Math Exam 1: Grade 7 ISCE

Section 1 (10 x 2 = 20)

1. A fraction that lies between 99/100 and 100/101 is _____________

2. The cube root of 2x is 4. Then x = _______________

3. x : y=x2: y

2 True/false? Justify!

4. The result of increasing a number by t % and reducing the obtained value by t %

will be __________ (bigger/smaller) than the original number.

5. Simple interest on Rs. 1400 for 2 years at 5% per annum is _____________

6. Sum of all interior angles of a _____________ is 1800 degrees

7. Can these be the measurements of the sides of a triangle: 4 cm, 5 cm, 10 cm ?

8. Perimeter of a square of area 100 sq cm = ___________________

9. A train covers 5 meters in 0.5 sec. Time taken to cover 7 km = _________________

10. The factors of 0.16 f2g

2− 0.6 f g are _______________________

Section 2 (10 x 3 = 30)

1. (2a

3)( x

2− 1)

= (9

4a2)(5− 3x

2)

; find 'x'

2. Locate a point that is 7 cm away from 2 points that are separated by a distance of 6

cm.

3. Isolate 'x' in 6 x2− 4 y + 3 = 7 a + b

4. It takes 2 years for an amount of money to grow to seven-sixths of itself with simple

interest. Find the rate % per annum.

5. 3 men of equal capacity can finish a work in 2 days. How long will it take if a fourth

person with half the capacity joins them?

6. A certain amount of money is divided among A, B & C in the ratio 1/3 : 1/2 : 1/5. If

C gets Rs. 1500, find how much A and B got.

7. Tug of war between Rhinos and Elephants! It's found that 7 Rhinos and 5 Elephants

are equally matched. What is the least number of Rhinos that can defeat 12

Elephants?

8. Here are the heights of 5 students: 170 cm, 1.6 m, 155 cm, 1.3m & x cm. If the

average is 1.5 m, find x.

9. Find a number that exactly divides 2340, but leaves a reminder of 40 and 51 when it

divides 1548 and 1663 respectively.

10. The mean height of 4 students is 150 cm. When a 5th students joins in, the average

height drops by 6%. Find the height of the 5th student.

Section 3 (10 x 5 = 50)

1. Derive a formula that relates Marked price, Discount, Cost Price, Selling Price,

Profit/Loss, Profit/Loss %

2. 3 alarms are set for 6:15 am, 5:50 am & 6:05 am. If left unattended they beep every

10, 15 and 20 min respectively. When would they first beep together? How many

times do they beep together before 10 am?

3. 17 soldiers have enough provisions left for 30 days. On the morning of day 5, 3

soldiers join in, and at the end of day 10, 10 soldiers leave. How many days will the

remaining provision last for the remaining soldiers?

4. A tractor or 5 bulls or 6 horses can plough a field in 2 days. How long will it take if

they all are put to work together? Also calculate how long it would take for 1 tractor

and 10 bulls and 15 horses working together.

5. (i) If a2−

1

a2

=5, find a4+ 1

a4

(ii) Solve 9952 using a suitable identity.

6. A store owner wants to make a profit of 12%. What percentage above the cost price

must he mark his goods, if he wants to allow a discount of 14%?

7. Construct a line parallel to a given line 10 cm away from it using compass and ruler.

State the principle used and explain the steps.

8. Results of Math, English and French are out! Here are the scores: 135/150, 94/100,

75/80. What should be the minimum score in Physics (in percentage) if the overall

percentage should exceed 90% ? (Maximum marks possible in Physics is 100)

9. Isolate any one variable of your choice in this equation.

7 a2+2 x+3 y

2

2b2

=1

3a

2+5 y2

10. In a small business the profit for the first year is 1.5L. And in the second year it

drops by 8% and the third year it grows by 15% (with respect to the 2nd year).

Express this data in a bar graph.