Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Part I — Short Answer Questions 12 × 2 = 24
Answer briefly. (Answer all questions.)
1.1. Copy the figures with punched holes and find the axes of symmetry for the following: (a) a rectangle with one punched hole at the left and one at the right, at the same height; (b) a square with two punched holes near the upper-right corner along the bottom-left to top-right diagonal; (c) a square with two punched holes on the right side, one above and one below the middle; (d) a square with two punched holes on the left and two on the right, paired above and below a horizontal middle line; (e) a square with one punched hole near each corner; (f) a square with its diagonals drawn and punched holes at the centre, lower-left corner and lower-right corner; (g) an isosceles triangle with two punched holes near the base, one on each side of the vertical middle line; (h) a right-pointing isosceles triangle with two punched holes on the left side, one above and one below the horizontal middle line; (i) an isosceles triangle with two punched holes on its vertical middle line; (j) a circle with punched holes at left and right; (k) a circle with punched holes at top, bottom, left and right; (l) a circle with punched holes at top, lower-left and lower-right. 2. Given the line(s) of symmetry, find the other hole(s): (a) a square with a diagonal mirror line from top-left to bottom-right and a hole on that line near the top-left; (b) a rectangle with a horizontal mirror line and a hole below it on the right; (c) a triangle with a vertical mirror line and a hole on the left of it; (d) an oval with a slant mirror line and a hole on one side of it; (e) a circle with a slant mirror line and a hole on one side of it. 3. In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete? The half-figures complete to (a) a square, (b) a triangle, (c) a rhombus, (d) a circle, (e) a pentagon and (f) an octagon. 4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry. Identify multiple lines of symmetry, if any, in each of the following figures: (a) three equal circular lobes around a central triangle; (b) a square with equal curved white sides at left and right and a central blue hourglass; (c) an equilateral triangle with a central curved blue region; (d) a square with equal quarter-circle white corners at top-right and bottom-left and a curved blue band; (e) a square filled by four congruent curved blue petals; (f) a U-shaped figure made from a semicircle and two equal vertical sides; (g) four equal circular lobes around a central square; (h) a six-petalled flower made from congruent circles. 5. Copy the figure given here. Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals? The figure is a $4 \times 4$ square grid with shaded squares in row 1 column 2, row 2 column 4, row 3 column 1 and row 4 column 3. 6. Copy the diagram and complete each shape to be symmetric about the mirror line(s): (a) a grid with a dotted diagonal mirror line and a polygon drawn on one side; (b) a grid with dotted vertical and horizontal mirror lines and an incomplete stepped shape in the upper-right part; (c) a grid with dotted vertical and horizontal mirror lines and an incomplete curve in the upper-left part. 7. State the number of lines of symmetry for the following figures: (a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle (d) A square (e) A rectangle (f) A rhombus (g) A parallelogram (h) A quadrilateral (i) A regular hexagon (j) A circle 8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about (a) a vertical mirror (b) a horizontal mirror (c) both horizontal and vertical mirrors 9. Give three examples of shapes with no line of symmetry. 10. What other name can you give to the line of symmetry of (a) an isosceles triangle? (b) a circle?[2]
2.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]
