HIGH SCHOOL MATH PROBLEMS WITH SOLUTIONS

Problem 1 :

Simplify the following

Solution :

L.H.S

  =  (1 + tan2A) / (1+cot2A)

sec2A - tan2A  =  1

sec2A  =  1 + tan2A

cosec2A - cot2A  =  1

cosec2A  =  1 + cot2A

  =  sec2A / cosec2A

  =  (1/cos2A) / (1/sin2A)

  =  sin2A/cos2A

  =  tan2A

Problem 2 :

From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff  from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (take √3 = 1.732)

Solution :

In triangle BCD,

tanθ  =  Opposite side / Adjacent side

tan 30  =  BC/CD

1/√3  =  10/CD

CD  =  10√3 ------(1)

In triangle ACD,

tan 45  =  AC/CD

1  =  (10 + x) /CD

CD  =  10 + x ------(2)

(1)  =  (2)

10√3  =  10 + x

x  =  10(√3 - 1)

x  =  10(10.732 - 1)

x  =  10(0.732)

x  =  7.32

The height of the flag staff is 7.32 m.

Problem 3 :

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower is 30°. Find the height of the tower.

Solution :

Height of the tower  =  AB, Distance between the foot of the tower and point of observation  =  BC.

tanθ  =  Opposite side / Adjacent side

tan θ  =  AB/BC

tan 30  =  AB/30

1/√3  =  AB/30

AB  =  30/√3

AB  =  (30/√3) ⋅ (√3/√3)

AB  =  30√3/3

AB  =  10√3

Problem 4 :

The coefficient of variation of a series is 69% and its standard deviation is 15. Find the mean.

Solution :

Coefficient of variation  =  (σ/x̅) ⋅ 100%

69/100  =  (15/⋅ 100%

0.69  =  15/

  =  15/0.69

  =  21.73

So, the required mean is 21.73.

Problem 5 :

If the two dice are thrown. what is the probability of getting the same number in both the dice.

Solution :

When two dice are thrown, the sample space

n(S)  =  36

Let A be the event of getting doublet.

A  =  { (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6) }

n(A)  =  6

p(A)  =  n(A)/n(S)

p(A)  =  6/36

Problem 6 :

2 cubes each of volume 64 cm3 are joined end to end. Determine the surface area of the resulting cuboid.

Solution :

Volume of one cuboid  =  64 cm3

a3  =  64

Side length of cube is 4 cm.

Side length of cuboid  =  4 + 4  =  8 cm

breadth  =  4 cm and height  =  4 cm

Surface area of cuboid  =  2(lb + bh + hl)

  =  2(8⋅4 + 4⋅4 + 4⋅8)

  =  2(32 + 16 + 32)

  =  2(80)

  =  160 cm2

Problem 7 :

A metallic sphere of radius 4.2 cm is melted and recast into a shape of a cylinder of radius 6 cm. Determine the height of the cylinder.

Solution :

Radius of sphere  =  4.2 cm

Radius of cylinder  =  6

Volume of sphere  =  Volume of cylinder

(4/3) πr =  πr2 h

(4/3) 4.2 =  62 h

h  =  98.784/36

h  =  2.744

So, the height of the cylinder is 2.744 cm.

Problem 8 :

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Determine the curved surface area of the frustum.

Solution :

Slant height (l)  =  4 cm

Circumference of larger circle  =  18

2πR  = 18 

R  =  18/2π

R  =  9/π

2πr  = 6 

r  =  6/2π

r  =  3/π

Surface area of the frustum cone  =  πl (R + r)

  =  π ⋅ 6(9/π + 3/π)

  =  6(9+3)

  =  12(6)

  =  72

Problem 9 :

Find the HCF of 96 and 404 by the prime factorization method. Find their LCM.

Solution :

  =  2 ⋅ 2

  =  4

Problem 10 :

The angle in a semi circle is

Solution :

Angle in a semi circle is right angle.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. How to Solve Age Problems with Ratio

    Mar 28, 24 02:01 AM

    How to Solve Age Problems with Ratio

    Read More

  2. AP Calculus BC Integration of Rational Functions by Partical Fractions

    Mar 26, 24 11:25 PM

    AP Calculus BC Integration of Rational Functions by Partical Fractions (Part - 1)

    Read More

  3. SAT Math Practice

    Mar 26, 24 08:53 PM

    satmathquestions1.png
    SAT Math Practice - Different Topics - Concept - Formulas - Example problems with step by step explanation

    Read More