Practice Question Papers · with Answers

CBSE / NCERT Class 7 Maths Practice Question Papers

Download free CBSE / NCERT Class 7 Maths practice question papers with full answer keys. These are original Brain Grain model papers — built from our verified question bank to the real exam blueprint (sections, marks and solutions) — perfect for board revision and model tests.

Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Class: 7CBSE / NCERTMax Marks: 24
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

1.Exercise 7.1 asks students to convert fractions and decimals to percentages, convert percentages to fractions or decimals, find percentages of quantities, find whole quantities from percentages, compare percentages and solve percentage word problems.[2]
2.Exercise 11.2 asks students to simplify expressions using laws of exponents, say true or false with justification, express products in prime-factor exponential form and simplify expressions involving powers and variables.[2]
3.1. Find: (i) $12\div\frac{3}{4}$[2]
4.1. Set up equations and solve them to find the unknown numbers in statements (a) to (g). 2. Solve the word problems on lowest score, equal angles, and runs scored by Sachin and Rahul. 3. Solve the given age and number problems. 4. Solve the perimeter problem in the exercise.[2]
5.Exercise 11.1 asks students to evaluate powers, express repeated products in exponential form, write numbers as powers, express numbers as products of prime factors in exponential form, simplify expressions using powers, evaluate powers with negative bases and compare large numbers written in standard form.[2]
6.Exercise 8.2 asks students to add, subtract, multiply and divide rational numbers in the listed subparts.[2]
7.1. Find: (i) $0.2\times6$[2]
8.Exercise 10.2 asks students to add and subtract algebraic expressions, simplify expressions, evaluate simplified expressions for given variable values, and solve a perimeter/algebraic-expression problem.[2]
9.1. Give first the step you will use to separate the variable and then solve the equation. 2. Give the steps you will use to separate the variable and then solve the equation. 3. Solve the equations given in paired form. 4. Solve the listed simple equations involving $p,s,q$[2]
10.1. Find: (i) $0.4\div2$[2]
11.Exercise 7.2 asks questions on profit, loss, profit percentage, loss percentage, discount, sales tax, simple interest, amount and rate/time/principal word problems.[2]
12.1. Find each of the following products: (a) $3\times(-1)$[2]
🔑 Show Answer Key — Set 1
  1. 1. 1. (a) $12.5\%$ (b) $125\%$ (c) $7.5\%$ (d) $28\frac{4}{7}\%$ . 2. (a) $65\%$ (b) $210\%$ (c) $2\%$ (d) $1235\%$ . 3. (i) $25\%$ (ii) $\frac{3}{5};60\%$ (iii) $\frac{3}{8};37.5\%$ . 4. (a) 37.5 (b) $\frac{3}{5}$ minute or 36 seconds (c) Rs 500 (d) 0.75 kg or 750 g. 5. (a) 12000 (b) Rs 9000 (c) 1250 km (d) 20 minutes (e) 500 litres. 6. (a) $0.25;\frac{1}{4}$ (b) $1.5;\frac{3}{2}$ (c) $0.2;\frac{1}{5}$ (d) $0.05;\frac{1}{20}$ . 7. $30\%$ . 8. $40\%;6000$ . 9. Rs 40,000. 10. 5 matches.
  2. 2. 1. (i) $3^{14}$ (ii) $6^5$ (iii) $a^5$ (iv) $7^{x+2}$ (v) $5^3$ (vi) $10^5$ (vii) $(ab)^4$ (viii) $3^{12}$ (ix) $2^8$ (x) $8^{t-2}$ . 2. (i) $3^3$ (ii) $5^3$ (iii) $5^5$ (iv) $7\times11^5$ (v) $3^0$ or 1 (vi) 3 (vii) 1 (viii) 2 (ix) $(2a)^2$ (x) $a^{10}$ (xi) $a^3b$ (xii) $2^8$ . 3. (i) False; $10\times10^{11}=10^{12}$ and $(100)^{11}=10^{22}$ (ii) False; $2^3=8$ , $5^2=25$ (iii) False; $6^5=2^5\times3^5$ (iv) True; $3^0=1$ , $(1000)^0=1$ . 4. (i) $2^8\times3^4$ (ii) $2\times3^3\times5$ (iii) $3^6\times2^6$ (iv) $2^8\times3$ . 5. (i) 98 (ii) $\frac{4}{5t^8}$ (iii) 1.