3.1. Find the value of the unknown exterior angle $x$ in the following diagrams: (i) the two interior opposite angles are $50^\circ$ and $70^\circ$ ; (ii) the two interior opposite angles are $65^\circ$ and $45^\circ$ ; (iii) the two interior opposite angles are $30^\circ$ and $40^\circ$ ; (iv) the two interior opposite angles are $60^\circ$ and $60^\circ$ ; (v) the two interior opposite angles are $50^\circ$ and $50^\circ$ ; (vi) the two interior opposite angles are $30^\circ$ and $60^\circ$ . 2. Find the value of the unknown interior angle $x$ in the following figures: (i) exterior angle $115^\circ$ and other interior opposite angle $50^\circ$ ; (ii) exterior angle $100^\circ$ and other interior opposite angle $70^\circ$ ; (iii) exterior angle $125^\circ$ and the other marked angle is a right angle; (iv) exterior angle $120^\circ$ and other interior opposite angle $60^\circ$ ; (v) exterior angle $80^\circ$ and other interior opposite angle $30^\circ$ ; (vi) exterior angle $75^\circ$ and other interior opposite angle $35^\circ$ .[2]
4.1. Find the complement of each of the following angles: (i) $20^\circ$ (ii) $63^\circ$ (iii) $57^\circ$ . 2. Find the supplement of each of the following angles: (i) $105^\circ$ (ii) $87^\circ$ (iii) $154^\circ$ . 3. Identify which of the following pairs of angles are complementary and which are supplementary. (i) $65^\circ,115^\circ$ (ii) $63^\circ,27^\circ$ (iii) $112^\circ,68^\circ$ (iv) $130^\circ,50^\circ$ (v) $45^\circ,45^\circ$ (vi) $80^\circ,10^\circ$ . 4. Find the angle which is equal to its complement. 5. Find the angle which is equal to its supplement. 6. In the given figure, $\angle1$ and $\angle2$ are supplementary angles. The figure shows two adjacent angles $\angle1$ and $\angle2$ forming a straight line. If $\angle1$ is decreased, what changes should take place in $\angle2$ so that both the angles still remain supplementary. 7. Can two angles be supplementary if both of them are: (i) acute? (ii) obtuse? (iii) right? 8. An angle is greater than $45^\circ$ . Is its complementary angle greater than $45^\circ$ or equal to $45^\circ$ or less than $45^\circ$ ? 9. Fill in the blanks: (i) If two angles are complementary, then the sum of their measures is _______. (ii) If two angles are supplementary, then the sum of their measures is ______. (iii) If two adjacent angles are supplementary, they form a ___________. 10. In the adjoining figure, name the following pairs of angles. The figure has point O with rays OB and OD forming a straight horizontal line, rays OA and OC forming another straight line through O, and ray OE vertical upward. (i) Obtuse vertically opposite angles (ii) Adjacent complementary angles (iii) Equal supplementary angles (iv) Unequal supplementary angles (v) Adjacent angles that do not form a linear pair.[2]
5.1. Evaluate each of the following: (a) $(-30)\div10$ (b) $50\div(-5)$ (c) $(-36)\div(-9)$ (d) $(-49)\div49$ (e) $13\div[(-2)+1]$ (f) $0\div(-12)$ (g) $(-31)\div[(-30)+(-1)]$ (h) $[(-36)\div12]\div3$ (i) $[(-6)+5]\div[(-2)+1]$ 2. Verify that $a\div(b+c)\ne(a\div b)+(a\div c)$ for each of the following values of $a$ , $b$ and $c$ : (a) $a=12,b=-4,c=2$ (b) $a=-10,b=1,c=1$ 3. Fill in the blanks: (a) $369\div\ldots=369$ (b) $(-75)\div\ldots=-1$ (c) $(-206)\div\ldots=1$ (d) $-87\div\ldots=87$ (e) $\ldots\div1=-87$ (f) $\ldots\div48=-1$ (g) $20\div\ldots=-2$ (h) $\ldots\div4=-3$ 4. Write five pairs of integers $(a,b)$ such that $a\div b=-3$ . One such pair is $(6,-2)$ because $6\div(-2)=-3$ . 5. The temperature at 12 noon was $10^\circ C$ above zero. If it decreases at the rate of $2^\circ C$ per hour until midnight, at what time would the temperature be $8^\circ C$ below zero? What would be the temperature at mid-night? 6. In a class test $(+3)$ marks are given for every correct answer and $(-2)$ marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores -5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly? 7. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach -350 m.[2]
