Practice Test on Framing the Formula

Math practice test on framing the formula will help us to practice math questions before the examination. Math practice test questions are mainly based on formulas, framing a formula, change the subject of the formula and find the value of the variable using change of subject of formula or an equation and method of substitution.

1. Write the formulas for the following statements.

(a) Area of the square is equal to the square of its side (a) .

(b) Area A of the rhombus is equal to half the product of its
diagonals (d₁, d₂).

(c) Perimeter (p) of a parallelogram is twice the sum of its adjacent sides.

(d) Area of four walls (A) of a room is the product of two times the sum of length (l), breadth (b) and height (h).

(e) Profit (P) is calculated by taking the difference of selling price (S) and cost price (C).

(f) Perimeter of the circle is 3.14 times the diameter (d) of the circle.

(g) The difference between a two-digit number and the number obtained by reversing the digits is 18.

(h) The sum (S) of all the interior angles of a regular polygon of n sides is 2 less than n times 180°.

(i) Subtracting 5/2 from a number and multiplying this difference by 8 gives three times the same number.

(j) Fifteen years from now Rachel's age will be four times her present age.

Practice Test on Framing the Formula

2. Change the subject of the formula and find the value of the new subject.

(a) V = 1/3 πr²h make the subject r. V is the volume of cone of height h. V = 2310 cm² h = 15 cm π = 22/7

(b) l² = r² + h², l is the slant height of the cone, r is the radius and h is the height. Make the subject h when l = 20 and r = 12.

(c) A = 1/2 × b × h where A is the area of triangle with base b and height h. Make h the subject, find h when A = 25, b = 12.

(d) D = d × q + r where D is the dividend, d the divisor, q is the quotient and r is the remainder. Make the subject r, when D = x² - x - 2, d = x - 3, q = x + 2.

(e) S.I. = (P × R × T)/100 where S.I. is the simple interest, P is the principal, R is the rate and T is the time. Make P the subject and find P when S.I. = $ 740, T = 2 years, R = 5%.

(f) H × L = a × b, where H denotes the H.C.F., L denotes L.C.M. and a and b denote the two numbers. Make L as the subject where H = 2, a = 4, b = 10.

(g) C = 5/9 (F - 32). C denotes Centigrade or Celsius scale and F the Fahrenheit scale. Make F the subject of the formula. Find F, when C = 37°.

(h) A = P (1 + r/100)ⁿ. Here A denotes the amount, P the principal, r the rate, n denotes the time. Find n when A = $ 8820, P = $ 8000, r = 5% p.a.

(i) S = 1/2 (a + b + c) where a, b, c are the 3 sides of the triangle whose semi-perimeter is S. S = 48 cm, a = 14, b = 18. Make c as the subject and find c.

(j) E = {(2n - 4) 90°}/n. E denotes each interior angle of polygon, x the number of a polygon. Make ‘n’ as the subject and find n if E = 135°.

Practice Test on Framing the Formula

3. If x boys collected a coins each and y girls collected b coins each of different countries, find the total number of coins collected.

4. If the base of the triangle is 2/3 times its height, then find the area of the triangle.

5. If x dolls cost $ y, what do z dolls cost?

6. If ‘p’ is the third proportional of q and r, then find r.

7. If a, b, c are in continued proportion, then find the value of b.

8. If x workers can build a wall in 12 days, in 16 days how many workers will build the wall.

9. A shirt is marked $ x and the shopkeeper allows a discount of 10% on it. What is its selling price?

10. A weighs 2 kg more than B and B weighs 7 kg less than C. If the weights of A, B, C is m, find the weights of A, B, C separately.

11. Find the number of deer in the herd if half of the deer are grazing in the field and 3/4th of the remaining are drinking water and the rest p are drinking water.

12. Five years ago, Arnold whose present age is twice his sister's age was three times his sister's age Find their present ages.

13. A car travels 10 km at the speed of x km/hr. Find the time taken by the car to reach the destination.

14. Mohan had $ 192 with him. He purchased x kg potatoes for $ 10 a kg and y kg tomatoes for $ 20 a kg and z kg onions at $ 12 a kg. Find the money left with him.

Answers for practice test on framing the formula are given below to check the exact answers of the above questions on formulas.