  3. 3. 1. (i) 16 (ii) $\frac{84}{5}$ (iii) $\frac{24}{7}$ (iv) $\frac{3}{2}$ (v) $\frac{9}{7}$ (vi) $\frac{7}{5}$ . 2. (i) $\frac{7}{3}$ , improper fraction (ii) $\frac{8}{5}$ , improper fraction (iii) $\frac{7}{9}$ , proper fraction (iv) $\frac{5}{6}$ , proper fraction (v) $\frac{7}{12}$ , proper fraction (vi) $8$ , whole number (vii) $11$ , whole number. 3. (i) $\frac{2}{21}$ (ii) $\frac{5}{36}$ (iii) $\frac{7}{78}$ (iv) $\frac{5}{6}$ (v) $\frac{11}{14}$ (vi) $\frac{13}{14}$ . 4. (i) $\frac{4}{5}$ (ii) $\frac{2}{3}$ (iii) $\frac{3}{8}$ (iv) $\frac{35}{54}$ (v) $14$ (vi) $\frac{14}{5}$ (vii) $\frac{48}{25}$ (viii) $1$ .
  4. 4. 1. (a) $8x+4=60$ , $x=7$ (b) $\frac{x}{5}-4=3$ , $x=35$ (c) $\frac{3y}{4}+3=21$ , $y=24$ (d) $2m-11=15$ , $m=13$ (e) $50-3x=8$ , $x=14$ (f) $\frac{x+19}{5}=8$ , $x=21$ (g) $\frac{5n}{2}-7=23$ , $n=12$ . 2. (a) Lowest score $=40$ (b) $70^\circ$ each (c) Sachin: 132 runs, Rahul: 66 runs. 3. (i) 6 (ii) 15 years (iii) 25. 4. 30.
  5. 5. 1. (i) 64 (ii) 729 (iii) 121 (iv) 625. 2. (i) 64 (ii) $t^2$ (iii) $b^4$ (iv) $5^2\times7^3$ (v) $2^2\times a^2$ (vi) $a^3\times c^4\times d$ . 3. (i) $2^9$ (ii) $7^3$ (iii) $3^6$ (iv) $5^5$ . 4. (i) $3^4$ (ii) $3^5$ (iii) $2^8$ (iv) $2^{100}$ (v) $2^{10}$ . 5. (i) $2^3\times3^4$ (ii) $5\times3^4$ (iii) $2^2\times3^3\times5$ (iv) $2^4\times3^2\times5^2$ . 6. (i) 2000 (ii) 196 (iii) 40 (iv) 768 (v) 0 (vi) 675 (vii) 144 (viii) 90000. 7. (i) $-64$ (ii) 24 (iii) 225 (iv) 8000. 8. (i) $2.7\times10^{12}>1.5\times10^8$ (ii) $4\times10^{14}<3\times10^{17}$ .
  6. 6. 1. (i) $-\frac{3}{2}$ (ii) $\frac{34}{15}$ (iii) $\frac{17}{30}$ (iv) $\frac{82}{99}$ (v) $-\frac{26}{57}$ (vi) $-\frac{2}{3}$ (vii) $\frac{34}{15}$ . 2. (i) $-\frac{13}{72}$ (ii) $\frac{23}{63}$ (iii) $\frac{1}{195}$ (iv) $-\frac{89}{88}$ (v) $-\frac{73}{9}$ . 3. (i) $-\frac{63}{8}$ (ii) $-\frac{27}{10}$ (iii) $-\frac{54}{55}$ (iv) $-\frac{6}{35}$ (v) $\frac{6}{55}$ (vi) 1. 4. (i) $-6$ (ii) $-\frac{3}{10}$ (iii) $\frac{4}{15}$ (iv) $-\frac{1}{6}$ (v) $-\frac{14}{13}$ (vi) $\frac{91}{24}$ (vii) $-\frac{15}{4}$ .
  7. 7. 1. (i) 1.2 (ii) 36.8 (iii) 13.55 (iv) 80.4 (v) 0.35 (vi) 844.08 (vii) 1.72. 2. $17.1\text{ cm}^2$ . 3. (i) 13 (ii) 368 (iii) 1537 (iv) 1680.7 (v) 3110 (vi) 15610 (vii) 362 (viii) 4307 (ix) 5 (x) 0.8 (xi) 90 (xii) 30. 4. 553 km. 5. (i) 0.75 (ii) 5.17 (iii) 63.36 (iv) 4.03 (v) 0.025 (vi) 1.68 (vii) 0.0214 (viii) 10.5525 (ix) 1.0101 (x) 110.011.
  8. 8. 1. (i) 0 (ii) 1 (iii) $-1$ (iv) 1 (v) 1. 2. (i) $-1$ (ii) $-13$ (iii) 3. 3. (i) $-9$ (ii) 3 (iii) 0 (iv) 1. 4. (i) 8 (ii) 4 (iii) 0. 5. (i) $-2$ (ii) 2 (iii) 0 (iv) 2. 6. (i) $5x-13$ ; at $x=2$ , value $=-3$ (ii) $8x-1$ ; value $15$ (iii) $11x-10$ ; value $12$ (iv) $11x+7$ ; value $29$ . 7. (i) $2x+4$ ; 10 (ii) $-4x+6$ ; $-6$ (iii) $-5a+6$ ; 11 (iv) $-8b+6$ ; 22 (v) $3a-2b-9$ ; $-8$ . 8. (i) 1000 (ii) 20. 9. $-5$ . 10. $2a^2+ab+3$ ; value $38$ .