6.1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions). (i) A ball (ii) A cylindrical pipe (iii) A book. 2. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!) (i) A circle (ii) A square (iii) A triangle (iv) A rectangle. 3. Examine if the following are true statements: (i) The cube can cast a shadow in the shape of a rectangle. (ii) The cube can cast a shadow in the shape of a hexagon.[2]
7.1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it): (i) a chain of six squares with two adjacent squares at the left forming a step and four squares running to the right; (ii) six squares arranged as two offset rows of three; (iii) six squares arranged as a descending staircase of pairs; (iv) a cross net with four squares in a row and one square attached above and below the second square; (v) a T-shaped net with four squares in a row and two squares attached below the second square; (vi) a cross net with four squares in a row and one square attached above and below the third square. 2. Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them. Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box. Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7. In the first net, there is one blank square above the left end of a row of four squares; in that row the third square is 4 and the fourth is 5; a square marked 6 is below the fourth square. In the second net, the top row has 1 and 2; the square below 1 is 3; there are three blanks continuing down-left in a staircase. 3. Can this be a net for a die? Explain your answer. The given six-square net has 1 and 2 in the top row, 3 and 4 in the next offset row, and 5 and 6 in the bottom offset row. 4. Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.) The incomplete net has three squares in one horizontal row. 5. Match the nets with appropriate solids: solids are (a) cube, (b) cylinder, (c) cone, (d) triangular pyramid; nets are (i) a square with four triangles attached, (ii) six squares in a cross, (iii) a rectangle with a circle at each end, (iv) a circle attached to a sector.[2]
8.1. Find the circumference of the circles with the following radius: (Take $\pi=\frac{22}{7}$ ) (a) 14 cm (b) 28 mm (c) 21 cm. 2. Find the area of the following circles, given that: (a) radius = 14 mm (Take $\pi=\frac{22}{7}$ ) (b) diameter = 49 m (c) radius = 5 cm. 3. If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take $\pi=\frac{22}{7}$ ) 4. A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs Rs 4 per meter. (Take $\pi=\frac{22}{7}$ ) 5. From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take $\pi=3.14$ ) 6. Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs Rs 15. (Take $\pi=3.14$ ) 7. Find the perimeter of the adjoining figure, which is a semicircle including its diameter. The semicircle has diameter 10 cm. 8. Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs $15/\text{m}^2$ . (Take $\pi=3.14$ ) 9. Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $\pi=\frac{22}{7}$ ) 10. From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed. Find the area of the remaining sheet. (Take $\pi=\frac{22}{7}$ ) 11. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take $\pi=3.14$ ) 12. The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take $\pi=3.14$ ) 13. A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? ( $\pi=3.14$ ) 14. A circular flower garden has an area of $314\text{ m}^2$ . A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take $\pi=3.14$ ) 15. Find the circumference of the inner and the outer circles, shown in the adjoining figure. The outer circle has radius 19 m and the distance from the outer circle to the inner circle along a radius is 10 m, so the inner radius is 9 m. (Take $\pi=3.14$ ) 16. How many times a wheel of radius 28 cm must rotate to go 352 m? (Take $\pi=\frac{22}{7}$ ) 17. The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take $\pi=3.14$ )[2]
