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GRADE 10 MATHEMATICS ASSESSMENT BOOKLET TERM 2 MATHEMATICS (MATHC1002) Topic Mathematics (MATHC1002) ASSESSMENT TASK COVER PAGE STS Performance Assessment Event Date criteria Project/Investigation Student Name Teacher Class Time Total Mark I certify that the work presented is my own. Student signature: Date: Marked and feedback provided by: Signature: Teacher comment/s: Student Comment/s: Feedback acknowledgement I acknowledge that I have received and understood feedback about this assessment. Student signature: i Date: 1. Look at the sequence of numbers 7, 11, 15, 19,………. (a) Write down the next number in the sequence. 23 Answer (a) ……….…………………….…… [1] (b) Find the 10th number in the sequence. 43 Answer (b) ……….…………………….…… [1] (c) Write an expression, in terms of n, for the nth number in the sequence. 4n + 3 Answer (c) ……….…………………….…… [1] 2. Pattern 1 Pattern 2 Pattern 3 The first three patterns in a sequence are shown above. (a) Complete the table. Pattern number 1 2 Number of dots 5 8 3 11 4 14 [1] (b) Find a formula for the number of dots, d, in the nth pattern. 3n + 2 Answer (b) d = ………………………….…… [1] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 1 | 16 (c) Find the number of dots in the 60th pattern. 182 Answer (c) …….…..………………….…… [1] (d) Find the number of the pattern that has 89 dots. 29 Answer (d) …….…..………………….…… [1] 3. The diagram below shows a sequence of patterns made from dots and lines. draw here 1 dot 2 dots 3 dots 4 dots (a) Draw the next pattern in the sequence in the space above. [1] (b) Complete the table for the numbers of dots and lines. Dots 1 2 3 4 Lines 4 7 10 5 13 16 6 19 [2] (c) How many lines are in the pattern with 99 dots? 298 Answer (c) ……………………..….……… [2] (d) How many lines are in the pattern with n dots? 3n + 1 Answer (d) ………………….….….……… [2] (e) Complete the following statement. 28 There are 85 lines in the pattern with ……………… dots. [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 2 | 16 4. (a) 4𝑝 × 45 = 415 . Find the value of 𝑝. 10 Answer (a) 𝑝 = ………..……..……………… [1] (b) 27 ÷ 2𝑞 = 24 . Find the value of 𝑞. 3 Answer (b) 𝑞 = ………..……..……………… [1] 5. (a) 3𝑝 × 35 = 314 . Find the value of 𝑝. 9 Answer (a) 𝑝 = ………..……..……………… [1] (b) 28 ÷ 2𝑞 = 23 . Find the value of 𝑞. 5 Answer (b) 𝑞 = ………..……..……………… [1] 6. Simplify (a) 1 0 (𝑝) , 1 Answer (a) ………..……..……………… [1] (b) 𝑞3 × 𝑞5 , q8 Answer (b) ………..……..……………… [1] (c) (𝑟 4 )−2 . r -8 Answer (c) ………..……..……………… [1] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 3 | 16 7. Simplify 3𝑥 2 𝑦 × 𝑥 4 𝑦 2 6 3x y 3 Answer ………..……..……………… [2] 8. Simplify (a) 4𝑑 × 6𝑑4 24d 5 Answer (a) ………..……..……………… [2] 28𝑡 3 ÷ 7𝑡 −4 (b) 4t 7 Answer (b) ………..……..……………… [2] 9. In the diagram AB is parallel to CD. Calculate the value of 𝑎. B a° D A 5a° C NOT TO SCALE 30 Answer 𝑎 = ………..…………………. [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 4 | 16 10. A B D C 35° NOT TO SCALE E In the diagram BC is parallel to DE. ABD and ACE are straight lines. Angle BDE = 35o. Calculate the size of angle DBC 145 Answer (b) Angle DBC = ………..……………. [1] 11. A B 25 C D 130 E NOT TO SCALE F In the diagram, AB, CD and EF are parallel lines. Angle ABC = 25o and angle CEF = 130o. Calculate angle BCE. 75 Answer Angle BCE = ………..……………. [2] 12. D A E s° r° t° 130° p° F B STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI q° C G Version 1.0 2013 NOT TO SCALE 5 | 16 In the diagram above, DAE and FBCG are parallel lines. AC = BC and angle FBA = 130o. (i) What is the special name given to triangle ABC? isosceles Answer (i) ………..……………………. [1] (ii) Work out the values of p, q, r, s and t. 50 50 80 𝑟 =………….. Answer (ii) ……….. 𝑝 = …………. 𝑞 = …………… 80 50 𝑠 = …………… 𝑡 =…….……. 13. [5] In the diagram below, AB and CD are straight lines which intersect at M. LMN and PQRS are parallel straight lines. Angle QMR = 35o and angle BMN = 64o. D L B M x° 64° N 35° P Q y° A R S z° NOT TO SCALE C Find the value of 𝑥, 𝑦 and 𝑧. 35 Answer 𝑥 = ………..……………………. [1] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 6 | 16 64 Answer 𝑦 = ………..……………………. [2] 81 Answer 𝑧 = ………..……………………. [2] 14. Q P x y T z 100 63 S R NOT TO SCALE In the diagram PQ is parallel to SR, and QR is parallel to PT. PQ = QR, angle PRS = 63o and angle RST = 100o. Find the value of (i) 𝑥, 63 Answer (i) 𝑥 = ………..……………………. [1] (ii) 𝑦, 54 Answer (ii) 𝑦 = ………..……………………. [2] (iii) 𝑧. 134 Answer (iii) 𝑧 = ………..