Practice Question Papers · with Answers

CBSE / NCERT Class 9 Maths Practice Question Papers

Download free CBSE / NCERT Class 9 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: 9CBSE / NCERTMax Marks: 36
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

1.One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area $128\text{ cm}^2$[2]
2.Which term of the sequence $t_n = 5n - 3$[2]
3.An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended by the arc at a point on the circle?[2]
4.Use the Baudhāyana–Pythagoras theorem to show why Theorem 6 must be true.[2]
5.Find the sum: (i) $\dfrac{2}{5}+\dfrac{3}{10}$[2]
6.Find the values of the following polynomials at the indicated values of the variables. (i) $5x^2 - 3x + 7$[2]
7.Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.[2]
8.There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket. (i) Draw a tree diagram showing all possible pairs of fruits. (ii) List the sample space. (iii) What is the probability of picking one apple and one banana?[2]
9.If the diameter of a car tyre is 56 cm, then: (i) How far does the car need to travel for the tyre to complete one revolution? (ii) How many revolutions does the tyre make if the car travels 10 km?[2]
10.Factor the following algebraic expressions: (i) $4y^2 + 1 + \dfrac{1}{16y^2}$[2]
11.The number $0.\overline{9}$[2]
12.We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.[2]
13.Can you think of other way(s) to find a rational number between any two rational numbers?[2]
14.Find the values using suitable identities: (i) $17 \times 21$[2]
15.Represent the rational numbers $\dfrac{2}{3}$[2]
16.Find possible expressions for the length and breadth of each of the following rectangles whose areas are given by the following expressions in square units. (i) $25a^2 - 30ab + 9b^2$[2]
17.Show that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.[2]
18.Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?[2]
🔑 Show Answer Key — Set 1
  1. 1. $8\sqrt{2}$ cm.
  2. 2. $607$ is the 122nd term.
  3. 3. $35°$ .
  4. 4. Theorem 6 says that equal chords of a circle are equidistant from the centre. If two equal chords have length $2a$ in a circle of radius r, the perpendicular from the centre bisects each chord. For each chord, the distance d from the centre satisfies $d^2+a^2=r^2$ , so $d=\sqrt{r^2-a^2}$ . Since r and a are the same for both chords, their distances from the centre are equal.
  5. 5. (i) $\dfrac{7}{10}$ (ii) $\dfrac{29}{24}$ (iii) $-\dfrac{5}{14}$
  6. 6. (i) $9$ (ii) $4a^3-a^2+6$
  7. 7. They are prime numbers between 10 and 20. The next three primes after 19 are $23, 29, 31$ .
