 1 =0

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = bx2 – 4ac

Compare the above equation 3x2 – 5x + 1 =0 with ax2 + bx + c = 0

We get, a = 3, b = -5, c = 1

Put the value of a, b and c;

Discriminant = bx2 – 4ac

Discriminant = (-5)2 - 4 × 3 × 1

= 25 – 12

= 13 [13 > 0]

Therefore, discriminant is positive.

So the given equation has two distinct real roots.

13. Use the discriminant to determine the number of real roots the equation has. 7x2 + 3x + 1 =0.

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = b2 – 4ac

Compare the above equation 7x2 + 3x + 1 =0 with ax2 + bx + c = 0

We get, a = 7, b = 3, c = 1

Put the value of a, b and c;

Discriminant = b2 – 4ac

Discriminant = (3)2 - 4 × 7 × 1

= 9 – 28

= -19 [13 < 0]

Therefore, discriminant is negative.

So the given equation has none (two imaginary roots).

14. Fill in the blank:

(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.

(b) To find the x-intercept of a line, we let....equal 0 and solve for ......; to find y-intercept, we let ......equal 0 and solve for.......

Solution:

(a) The point with coordinates (0,0) is called origin of a rectangular coordinate system.

(b) To find the x-intercept of a line, we let y equal 0 and solve for x ; to find y-intercept, we let x equal 0 and solve for y .

15. Name the quadrant, if any, in which each point is located.

(a) (1, 6)

(b) (-4, -2)

Solution:

(a) (1, 6) --------- I Quadrant.

(b) (-4, -2) --------- III Quadrant.