9.1. Which of the drawings (a) to (d) show: (i) $2\times\frac{1}{5}$ (ii) $2\times\frac{1}{2}$ (iii) $3\times\frac{2}{3}$ (iv) $3\times\frac{1}{4}$ ? Drawing (a) shows three circles divided into thirds with two-thirds shaded in each circle; drawing (b) shows two rectangles divided into halves with one-half shaded in each rectangle; drawing (c) shows three rectangles divided into four equal parts with one-fourth shaded in each rectangle; drawing (d) shows two circles divided into fifths with one-fifth shaded in each circle. 2. Some pictures (a) to (c) are given below. Tell which of them show: (i) $3\times\frac{1}{5}=\frac{3}{5}$ (ii) $2\times\frac{1}{3}=\frac{2}{3}$ (iii) $3\times\frac{3}{4}=2\frac{1}{4}$ ? Picture (a) shows two one-third circle parts making two-thirds; picture (b) shows three triangles each with three-fourths shaded, making two whole triangles and one-fourth; picture (c) shows three one-fifth strips making three-fifths. 3. Multiply and reduce to lowest form and convert into a mixed fraction: (i) $7\times\frac{3}{5}$ (ii) $4\times\frac{1}{3}$ (iii) $2\times\frac{6}{7}$ (iv) $5\times\frac{2}{9}$ (v) $\frac{2}{3}\times4$ (vi) $\frac{5}{2}\times6$ (vii) $11\times\frac{4}{7}$ (viii) $20\times\frac{4}{5}$ (ix) $13\times\frac{1}{3}$ (x) $15\times\frac{3}{5}$ . 4. Shade: (i) $\frac{1}{2}$ of the circles in box (a), where box (a) has 12 circles (ii) $\frac{2}{3}$ of the triangles in box (b), where box (b) has 9 triangles (iii) $\frac{3}{5}$ of the squares in box (c), where box (c) has 15 squares. 5. Find: (a) $\frac{1}{2}$ of (i) 24 (ii) 46 (b) $\frac{2}{3}$ of (i) 18 (ii) 27 (c) $\frac{3}{4}$ of (i) 16 (ii) 36 (d) $\frac{4}{5}$ of (i) 20 (ii) 35. 6. Multiply and express as a mixed fraction: (a) $3\times5\frac{1}{5}$ (b) $5\times6\frac{3}{4}$ (c) $7\times2\frac{1}{4}$ (d) $4\times6\frac{1}{3}$ (e) $3\frac{1}{4}\times6$ (f) $3\frac{2}{5}\times8$ . 7. Find: (a) $\frac{1}{2}$ of (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$ (b) $\frac{5}{8}$ of (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$ . 8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}$ of the water. Pratap consumed the remaining water. (i) How much water did Vidya drink? (ii) What fraction of the total quantity of water did Pratap drink?[2]
10.1. Find the area of each of the following parallelograms: (a) base 7 cm, height 4 cm (b) base 5 cm, height 3 cm (c) base 2.5 cm, height 3.5 cm (d) base 5 cm, height 4.8 cm (e) base 2 cm, height 4.4 cm. 2. Find the area of each of the following triangles: (a) base 4 cm, height 3 cm (b) base 5 cm, height 3.2 cm (c) base 3 cm, height 4 cm (d) base 3 cm, height 2 cm. 3. Find the missing values in the table for parallelograms: (a) base 20 cm, height blank, area $246\text{ cm}^2$ (b) base blank, height 15 cm, area $154.5\text{ cm}^2$ (c) base blank, height 8.4 cm, area $48.72\text{ cm}^2$ (d) base 15.6 cm, height blank, area $16.38\text{ cm}^2$ . 4. Find the missing values in the table for triangles: (a) base 15 cm, height blank, area $87\text{ cm}^2$ (b) base blank, height 31.4 mm, area $1256\text{ mm}^2$ (c) base 22 cm, height blank, area $170.5\text{ cm}^2$ . 5. PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If $SR=12$ cm and $QM=7.6$ cm, find: (a) the area of the parallelogram PQRS (b) QN, if $PS=8$ cm. 6. DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is $1470\text{ cm}^2$ , $AB=35$ cm and $AD=49$ cm, find the length of BM and DL. 7. $\triangle ABC$ is right angled at A. AD is perpendicular to BC. If $AB=5$ cm, $BC=13$ cm and $AC=12$ cm, find the area of $\triangle ABC$ . Also find the length of AD. 8. $\triangle ABC$ is isosceles with $AB=AC=7.5$ cm and $BC=9$ cm. The height AD from A to BC is 6 cm. Find the area of $\triangle ABC$ . What will be the height from C to AB i.e., CE?[2]
11.Exercise 8.2 asks students to add, subtract, multiply and divide rational numbers in the listed subparts.[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 1