  9. 9. 1. (a) Add 1 to both sides; $x=1$ (b) Subtract 1 from both sides; $x=-1$ (c) Add 1 to both sides; $x=6$ (d) Subtract 6 from both sides; $x=-4$ (e) Add 4 to both sides; $y=-3$ (f) Add 4 to both sides; $y=8$ (g) Subtract 4 from both sides; $y=0$ (h) Subtract 4 from both sides; $y=-8$ . 2. (a) Divide both sides by 3; $l=14$ (b) Multiply both sides by 2; $b=12$ (c) Multiply both sides by 7; $p=28$ (d) Divide both sides by 4; $x=\frac{25}{4}$ (e) Divide both sides by 8; $y=\frac{36}{8}$ (f) Multiply both sides by 3; $z=\frac{15}{4}$ (g) Multiply both sides by 5; $a=\frac{7}{3}$ (h) Divide both sides by 20; $t=\frac{1}{2}$ . 3. (a) Add 2 to both sides, then divide by 3; $n=16$ . (b) Subtract 7…
  10. 10. 1. (i) 0.2 (ii) 0.07 (iii) 0.62 (iv) 10.9 (v) 162.8 (vi) 2.07 (vii) 0.99 (viii) 0.16. 2. (i) 0.48 (ii) 5.25 (iii) 0.07 (iv) 3.31 (v) 27.223 (vi) 0.056 (vii) 0.397. 3. (i) 0.027 (ii) 0.003 (iii) 0.0078 (iv) 4.326 (v) 0.236 (vi) 0.9853. 4. (i) 0.0079 (ii) 0.0263 (iii) 0.03853 (iv) 0.1289 (v) 0.0005. 5. (i) 2 (ii) 180 (iii) 6.5 (iv) 44.2 (v) 2 (vi) 31 (vii) 510 (viii) 27 (ix) 2.1. 6. 18 km.
  11. 11. 1. (a) Profit = Rs 75; Profit % = 30 (b) Profit = Rs 1500; Profit % = 12.5 (c) Profit = Rs 500; Profit % = 20 (d) Loss = Rs 100; Loss % = 40. 2. (a) $75\%;25\%$ (b) $20\%,30\%,50\%$ (c) $20\%;80\%$ (d) $12.5\%;25\%;62.5\%$ . 3. $2\%$ . 4. $5\frac{5}{7}\%$ . 5. Rs 12,000. 6. Rs 16,875. 7. (i) $12\%$ (ii) 25 g. 8. Rs 233.75. 9. (a) Rs 1,632 (b) Rs 8,625. 10. $0.25\%$ . 11. Rs 500.
  12. 12. 1. (a) $-3$ (b) $-225$ (c) $630$ (d) $316$ (e) $0$ (f) $1320$ (g) $162$ (h) $-360$ (i) $-24$ (j) $36$ . 2. (a) LHS $=18\times4=72$ and RHS $=126-54=72$ . (b) LHS $=(-21)\times(-10)=210$ and RHS $=84+126=210$ . 3. (i) $(-1)\times a=-a$ (ii) (a) $22$ (b) $-37$ (c) $0$ . 4. A pattern is $-1\times5=-5$ , $-1\times4=-4$ , $-1\times3=-3$ , $-1\times2=-2$ , $-1\times1=-1$ , $-1\times0=0$ , so continuing the pattern gives $-1\times(-1)=1$ .