  8. 8. (i) The tree branches from Basket A to Apple or Orange, and from each of these to Banana or Mango. (ii) By fruit type, $S=\{(\text{Apple},\text{Banana}),(\text{Apple},\text{Mango}),(\text{Orange},\text{Banana}),(\text{Orange},\text{Mango})\}$ . (iii) $P(\text{Apple and Banana})=\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{6}$ .
  9. 9. (i) $176$ cm (ii) $\dfrac{62500}{11}\approx 5682$ revolutions
  10. 10. (i) $\left(2y+\dfrac{1}{4y}\right)^2$ (ii) $\left(3m-\dfrac{1}{5n}\right)\left(3m+\dfrac{1}{5n}\right)$ (iii) $\left(3b-\dfrac{1}{4b}\right)\left(9b^2+\dfrac{3}{4}+\dfrac{1}{16b^2}\right)$ (iv) $\left(x+\dfrac{1}{2}\right)\left(x+\dfrac{1}{3}\right)$ (v) $\left(3u-\dfrac{1}{5}\right)^3$ (vi) $\left(4y+\dfrac{z}{5}\right)\left(16y^2-\dfrac{4}{5}yz+\dfrac{z^2}{25}\right)$ (vii) $(p+3q+r)(p^2+9q^2+r^2-3pq-3qr-pr)$ (viii) $(3m-2)^2$ (ix) $\dfrac{1}{3}(3x-2y+z)(9x^2+4y^2+z^2+6xy+2yz-3xz)$ (x) As printed, the $xy$ and $xz$ coefficients are interchanged from a perfect square. The intended expression $4x^2+9y^2+36z^2+12xy+36yz+24xz$ factors as $(2x+3y+6z)^2$ . (xi) $\left(3u-\dfrac{1}{6}\right)^3$
  11. 11. $0.\overline{9}=1$ .
  12. 12. No. Natural numbers are not closed under subtraction. For example, $5-2=3$ is natural, but $2-5=-3$ is not a natural number. Also, $4-4=0$ , and 0 is not a natural number in the usual NCERT convention $\mathbb{N}=\{1,2,3,\ldots\}$ .
  13. 13. Yes. One simple method is to take the average. For any two rational numbers $a$ and $b$ with $a\lt b$ , the number $\dfrac{a+b}{2}$ is rational and lies between them.
  14. 14. (i) $357$ (ii) $9984$ (iii) $384$ (iv) $3176523$ (v) $7880599$ (vi) $2048383$ (vii) $-1225043$ (viii) $-26730899$
  15. 15. $\dfrac{2}{3}$ lies between 0 and 1, two-thirds of the way from 0 to 1. $-\dfrac{5}{4}=-1.25$ lies between $-2$ and $-1$ . $\dfrac{11}{2}=5.5$ lies halfway between 5 and 6.
  16. 16. (i) Length $=5a-3b$ , breadth $=5a-3b$ . (ii) Length $=6s+7t$ , breadth $=6s-7t$ .
  17. 17. Let the two chords be AB and DE in the same circle with centre O, and suppose $AB=DE$ . Join OA, OB, OD and OE. Since all four are radii, $OA=OB=OD=OE$ . Also $AB=DE$ . Thus $\triangle AOB$ and $\triangle DOE$ have three corresponding sides equal, so they are congruent by SSS.
  18. 18. Using the thumb to count the three joints on each of the four fingers, one can count $4\times 3=12$ positions on one hand. This naturally supports counting in groups of 12, which is the idea behind base-12 systems.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 9CBSE / NCERTMax Marks: 36
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