- 1. 1. The axes of symmetry are: (a) vertical line through the centre; (b) diagonal from bottom-left to top-right; (c) horizontal line through the centre; (d) horizontal line through the centre; (e) vertical, horizontal and both diagonal lines through the centre; (f) vertical line through the centre; (g) vertical line through the apex and midpoint of the base; (h) horizontal line through the middle; (i) vertical line through the apex and midpoint of the base; (j) vertical line through the centre; (k) vertical and horizontal lines through the centre; (l) vertical line through the centre. 2. The other hole(s) are the reflections of the given holes in the dotted line: (a) no new hole is needed because the given hole lies on the mirror line; (b) add a hole the same distance above the horizontal line on the right; (c) add a matching hole on the right of the vertical line; (d) add a matching hole on the opposite side of the slant line; (e) add a matching hole on the opposite side of the slant line. 3. The completed figures are: (a) square (b) triangle (c) rhombus (d) circle (e) pentagon (f) octagon. 4. The multiple lines of symmetry are: (a) 3 lines through the centre; (b) vertical and horizontal lines; (c) 3 lines through the vertices and the centre; (d) the two diagonals; (e) vertical, horizontal and both diagonals; (f) only one line of symmetry, the vertical line, so no multiple lines; (g) vertical, horizontal and both diagonals; (h) 6 lines through opposite petals/centres. 5. Shade the mirror images of the four given shaded squares in the chosen diagonal. Yes, there is more than one way, because either diagonal can be chosen. The figure will be symmetric about both diagonals only if all squares needed by both diagonal reflections are shaded. 6. Complete each diagram by drawing the mirror image of the given part in every dotted mirror line: (a) reflect the polygon across the diagonal; (b) reflect the stepped shape first across the vertical line and then across the horizontal line so all four parts match; (c) reflect the curve across the vertical and horizontal lines so the completed curve has both symmetries. 7. (a) 3 (b) 1 (c) 0 (d) 4 (e) 2 (f) 2 (g) 0 (h) 0 (i) 6 (j) infinitely many. 8. (a) A, H, I, M, O, T, U, V, W, X, Y (b) B, C, D, E, H, I, O, X (c) O, X, I, H. 9. Examples: a scalene triangle, a parallelogram that is not a rectangle or rhombus, and an irregular quadrilateral. 10. (a) Median (b) Diameter.
- 2. 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.
- 3. 1. (i) $120^\circ$ (ii) $110^\circ$ (iii) $70^\circ$ (iv) $120^\circ$ (v) $100^\circ$ (vi) $90^\circ$ . 2. (i) $65^\circ$ (ii) $30^\circ$ (iii) $35^\circ$ (iv) $60^\circ$ (v) $50^\circ$ (vi) $40^\circ$ .
- 4. 1. (i) $70^\circ$ (ii) $27^\circ$ (iii) $33^\circ$ . 2. (i) $75^\circ$ (ii) $93^\circ$ (iii) $26^\circ$ . 3. (i) supplementary (ii) complementary (iii) supplementary (iv) supplementary (v) complementary (vi) complementary. 4. $45^\circ$ . 5. $90^\circ$ . 6. $\angle2$ should be increased by the same measure by which $\angle1$ is decreased, so that their sum remains $180^\circ$ . 7. (i) No (ii) No (iii) Yes. 8. Its complementary angle is less than $45^\circ$ . 9. (i) $90^\circ$ (ii) $180^\circ$ (iii) linear pair. 10. (i) $\angle AOD$ and $\angle BOC$ (ii) $\angle EOA$ and $\angle AOB$ (iii) $\angle EOB$ and $\angle EOD$ (iv) $\angle EOA$ and $\angle EOC$ (v) $\angle AOB$ and $\angle AOE$ ; $\angle AOE$ and $\angle EOD$ ; $\angle EOD$ and $\angle COD$ .
- 5. 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.
- 6. 1. (i) A ball gives a circular shadow. (ii) A cylindrical pipe, placed as shown horizontally under the bulb, gives a rectangular shadow. (iii) A book gives a rectangular shadow. 2. (i) A circle can be the shadow of a ball, a cone or a cylinder. (ii) A square can be the shadow of a cube. (iii) A triangle can be the shadow of a cone or a triangular pyramid. (iv) A rectangle can be the shadow of a cuboid, book or cylinder. 3. (i) True. (ii) True.