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 7CBSE / NCERTMax Marks: 24
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

1.1. Write the following numbers in the expanded forms: 279404, 3006194, 2806196, 120719, 20068. 2. Find the number from each of the following expanded forms: (a) $8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^0$[2]
2.1. Find: (i) $\frac{1}{4}$[2]
3.1. Evaluate each of the following: (a) $(-30)\div10$[2]
4.1. Write down a pair of integers whose: (a) sum is -7 (b) difference is -10 (c) sum is 0 2. (a) Write a pair of negative integers whose difference gives 8. (b) Write a negative integer and a positive integer whose sum is -5. (c) Write a negative integer and a positive integer whose difference is -3. 3. In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order? 4. Fill in the blanks to make the following statements true: (i) $(-5)+(-8)=(-8)+(\ldots)$[2]
5.Exercise 6.4 asks whether triangles can be constructed from given side lengths and uses the triangle inequality property.[2]
6.Exercise 7.1 asks students to convert fractions and decimals to percentages, convert percentages to fractions or decimals, find percentages of quantities, find whole quantities from percentages, compare percentages and solve percentage word problems.[2]
7.Exercise 11.2 asks students to simplify expressions using laws of exponents, say true or false with justification, express products in prime-factor exponential form and simplify expressions involving powers and variables.[2]
8.1. Find: (i) $12\div\frac{3}{4}$[2]
9.1. Set up equations and solve them to find the unknown numbers in statements (a) to (g). 2. Solve the word problems on lowest score, equal angles, and runs scored by Sachin and Rahul. 3. Solve the given age and number problems. 4. Solve the perimeter problem in the exercise.[2]
10.Exercise 11.1 asks students to evaluate powers, express repeated products in exponential form, write numbers as powers, express numbers as products of prime factors in exponential form, simplify expressions using powers, evaluate powers with negative bases and compare large numbers written in standard form.[2]
11.Exercise 8.2 asks students to add, subtract, multiply and divide rational numbers in the listed subparts.[2]
12.1. Find: (i) $0.2\times6$[2]
🔑 Show Answer Key — Set 2
  1. 1. 1. $279404=2\times10^5+7\times10^4+9\times10^3+4\times10^2+0\times10^1+4\times10^0$ ; $3006194=3\times10^6+0\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+4\times10^0$ ; $2806196=2\times10^6+8\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+6\times10^0$ ; $120719=1\times10^5+2\times10^4+0\times10^3+7\times10^2+1\times10^1+9\times10^0$ ; $20068=2\times10^4+0\times10^3+0\times10^2+6\times10^1+8\times10^0$ . 2. (a) 86045 (b) 405302 (c) 30705 (d) 900230. 3. (i) $5\times10^7$ (ii) $7\times10^6$ (iii) $3.1865\times10^9$ (iv) $3.90878\times10^5$ (v) $3.90878\times10^4$ (vi) $3.90878\times10^3$ . 4. (a) $3.84\times10^8$ m (b) $3\times10^8$ m/s (c) $1.2756\times10^7$ m (d) $1…
  2. 2. 1. (i) (a) $\frac{1}{16}$ (b) $\frac{3}{20}$ (c) $\frac{1}{3}$ (ii) (a) $\frac{2}{63}$ (b) $\frac{6}{35}$ (c) $\frac{3}{70}$ . 2. (i) $1\frac{7}{9}$ (ii) $\frac{2}{9}$ (iii) $\frac{9}{16}$ (iv) $\frac{27}{25}$ or $1\frac{2}{25}$ (v) $\frac{5}{8}$ (vi) $1\frac{13}{20}$ (vii) $1\frac{13}{35}$ . 3. (i) $2\frac{1}{10}$ (ii) $4\frac{44}{45}$ (iii) $\frac{13}{15}$ (iv) $10\frac{1}{14}$ (v) $20\frac{33}{35}$ (vi) $2\frac{2}{5}$ (vii) $13\frac{1}{35}$ . 4. (i) $\frac{3}{5}$ of $\frac{5}{8}$ is greater. (ii) Both are equal, $\frac{3}{7}$ . 5. $2\frac{1}{4}$ m. 6. $10\frac{1}{2}$ hours. 7. 44 km. 8. (a) (i) $\frac{5}{10}$ (ii) $\frac{1}{2}$ (b) (i) $\frac{8}{15}$ (ii) $\frac{8}{15}$ .
  3. 3. 1. (a) $-3$ (b) $-10$ (c) $4$ (d) $-1$ (e) $-13$ (f) $0$ (g) $1$ (h) $-1$ (i) $1$ . 2. (a) $12\div(-2)=-6$ , while $12\div(-4)+12\div2=-3+6=3$ , so they are not equal. (b) $-10\div2=-5$ , while $-10\div1+(-10)\div1=-20$ , so they are not equal. 3. (a) $1$ (b) $75$ (c) $-206$ (d) $-1$ (e) $-87$ (f) $-48$ (g) $-10$ (h) $-12$ . 4. Examples: $(-6,2)$ , $(-12,4)$ , $(12,-4)$ , $(9,-3)$ , $(-9,3)$ . 5. The temperature is $-8^\circ C$ at 9 p.m.; at midnight it is $-14^\circ C$ . 6. (i) 8 incorrect answers (ii) 13 incorrect answers. 7. It will take 1 hour.
  4. 4. 1. One possible set of answers is: (a) $-10, 3$ (b) $-6, 4$ because $-6-4=-10$ (c) $-3, 3$ . 2. One possible set is: (a) $-2, -10$ because $-2-(-10)=8$ (b) $-6, 1$ (c) $-1, 2$ because $-1-2=-3$ . 3. Both teams scored the same total, $-30$ . Yes, integers can be added in any order. 4. (i) $-5$ (ii) $0$ (iii) $-17$ (iv) $-7$ (v) $-3$ .
  5. 5. 1. (i) Not possible (ii) Possible (iii) Not possible. 2. (i) Yes (ii) Yes (iii) Yes. 3. Yes. 4. Yes. 5. Yes. 6. The third side must be between 3 and 27.
