7th GRADE MATH TEST PRACTICE

Question 1 :

Suman studies for 17/3 hours daily. She devotes 14/5 hours of her time for Science and Mathematics. How much time does she devote for other subjects?

(A)   23/15          (B)  43/15             (C)  14/15

Solution :

Time devoted by her for Science and Mathematics 

  =  14/5

Total times of Suman's study  =  17/3

Thus, time devoted by her for other subjects

  =  17/3 - 14/5

  =  (85 - 42)/15

  =  43/15

Question 2 :

If A + B = √8 and A - B = √5, what is A ⋅ B is ?

(A)  5/4            (B)  8/7             (C)  3/4

Solution :

A + B = √8  ---(1)

A - B = √5  ---(2)

(1) + (2)  ==>  2A  =  √8 + √5

A  =  (√8 + √5)/2

(1) - (2)  ==>  2B  =  √8 - √5

B  =  (√8 - √5)/2

A ⋅ B  =  [(√8 + √5)/2] [(√8 - √5)/2]

=  (√8² - √5²)/4

=  (8 - 5)/4

=  3/4

So, the value of A ⋅ B is 3/4.

Question 3 :

In a class of 35 students, 7 students were absent on a particular day. What percentage of the students were absent?

(A)  50%     (B)  33%     (C)  20%

Solution :

Total number of students  =  35

Number of students absent  =  7

Percentage of students were absent 

=  (7/35) 100

=  (1/5) 100

=  20%

Question 4 :

The last two digits of of 5²⁰⁰³ is

(A)   30        (B) 50         (C)  25

Solution :

The last two digits of the expansion will be 25.

Question 5 :

Calculate the unit digit of 12³

(A) 4              (B) 6            (C)  8

Solution :

12³  =  12 ⋅ 12 ⋅ 12

The of unit digit of 12 is 2. If we multiply 2 three times, we will get 8.

So, the unit 12³ is 8.

Question 6 :

What is the complementary angle of 35 degree

(A)   65    (B)   75   (C)   55

Solution : 

Complementary angles means sum of those angles would be 90 degree.

Let "x" be the unknown angle

x + 35  =  90

Subtract 35 on both sides

x  =  90 - 35

=  55

So, the complementary angle of 35 degree is 55.

Question 7 :

The sum of 2 consecutive integers is 75. Find the numbers.

(A)   37 and 38        (B)  47 and 28           (C)  28 and 37

Solution :

let x and x + 1 be two consecutive numbers

x + x + 1  =  75

2x + 1  =  75

Subtract both sides by 1

2x  =  74

Divide both sides by 2

x  =  74/2  =  37

So, the required numbers are 37 and 38.

Question 8 :

The percentage of literacy in a village is 47%. Find the number of illiterates in the village, if the population is 7,500.

(A)   6              (B)   8                 (C)  5

Solution :

Total population  =  7500

Percentage of illiterates  =  47

Number of illiterates  =  47% of 7500

  =  (47/100) ⋅ 7500

  =  47 (75)

  = 3525

So, the number of illiterates is 3525.

Question 9 :

The area of a trapezium is 102 sq. cm and its height is 12 cm. If one of its parallel sides is 8 cm. Find the length of the other side.

(A)  12 cm          (B)   9 cm             (C)   22 cm

Solution :

Area = 102 cm², h = 12 cm, a = 8 cm.

Area of a trapezium = 102

(1/2) h (a + b)= 102

(1/2) (12) (a + b)= 102

6 (8 + b) = 102

8 + b = 17 ==> b = 17 – 8 = 9

length of the other side = 9 cm

Question 10 :

Find out the circumference of a circle whose radius is 3.5 m.

(A)  22 m       (B)  32 m       (C)   42 m

Solution :

r  =  3.5 m

Circumference of a circle = 2∏ r

  =  2 ⋅ (22/7) ⋅ 3.5

  =  22 m

So, the circumference of the circle is 22 m.

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