1.What are the coefficients of $x^2$[2]
2.Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. (i) $y = -3x + 4$[2]
3.For the following experiments write down the sample space S. (i) Rolling a die and tossing a coin together. (ii) Choosing a random integer between $-5$[2]
4.Use your method (from Problem 6) to check if the points $R(-5,-1)$[2]
5.Three rational numbers x, y, z satisfy $x + y + z = 0$[2]
6.In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm, what is the length of the chord AB?[2]
7.A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area.[2]
8.Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month. (i) Find the height after 7 months. (ii) Make a table of values for t varying from 0 to 10 months and show how the height, h, increases every month. (iii) Find an expression that relates h and t, and explain why it represents linear growth.[2]
9.The difference between two positive integers is 63. The ratio of the two integers is $2:5$[2]
10.Three problems about fitting congruent shapes together: (i) Rectangle ABCD has sides a, b, and rectangle PQRS has sides $2a, 2b$[2]
11.Find the difference: (i) $\dfrac{5}{6}-\dfrac{1}{4}$[2]
12.Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.[2]
13.Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle of radius 14 cm and sector angle 75°.[2]
14.Using the origin as one vertex, plot the vertices of: (i) A right-angled isosceles triangle. (ii) An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV.[2]
15.Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.[2]
16.A rational number in its lowest form has denominator $2^3 \times 5$[2]
17.Find the values of the following using the identity $(a - b)^2 = a^2 - 2ab + b^2$[2]
18.The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle.[2]
🔑 Show Answer Key — Set 2
  1. 1. The coefficient of $x^2$ is $6$ and the coefficient of $x^3$ is $-3$ .
  2. 2. (i) Slope $=-3$ , y-intercept $=4$ , y-axis point $(0,4)$ . (ii) $y=2x+\dfrac{7}{2}$ ; slope $=2$ , y-intercept $=\dfrac{7}{2}$ , y-axis point $\left(0,\dfrac{7}{2}\right)$ . (iii) $y=\dfrac{6}{5}x-2$ ; slope $=\dfrac{6}{5}$ , y-intercept $=-2$ , y-axis point $(0,-2)$ . (iv) $y=2x-\dfrac{11}{3}$ ; slope $=2$ , y-intercept $=-\dfrac{11}{3}$ , y-axis point $\left(0,-\dfrac{11}{3}\right)$ .
  3. 3. (i) $S=\{(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)\}$ . (ii) $S=\{-5,-4,-3,-2,-1,0,1,2,3,4,5\}$ . (iii) By colour, $S=\{\text{green},\text{red}\}$ .
  4. 4. No, the points $R$ , $B$ and $C$ are not on the same straight line. From R to B, $\Delta x=3$ and $\Delta y=-4$ , so the ratio is $-\dfrac{4}{3}$ . From B to C, $\Delta x=6$ and $\Delta y=-7$ , so the ratio is $-\dfrac{7}{6}$ . These are not equal.
  5. 5. Since $x+y+z=0$ , squaring gives $(x+y+z)^2=0$ . Thus $x^2+y^2+z^2+2(xy+yz+zx)=0$ . Given $xy+yz+zx=0$ , we get $x^2+y^2+z^2=0$ . Squares of rational numbers are non-negative, so each square must be 0. Hence $x=y=z=0$ .
  6. 6. $AB=12$ cm.
  7. 7. The area is $60$ square units.
  8. 8. (i) $5.25$ feet. (ii) For $t=0,1,2,3,4,5,6,7,8,9,10$ , $h=1.75,2.25,2.75,3.25,3.75,4.25,4.75,5.25,5.75,6.25,6.75$ feet. (iii) $h=1.75+0.5t$ ; it is linear growth because the height increases by a constant $0.5$ feet each month.
  9. 9. The two integers are $42$ and $105$ .
  10. 10. (i) Area scales by $2\times2=4$ , and 4 copies of the smaller rectangle fit in a $2$ by $2$ arrangement. (ii) The triangles are similar with scale factor 2, so area scale factor is $2^2=4$ ; 4 congruent copies can tile the larger similar triangle. (iii) The triangles are similar with scale factor 3, so area scale factor is $3^2=9$ ; 9 congruent copies can tile the larger similar triangle.
  11. 11. (i) $\dfrac{7}{12}$ (ii) $\dfrac{5}{8}$ (iii) $-\dfrac{1}{9}$
  12. 12. After 15 days, $200$ pages will be left. The linear pattern is $P=500-20d$ , where $P$ is the number of pages left after $d$ days.
  13. 13. $\dfrac{139}{3}$ cm, i.e. about $46.3$ cm.
  14. 14. (i) One example is $O(0,0)$ , $A(3,0)$ and $B(0,3)$ . (ii) One example is $O(0,0)$ , $C(-3,-4)$ and $D(3,-4)$ .
  15. 15. The 31st term is $178$ .
  16. 16. It will have $3$ decimal places.
  17. 17. (i) $6241$ (ii) $37249$ (iii) $89401$
  18. 18. The radius is $10$ cm.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 9CBSE / NCERTMax Marks: 36
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