  6. 6. 1. (a) $12.5\%$ (b) $125\%$ (c) $7.5\%$ (d) $28\frac{4}{7}\%$ . 2. (a) $65\%$ (b) $210\%$ (c) $2\%$ (d) $1235\%$ . 3. (i) $25\%$ (ii) $\frac{3}{5};60\%$ (iii) $\frac{3}{8};37.5\%$ . 4. (a) 37.5 (b) $\frac{3}{5}$ minute or 36 seconds (c) Rs 500 (d) 0.75 kg or 750 g. 5. (a) 12000 (b) Rs 9000 (c) 1250 km (d) 20 minutes (e) 500 litres. 6. (a) $0.25;\frac{1}{4}$ (b) $1.5;\frac{3}{2}$ (c) $0.2;\frac{1}{5}$ (d) $0.05;\frac{1}{20}$ . 7. $30\%$ . 8. $40\%;6000$ . 9. Rs 40,000. 10. 5 matches.
  7. 7. 1. (i) $3^{14}$ (ii) $6^5$ (iii) $a^5$ (iv) $7^{x+2}$ (v) $5^3$ (vi) $10^5$ (vii) $(ab)^4$ (viii) $3^{12}$ (ix) $2^8$ (x) $8^{t-2}$ . 2. (i) $3^3$ (ii) $5^3$ (iii) $5^5$ (iv) $7\times11^5$ (v) $3^0$ or 1 (vi) 3 (vii) 1 (viii) 2 (ix) $(2a)^2$ (x) $a^{10}$ (xi) $a^3b$ (xii) $2^8$ . 3. (i) False; $10\times10^{11}=10^{12}$ and $(100)^{11}=10^{22}$ (ii) False; $2^3=8$ , $5^2=25$ (iii) False; $6^5=2^5\times3^5$ (iv) True; $3^0=1$ , $(1000)^0=1$ . 4. (i) $2^8\times3^4$ (ii) $2\times3^3\times5$ (iii) $3^6\times2^6$ (iv) $2^8\times3$ . 5. (i) 98 (ii) $\frac{4}{5t^8}$ (iii) 1.
  8. 8. 1. (i) 16 (ii) $\frac{84}{5}$ (iii) $\frac{24}{7}$ (iv) $\frac{3}{2}$ (v) $\frac{9}{7}$ (vi) $\frac{7}{5}$ . 2. (i) $\frac{7}{3}$ , improper fraction (ii) $\frac{8}{5}$ , improper fraction (iii) $\frac{7}{9}$ , proper fraction (iv) $\frac{5}{6}$ , proper fraction (v) $\frac{7}{12}$ , proper fraction (vi) $8$ , whole number (vii) $11$ , whole number. 3. (i) $\frac{2}{21}$ (ii) $\frac{5}{36}$ (iii) $\frac{7}{78}$ (iv) $\frac{5}{6}$ (v) $\frac{11}{14}$ (vi) $\frac{13}{14}$ . 4. (i) $\frac{4}{5}$ (ii) $\frac{2}{3}$ (iii) $\frac{3}{8}$ (iv) $\frac{35}{54}$ (v) $14$ (vi) $\frac{14}{5}$ (vii) $\frac{48}{25}$ (viii) $1$ .
  9. 9. 1. (a) $8x+4=60$ , $x=7$ (b) $\frac{x}{5}-4=3$ , $x=35$ (c) $\frac{3y}{4}+3=21$ , $y=24$ (d) $2m-11=15$ , $m=13$ (e) $50-3x=8$ , $x=14$ (f) $\frac{x+19}{5}=8$ , $x=21$ (g) $\frac{5n}{2}-7=23$ , $n=12$ . 2. (a) Lowest score $=40$ (b) $70^\circ$ each (c) Sachin: 132 runs, Rahul: 66 runs. 3. (i) 6 (ii) 15 years (iii) 25. 4. 30.
  10. 10. 1. (i) 64 (ii) 729 (iii) 121 (iv) 625. 2. (i) 64 (ii) $t^2$ (iii) $b^4$ (iv) $5^2\times7^3$ (v) $2^2\times a^2$ (vi) $a^3\times c^4\times d$ . 3. (i) $2^9$ (ii) $7^3$ (iii) $3^6$ (iv) $5^5$ . 4. (i) $3^4$ (ii) $3^5$ (iii) $2^8$ (iv) $2^{100}$ (v) $2^{10}$ . 5. (i) $2^3\times3^4$ (ii) $5\times3^4$ (iii) $2^2\times3^3\times5$ (iv) $2^4\times3^2\times5^2$ . 6. (i) 2000 (ii) 196 (iii) 40 (iv) 768 (v) 0 (vi) 675 (vii) 144 (viii) 90000. 7. (i) $-64$ (ii) 24 (iii) 225 (iv) 8000. 8. (i) $2.7\times10^{12}>1.5\times10^8$ (ii) $4\times10^{14}<3\times10^{17}$ .
