GRADE 7 MATH WORKSHEET 12 ANSWERS

About "Grade 7 math worksheet 12 answers"  

Grade 7 math worksheet 12 answers :

Here we are going to see 10 practice questions of mixed topics. We have been preparing this set of questions in order to test how you understood the topics.

Practice questions of mixed topics in 7th grade math

Question 1 :

The sum of the digits of a two digit number is 15 and if 9 is added to the number the digits are interchanged.Find the required number. 

(A) 78               (B) 19           (C) 82

Solution :

Let "xy" be the required two digit number

x + y  =  15  ------(1)

xy + 9  =  yx

10x + 1y + 9  =  10y + 1x

10x - x + 1y - 10y  =  -9

9x - 9y  =  -9  ------(2)

Divide (2) by 9, we get

x - y  =  -1 ------(2)

                  x + y  =  15

                 x - y  =  -1

               ------------------

                2x  =  14  ==> x  =  7

By applying the value of x in the first equation, we get

7 + y  =  15

Subtract both sides by 7, 

y  =  15 - 7  =  8

Hence the required number is 78.

Question 2 :

Two trains with a speed of 35km per hour and 28 km per hour respectively,starting at the same time, run in the opposite directions between two stations A and B, 315 km apart.Find where they will meet

(A) 180 km apart from A

(B) 130 km apart from A

(C) 175 km apart from A

Solution :

Let both trains meet at x distance from station A

TRAIN 1 :

distance = x

speed= 35

time = x/35

TRAIN 2

distance = 315-x

speed = 28

time = 315-x/28

the time when they meet will be equal

x/35 = 315-x/28

x/5 = 315-x/4

4x = 1575 - 5x

9x = 1575  ==> x = 175

& t = x/35  ==>  175/35 ==> 5

Hence the trains will meet at 175 km apart from station A and after 5 hrs.

Question 3 :

The sum of two number is 135 and are in the ratio 4:5.Find the required numbers. 

(A) 80,95      (B) 60,75        (C) 30,35

Solution :

Let the two numbers be "4x" and "5x"

4x + 5x  =  135

9x  =  135

x  =  135/9  ==>  15

4x  =  4(15)  =  60

5x  =   5(15)  =  75

Hence the required numbers are 60 and 75.

Question 4 :

The sum of two numbers is 3000. If 8% of one number is equal to 12% of the other, find the numbers.

(A) 1800 and 1200 

 (B) 2240 and 2800 

(C) 2700 and 3100

Solution :

Let the two numbers be x and y.

Given, x + y = 3000

Also, 

We got x = 3y/2

But x + y = 3000

3y/2 + y = 3000

5y/2 = 3000

y = 3000 × 2 / 5 = 1200

So, x = 3(1200)/2 = 1800

Hence the numbers are 1800 and 1200

Question 5 :

Solve the following 2(6x-5) = (3x+2) + 6

(A) 2               (B) 5                (C) 3

Solution :

2(6x-5) = (3x+2) + 6

12x - 10 = 3x + 2 + 6

12x - 3x  =  8 + 10

9x  =  18

Divide both sides by 9

x  =  18/9  =  2

Question 6 : 

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

(A) 30 cm          (B) 25 cm        (C) 12 cm

Solution :

AB is a chord of length 16 cm

C is the midpoint of AB.

OA is the radius of length 10 cm

AB = 16 cm

AC = (1/2) ⋅ 16 = 8 cm

OA = 10 cm

In a right triangle OAC.

OC2 = OA2 - AC2

OC2  = 102 - 82

OC2  = 100 - 64 = 36 cm

OC = 6 cm

Hence, the distance of the chord from the centre is 6 cm.

Let us look into the solution of the next problem on "Grade 7 math worksheet 12 answers".

Question 7 :

In the figure, O is the center of the circle, <ABO  =  30°, where A, B and C are points on the circle . What is the value of "x" ?

(A)  60°            (B)  100°             (C)  50°

Solution :

In triangle OAB, we have 

OA  =  OB

<OAB  =  <OBA  =  20°

In triangle OAB, we have 

OA  =  OC

<OAC  =  <OCA  =  30°

<BAC  =  <OAB + <OAC

    =  20° + 30°  =  50°

x  = <BOC  =  2<BAC

  =  2(50°)  =  100°

Hence the required angle is 100°.

Let us look into the solution of the next problem on "Grade 7 math worksheet 12 answers".

Question 8 :

The base of the parallelogram is twice the height.If the area is 578 find the base and height.

(A) Height = 10 cm and Base = 20 cm

(B) Height = 17cm and Base = 34 cm

(C) Height = 15 cm and Base = 10 cm

Solution :

Let "x" be the base of the parallelogram

height  =  2x

Area of parallelogram  =  578

x (2x)  =  578

2x2  =  578  ==> x2  =  289

x  =  17 cm

2x  =  2(17)  =  34 cm

Hence the base and height of the parallelogram are 17 and 34 cm respectively.

Let us look into the solution of the next problem on "Grade 7 math worksheet 12 answers".

Question 9 :

The perimeter of a triangle field is 144 m and the ratio of the sides is 3:4:5.Find the area of the field.

(A) 318 m2           (B) 522 m2          (C) 864 m 2

Solution :

Sides of the triangle are 3x, 4x and 5x

Perimeter of the triangle  =  144 m

3x + 4x + 5x  =  144

12x  =  144

Divide both sides by 12

x  =  144/12  =  12

3x  =  3(12)  =  36

4x  =  4(12)  =  48

5x  =  5(12)  =  60

Area of scalene triangle  =  √s(s-a)(s-b)(s-c)

s  =  144/2  =  72

s - a = 72 - 36  =  36

s - b = 72 - 48  =  24

s - c = 72 - 60  =  12

=  √(72 ⋅ 36 ⋅ 24 ⋅ 12)

   =  864 m2

Let us look into the solution of the next problem on "Grade 7 math worksheet 12 answers".

Question 10 :

The circumference of a circle exceeds the diameter by 20 cm. Find the radius of the circle. 

Solution :

Let the radius of circle of = r m. 

Then circumference = 2 πr 

Since, circumference exceeds diameter by 20 

2 πr = d + 20 

 2 πr = 2r + 20 

 2 × (22/7) × r = 2r + 20

 44r/7 - 2r = 20

 (44r - 14r)/7 = 20

 30r/7 = 20 

 r = (7 × 20)/30

 r =14/3

So, the radius of circle = 14/3 cm = 42/3 cm 

After having gone through the stuff given above, we hope that the students would have understood "Grade 7 math worksheet 12 answers". 

Apart from the stuff given above, if you want to know more about "Grade 7 math worksheet 12 answers", please click here

Apart from the stuff, 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