- 7. 1. Nets in (ii), (iii), (iv), (vi) form cubes. 2. One completed first net is: 1 in the square above the left end; the horizontal row is 3, 2, 4, 5; 6 remains below 5. One completed second net is: top row 1, 2; middle row 5, 3; bottom row 4, 6. 3. No, because one pair of opposite faces will have 1 and 4 on them whose total is not 7, and another pair of opposite faces will have 3 and 6 on them whose total is also not 7. 4. Three faces are there in the net. Two completions are: keep the three-square row and add one square above the middle square, one below the middle square and one below that; or keep the three-square row, add one square to extend the row at one end, and attach one square above and one below that end square. 5. (a) (ii) (b) (iii) (c) (iv) (d) (i).
- 8. 1. (a) 88 cm (b) 176 mm (c) 132 cm. 2. (a) $616\text{ mm}^2$ (b) $1886.5\text{ m}^2$ (c) $\frac{550}{7}\text{ cm}^2$ . 3. 24.5 m; $1886.5\text{ m}^2$ . 4. 132 m; Rs 528. 5. $21.98\text{ cm}^2$ . 6. 4.71 m; Rs 70.65. 7. 25.7 cm. 8. Rs 30.14 approximately. 9. 7 cm; $154\text{ cm}^2$ ; 11 cm; circle. 10. $536\text{ cm}^2$ . 11. $23.44\text{ cm}^2$ . 12. 5 cm; $78.5\text{ cm}^2$ . 13. $879.20\text{ m}^2$ . 14. Yes. 15. 119.32 m; 56.52 m. 16. 200 times. 17. 94.2 cm.
- 9. 1. (i) (d) (ii) (b) (iii) (a) (iv) (c). 2. (i) (c) (ii) (a) (iii) (b). 3. (i) $4\frac{1}{5}$ (ii) $1\frac{1}{3}$ (iii) $1\frac{5}{7}$ (iv) $1\frac{1}{9}$ (v) $2\frac{2}{3}$ (vi) $15$ (vii) $6\frac{2}{7}$ (viii) $16$ (ix) $4\frac{1}{3}$ (x) $9$ . 4. (i) Shade 6 of the 12 circles in box (a) (ii) shade 6 of the 9 triangles in box (b) (iii) shade 9 of the 15 squares in box (c). 5. (a) (i) 12 (ii) 23 (b) (i) 12 (ii) 18 (c) (i) 12 (ii) 27 (d) (i) 16 (ii) 28. 6. (a) $15\frac{3}{5}$ (b) $33\frac{3}{4}$ (c) $15\frac{3}{4}$ (d) $25\frac{1}{3}$ (e) $19\frac{1}{2}$ (f) $27\frac{1}{5}$ . 7. (a) (i) $1\frac{3}{8}$ (ii) $2\frac{1}{9}$ (b) (i) $2\frac{19}{48}$ (ii) $6\frac{1}{24}$ . 8. (i) 2 litres (ii) $\frac{3}{5}$ .
- 10. 1. (a) $28\text{ cm}^2$ (b) $15\text{ cm}^2$ (c) $8.75\text{ cm}^2$ (d) $24\text{ cm}^2$ (e) $8.8\text{ cm}^2$ . 2. (a) $6\text{ cm}^2$ (b) $8\text{ cm}^2$ (c) $6\text{ cm}^2$ (d) $3\text{ cm}^2$ . 3. (a) 12.3 cm (b) 10.3 cm (c) 5.8 cm (d) 1.05 cm. 4. (a) 11.6 cm (b) 80 cm (c) 15.5 cm. 5. (a) $91.2\text{ cm}^2$ (b) 11.4 cm. 6. Length of BM = 30 cm; length of DL = 42 cm. 7. Area of $\triangle ABC=30\text{ cm}^2$ ; length of AD $=\frac{60}{13}$ cm. 8. Area of $\triangle ABC=27\text{ cm}^2$ ; length of CE = 7.2 cm.
- 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. 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.