  11. 11. 1. (i) $-\frac{3}{2}$ (ii) $\frac{34}{15}$ (iii) $\frac{17}{30}$ (iv) $\frac{82}{99}$ (v) $-\frac{26}{57}$ (vi) $-\frac{2}{3}$ (vii) $\frac{34}{15}$ . 2. (i) $-\frac{13}{72}$ (ii) $\frac{23}{63}$ (iii) $\frac{1}{195}$ (iv) $-\frac{89}{88}$ (v) $-\frac{73}{9}$ . 3. (i) $-\frac{63}{8}$ (ii) $-\frac{27}{10}$ (iii) $-\frac{54}{55}$ (iv) $-\frac{6}{35}$ (v) $\frac{6}{55}$ (vi) 1. 4. (i) $-6$ (ii) $-\frac{3}{10}$ (iii) $\frac{4}{15}$ (iv) $-\frac{1}{6}$ (v) $-\frac{14}{13}$ (vi) $\frac{91}{24}$ (vii) $-\frac{15}{4}$ .
  12. 12. 1. (i) 1.2 (ii) 36.8 (iii) 13.55 (iv) 80.4 (v) 0.35 (vi) 844.08 (vii) 1.72. 2. $17.1\text{ cm}^2$ . 3. (i) 13 (ii) 368 (iii) 1537 (iv) 1680.7 (v) 3110 (vi) 15610 (vii) 362 (viii) 4307 (ix) 5 (x) 0.8 (xi) 90 (xii) 30. 4. 553 km. 5. (i) 0.75 (ii) 5.17 (iii) 63.36 (iv) 4.03 (v) 0.025 (vi) 1.68 (vii) 0.0214 (viii) 10.5525 (ix) 1.0101 (x) 110.011.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 7CBSE / NCERTMax Marks: 24
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 12 × 2 = 24

Answer briefly. (Answer all questions.)

1.Exercise 10.2 asks students to add and subtract algebraic expressions, simplify expressions, evaluate simplified expressions for given variable values, and solve a perimeter/algebraic-expression problem.[2]
2.1. Give first the step you will use to separate the variable and then solve the equation. 2. Give the steps you will use to separate the variable and then solve the equation. 3. Solve the equations given in paired form. 4. Solve the listed simple equations involving $p,s,q$[2]
3.1. Find: (i) $0.4\div2$[2]
4.Exercise 7.2 asks questions on profit, loss, profit percentage, loss percentage, discount, sales tax, simple interest, amount and rate/time/principal word problems.[2]
5.1. Find each of the following products: (a) $3\times(-1)$[2]
6.1. Write the following numbers in the expanded forms: 279404, 3006194, 2806196, 120719, 20068. 2. Find the number from each of the following expanded forms: (a) $8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^0$[2]
7.1. Find: (i) $\frac{1}{4}$[2]
8.1. Evaluate each of the following: (a) $(-30)\div10$[2]
9.1. Write down a pair of integers whose: (a) sum is -7 (b) difference is -10 (c) sum is 0 2. (a) Write a pair of negative integers whose difference gives 8. (b) Write a negative integer and a positive integer whose sum is -5. (c) Write a negative integer and a positive integer whose difference is -3. 3. In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order? 4. Fill in the blanks to make the following statements true: (i) $(-5)+(-8)=(-8)+(\ldots)$[2]
10.Exercise 6.4 asks whether triangles can be constructed from given side lengths and uses the triangle inequality property.[2]
11.Exercise 7.1 asks students to convert fractions and decimals to percentages, convert percentages to fractions or decimals, find percentages of quantities, find whole quantities from percentages, compare percentages and solve percentage word problems.[2]
12.Exercise 11.2 asks students to simplify expressions using laws of exponents, say true or false with justification, express products in prime-factor exponential form and simplify expressions involving powers and variables.[2]
🔑 Show Answer Key — Set 3
  1. 1. 1. (i) 0 (ii) 1 (iii) $-1$ (iv) 1 (v) 1. 2. (i) $-1$ (ii) $-13$ (iii) 3. 3. (i) $-9$ (ii) 3 (iii) 0 (iv) 1. 4. (i) 8 (ii) 4 (iii) 0. 5. (i) $-2$ (ii) 2 (iii) 0 (iv) 2. 6. (i) $5x-13$ ; at $x=2$ , value $=-3$ (ii) $8x-1$ ; value $15$ (iii) $11x-10$ ; value $12$ (iv) $11x+7$ ; value $29$ . 7. (i) $2x+4$ ; 10 (ii) $-4x+6$ ; $-6$ (iii) $-5a+6$ ; 11 (iv) $-8b+6$ ; 22 (v) $3a-2b-9$ ; $-8$ . 8. (i) 1000 (ii) 20. 9. $-5$ . 10. $2a^2+ab+3$ ; value $38$ .