1.Find all possible ways of expressing 100 as the sum of consecutive natural numbers.[2]
2.Let $a = \dfrac{7}{12}$[2]
3.You know that the area of a parallelogram is base × height. Using this and the figure, show that the area of a trapezium is half the sum of the parallel sides × height, i.e., $\dfrac{1}{2}(a+b)h$[2]
4.Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: $\dfrac{7}{20}$[2]
5.Look at Reiaan's bathroom. (i) What are the coordinates of the four corners O, F, R, and P of the bathroom? (ii) What is the shape of the showering area SHWR in Reiaan's bathroom? Write the coordinates of the four corners. (iii) Mark off a $3 \text{ ft} \times 2 \text{ ft}$[2]
6.Let $T_1 = 1$[2]
7.A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?[2]
8.The temperature in the high-altitude desert of Ladakh is recorded as 4 °C at noon. By midnight, it drops by 15 °C. What is the midnight temperature?[2]
9.The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete turn of the wheel, and how many times the wheel turns during a journey of 1 km.[2]
10.Plot point $Z(5,-6)$[2]
11.If you have `800 and you save `250 every month, find the amount you have after (i) 6 months (ii) 2 years. Express this as a linear pattern.[2]
12.Determine the AP whose third term is 16 and whose 7th term exceeds the 5th term by 12.[2]
13.Find the product: (i) $\dfrac{2}{3}\times\dfrac{3}{10}$[2]
14.Find the area of a quadrant of a circle whose circumference is 66 cm.[2]
15.ABCD is a cyclic quadrilateral inscribed in a circle. If $\angle A$[2]
16.If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?[2]
17.The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand in 10 minutes.[2]
18.Calculate, correct to 3 significant figures, the circumference of a circle with: (i) radius 7 cm (ii) radius 10 cm (iii) radius 12 cm.[2]
🔑 Show Answer Key — Set 3
  1. 1. $100=100$ ; $100=18+19+20+21+22$ ; $100=9+10+11+12+13+14+15+16$ .
  2. 2. Take $m=48$ . Then $a=\dfrac{7}{12}=\dfrac{28}{48}$ and $b=\dfrac{5}{6}=\dfrac{40}{48}$ , so $k_2-k_1=12>6$ . Five rational numbers between them are $\dfrac{29}{48}$ , $\dfrac{30}{48}$ , $\dfrac{31}{48}$ , $\dfrac{32}{48}$ and $\dfrac{33}{48}$ .
  3. 3. Two congruent copies of the trapezium can be arranged to form a parallelogram with base $a+b$ and height h. The parallelogram area is $(a+b)h$ , so one trapezium has half this area: $\dfrac12(a+b)h$ .
  4. 4. $\dfrac{7}{20}$ terminates: $0.35$ . $\dfrac{4}{15}$ is non-terminating repeating: $0.2\overline{6}$ . $\dfrac{13}{250}$ terminates: $0.052$ .
  5. 5. (i) The bathroom corners are $O(0,0)$ , $F(0,9)$ , $R(-6,9)$ and $P(-6,0)$ . (ii) $SHWR$ is a trapezium. Its corners are approximately $S(-6,6)$ , $H(-3,6)$ , $W(-2,9)$ and $R(-6,9)$ . (iii) One suitable choice is: washbasin rectangle with corners $(-6,0)$ , $(-3,0)$ , $(-3,2)$ and $(-6,2)$ ; toilet rectangle with corners $(-6,2)$ , $(-4,2)$ , $(-4,5)$ and $(-6,5)$ .
  6. 6. $T_4=7$ , $T_5=13$ , $T_6=24$ , $T_7=44$ , $T_8=81$ .
  7. 7. The shorter piece is $60$ feet and the longer piece is $240$ feet.
  8. 8. The midnight temperature is $-11$ °C.
  9. 9. One complete turn covers $176$ cm. In 1 km the wheel turns $\dfrac{6250}{11}\approx568.2$ times.
  10. 10. One possible triangle is obtained by taking $I(5,0)$ and $N(0,-6)$ . Then $ZI=6$ units, $ZN=5$ units and $IN=\sqrt{5^2+6^2}=\sqrt{61}$ units.
  11. 11. (i) `2300 (ii) `6800 The linear pattern is $A=800+250n$ , where $A$ is the amount after $n$ months.
  12. 12. The AP is $4,10,16,22,28,\ldots$ .
  13. 13. (i) $\dfrac{1}{5}$ (ii) $\dfrac{35}{88}$ (iii) $-\dfrac{10}{49}$
  14. 14. $86.625\text{ cm}^2$ .
  15. 15. $\angle C=105°$ and $\angle D=70°$ .
  16. 16. The width is $3$ cm and the length is $9$ cm.
  17. 17. $\dfrac{77}{3}\text{ cm}^2$ , i.e. about $25.7\text{ cm}^2$ .
  18. 18. (i) $44.0$ cm (ii) $62.9$ cm (iii) $75.4$ cm

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Class 9 does not have a public board examination, so there are no official board question papers for this class. The papers above are Brain Grain practice papers built to the standard exam pattern — ideal for unit tests, monthly tests and revision.

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