  2. 2. 1. (a) Add 1 to both sides; $x=1$ (b) Subtract 1 from both sides; $x=-1$ (c) Add 1 to both sides; $x=6$ (d) Subtract 6 from both sides; $x=-4$ (e) Add 4 to both sides; $y=-3$ (f) Add 4 to both sides; $y=8$ (g) Subtract 4 from both sides; $y=0$ (h) Subtract 4 from both sides; $y=-8$ . 2. (a) Divide both sides by 3; $l=14$ (b) Multiply both sides by 2; $b=12$ (c) Multiply both sides by 7; $p=28$ (d) Divide both sides by 4; $x=\frac{25}{4}$ (e) Divide both sides by 8; $y=\frac{36}{8}$ (f) Multiply both sides by 3; $z=\frac{15}{4}$ (g) Multiply both sides by 5; $a=\frac{7}{3}$ (h) Divide both sides by 20; $t=\frac{1}{2}$ . 3. (a) Add 2 to both sides, then divide by 3; $n=16$ . (b) Subtract 7…
  3. 3. 1. (i) 0.2 (ii) 0.07 (iii) 0.62 (iv) 10.9 (v) 162.8 (vi) 2.07 (vii) 0.99 (viii) 0.16. 2. (i) 0.48 (ii) 5.25 (iii) 0.07 (iv) 3.31 (v) 27.223 (vi) 0.056 (vii) 0.397. 3. (i) 0.027 (ii) 0.003 (iii) 0.0078 (iv) 4.326 (v) 0.236 (vi) 0.9853. 4. (i) 0.0079 (ii) 0.0263 (iii) 0.03853 (iv) 0.1289 (v) 0.0005. 5. (i) 2 (ii) 180 (iii) 6.5 (iv) 44.2 (v) 2 (vi) 31 (vii) 510 (viii) 27 (ix) 2.1. 6. 18 km.
  4. 4. 1. (a) Profit = Rs 75; Profit % = 30 (b) Profit = Rs 1500; Profit % = 12.5 (c) Profit = Rs 500; Profit % = 20 (d) Loss = Rs 100; Loss % = 40. 2. (a) $75\%;25\%$ (b) $20\%,30\%,50\%$ (c) $20\%;80\%$ (d) $12.5\%;25\%;62.5\%$ . 3. $2\%$ . 4. $5\frac{5}{7}\%$ . 5. Rs 12,000. 6. Rs 16,875. 7. (i) $12\%$ (ii) 25 g. 8. Rs 233.75. 9. (a) Rs 1,632 (b) Rs 8,625. 10. $0.25\%$ . 11. Rs 500.
  5. 5. 1. (a) $-3$ (b) $-225$ (c) $630$ (d) $316$ (e) $0$ (f) $1320$ (g) $162$ (h) $-360$ (i) $-24$ (j) $36$ . 2. (a) LHS $=18\times4=72$ and RHS $=126-54=72$ . (b) LHS $=(-21)\times(-10)=210$ and RHS $=84+126=210$ . 3. (i) $(-1)\times a=-a$ (ii) (a) $22$ (b) $-37$ (c) $0$ . 4. A pattern is $-1\times5=-5$ , $-1\times4=-4$ , $-1\times3=-3$ , $-1\times2=-2$ , $-1\times1=-1$ , $-1\times0=0$ , so continuing the pattern gives $-1\times(-1)=1$ .
  6. 6. 1. $279404=2\times10^5+7\times10^4+9\times10^3+4\times10^2+0\times10^1+4\times10^0$ ; $3006194=3\times10^6+0\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+4\times10^0$ ; $2806196=2\times10^6+8\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+6\times10^0$ ; $120719=1\times10^5+2\times10^4+0\times10^3+7\times10^2+1\times10^1+9\times10^0$ ; $20068=2\times10^4+0\times10^3+0\times10^2+6\times10^1+8\times10^0$ . 2. (a) 86045 (b) 405302 (c) 30705 (d) 900230. 3. (i) $5\times10^7$ (ii) $7\times10^6$ (iii) $3.1865\times10^9$ (iv) $3.90878\times10^5$ (v) $3.90878\times10^4$ (vi) $3.90878\times10^3$ . 4. (a) $3.84\times10^8$ m (b) $3\times10^8$ m/s (c) $1.2756\times10^7$ m (d) $1…
  7. 7. 1. (i) (a) $\frac{1}{16}$ (b) $\frac{3}{20}$ (c) $\frac{1}{3}$ (ii) (a) $\frac{2}{63}$ (b) $\frac{6}{35}$ (c) $\frac{3}{70}$ . 2. (i) $1\frac{7}{9}$ (ii) $\frac{2}{9}$ (iii) $\frac{9}{16}$ (iv) $\frac{27}{25}$ or $1\frac{2}{25}$ (v) $\frac{5}{8}$ (vi) $1\frac{13}{20}$ (vii) $1\frac{13}{35}$ . 3. (i) $2\frac{1}{10}$ (ii) $4\frac{44}{45}$ (iii) $\frac{13}{15}$ (iv) $10\frac{1}{14}$ (v) $20\frac{33}{35}$ (vi) $2\frac{2}{5}$ (vii) $13\frac{1}{35}$ . 4. (i) $\frac{3}{5}$ of $\frac{5}{8}$ is greater. (ii) Both are equal, $\frac{3}{7}$ . 5. $2\frac{1}{4}$ m. 6. $10\frac{1}{2}$ hours. 7. 44 km. 8. (a) (i) $\frac{5}{10}$ (ii) $\frac{1}{2}$ (b) (i) $\frac{8}{15}$ (ii) $\frac{8}{15}$ .
  8. 8. 1. (a) $-3$ (b) $-10$ (c) $4$ (d) $-1$ (e) $-13$ (f) $0$ (g) $1$ (h) $-1$ (i) $1$ . 2. (a) $12\div(-2)=-6$ , while $12\div(-4)+12\div2=-3+6=3$ , so they are not equal. (b) $-10\div2=-5$ , while $-10\div1+(-10)\div1=-20$ , so they are not equal. 3. (a) $1$ (b) $75$ (c) $-206$ (d) $-1$ (e) $-87$ (f) $-48$ (g) $-10$ (h) $-12$ . 4. Examples: $(-6,2)$ , $(-12,4)$ , $(12,-4)$ , $(9,-3)$ , $(-9,3)$ . 5. The temperature is $-8^\circ C$ at 9 p.m.; at midnight it is $-14^\circ C$ . 6. (i) 8 incorrect answers (ii) 13 incorrect answers. 7. It will take 1 hour.
  9. 9. 1. One possible set of answers is: (a) $-10, 3$ (b) $-6, 4$ because $-6-4=-10$ (c) $-3, 3$ . 2. One possible set is: (a) $-2, -10$ because $-2-(-10)=8$ (b) $-6, 1$ (c) $-1, 2$ because $-1-2=-3$ . 3. Both teams scored the same total, $-30$ . Yes, integers can be added in any order. 4. (i) $-5$ (ii) $0$ (iii) $-17$ (iv) $-7$ (v) $-3$ .
  10. 10. 1. (i) Not possible (ii) Possible (iii) Not possible. 2. (i) Yes (ii) Yes (iii) Yes. 3. Yes. 4. Yes. 5. Yes. 6. The third side must be between 3 and 27.
  11. 11. 1. (a) $12.5\%$ (b) $125\%$ (c) $7.5\%$ (d) $28\frac{4}{7}\%$ . 2. (a) $65\%$ (b) $210\%$ (c) $2\%$ (d) $1235\%$ . 3. (i) $25\%$ (ii) $\frac{3}{5};60\%$ (iii) $\frac{3}{8};37.5\%$ . 4. (a) 37.5 (b) $\frac{3}{5}$ minute or 36 seconds (c) Rs 500 (d) 0.75 kg or 750 g. 5. (a) 12000 (b) Rs 9000 (c) 1250 km (d) 20 minutes (e) 500 litres. 6. (a) $0.25;\frac{1}{4}$ (b) $1.5;\frac{3}{2}$ (c) $0.2;\frac{1}{5}$ (d) $0.05;\frac{1}{20}$ . 7. $30\%$ . 8. $40\%;6000$ . 9. Rs 40,000. 10. 5 matches.
  12. 12. 1. (i) $3^{14}$ (ii) $6^5$ (iii) $a^5$ (iv) $7^{x+2}$ (v) $5^3$ (vi) $10^5$ (vii) $(ab)^4$ (viii) $3^{12}$ (ix) $2^8$ (x) $8^{t-2}$ . 2. (i) $3^3$ (ii) $5^3$ (iii) $5^5$ (iv) $7\times11^5$ (v) $3^0$ or 1 (vi) 3 (vii) 1 (viii) 2 (ix) $(2a)^2$ (x) $a^{10}$ (xi) $a^3b$ (xii) $2^8$ . 3. (i) False; $10\times10^{11}=10^{12}$ and $(100)^{11}=10^{22}$ (ii) False; $2^3=8$ , $5^2=25$ (iii) False; $6^5=2^5\times3^5$ (iv) True; $3^0=1$ , $(1000)^0=1$ . 4. (i) $2^8\times3^4$ (ii) $2\times3^3\times5$ (iii) $3^6\times2^6$ (iv) $2^8\times3$ . 5. (i) 98 (ii) $\frac{4}{5t^8}$ (iii) 1.

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