……………………. [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 7 | 16 15. A square ABCD, of side 8 cm, has another square, PQRS, drawn inside it. P, Q, R and S are at the midpoints of each side of the square ABCD, as shown in the diagram. A P Q S D (a) B R C NOT TO SCALE Calculate the length of PQ. 5,66 Answer (a) ………..……………………. cm [2] (b) Calculate the area of the square PQRS. 32 Answer (b) ………..……………………. cm2 [1] 16. Each interior angle of a regular polygon is 150o. (a) Work out the size of each exterior angle. 30 Answer (a) ………..……………………. [1] (b) Work out the number of sides of this polygon. 12 Answer (b) ………..……………………. [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 8 | 16 17. ABCDE is a regular polygon with centre O. B A E (i) C O D NOT TO SCALE What is the special name for the polygon? pentagon Answer (i) ………..……………………. [1] (ii) Calculate angle EOD. 72 Answer (ii) Angle EOD = ………..……… [2] (iii) Calculate angle AED. 108 Answer (iiI) Angle AED = ………..……… [2] 18. (i) Calculate the interior angle of a regular heptagon (seven-sided polygon). Write down all the figures on your calculator display. 128.571... Answer (i) ………..……………………. [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 9 | 16 (ii) Round your answer to part (a)(i) to 1 decimal place. 128.6 Answer (ii) ………..……………………. [1] 19. The area of a square is 42.25 cm2. Work out the length of one side of the square. 6.5 Answer …………….…………… cm [1] 20. 14 cm 6 cm 10 cm NOT TO SCALE 22 cm For the shape above, work out (a) the perimeter, 64 Answer (a) …………….…………… cm [2] (b) the area. 172 Answer (b) …………….…………… cm2 [2] 21. Find the circumference of a circle of radius 5.7 cm. Write down your answer (a) exactly as it appears on your calculator, STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 10 | 16 35.81415... Answer (a) …………….…………… cm [1] (b) correct to the nearest centimetre. 36 Answer (b) …………….…………… cm [1] 22. Calculate the circumference of a circle of diameter 13 cm. 40.8 Answer …………..….…………… cm [2] 23. Calculate the area of a circle with radius 3.7 centimetres. 43 Answer ………..……..……… cm2 [2] 24. 3 cm 2 cm 4 cm NOT TO SCALE The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below. STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 11 | 16 *DRAW THE NET HERE **NET OF THE CUBOID [2] (b) Using your net, calculate the total surface area of the cuboid. 52 Answer (b) …………………………. cm2 [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 12 | 16 25. lm lm NOT TO SCALE lm A cube of side l metres has a volume of 20 cubic metres. Calculate the value of 𝑙. 2.71... Answer 𝑙 = ……………………………………. [2] 26. C A NOT TO SCALE B 6 cm C 4 cm *DRAW A LINE FROM A - C B A 8 cm STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 13 | 16 The diagram above shows a cuboid and its net. (a) Calculate the total surface area of the cuboid. 208 Answer (a) …………………………. cm2 [3] (b) Calculate the volume of the cuboid. 192 Answer (b) …………………………. cm3 [2] (c) An ant walks directly from A to C on the surface of the cuboid. (i) Draw a straight line on the net to show this route. [1] (ii) Calculate the length of the ant’s journey. 12.8 Answer (c)(ii) …………………………. cm [3] 27. A candle, made from wax, is in the shape of a cylinder. The radius is 1.5 centimetres and the height is 20 centimetres. NOT TO SCALE (a) Calculate, correct to the nearest cubic centimetre, the volume of wax in the candle. STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 14 | 16 [The volume of a cylinder, radius r, height h, is πr2h.] 141 Answer (a) …………………………. cm2 [2] (b) The candle burns 0.8 cm3 of wax every minute. How long, in hours and minutes, will it last? Write your answer correct to the nearest minute 56 2 Answer (b) …….……… h …….….…. min [3] 28. 30 mm 2 mm NOT TO SCALE An old Greek coin is a cylinder with a diameter of 30 millimetres and a thickness of 2 millimetres. Calculate, in cubic millimetres, the volume of the coin. [The volume of a cylinder, radius r, height h, is πr2h.] 1413 Answer ……………………………………. mm3 [2] 29. M 900 m O N 1200 m STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI NOT TO SCALE Version 1.0 2013 15 | 16 A hot air balloon, M, is 900 metres vertically above a point N on the ground. A boy stands at a point O, 1200 metres horizontally from N. (a) Calculate the distance, OM, of the boy from the balloon. 1500 Answer (a) OM = ………..……. m [2] (b) Calculate angle MON. XXX MNO MNO 90 Answer (b) Angle MON XXX = ………..……. [2] 30. A 4.2 m B 1.5 m C NOT TO SCALE ABC is a right angled triangle. AB = 4.2 m and BC = 1.5 m. Calculate the length of AC. 4.46 Answer AC = ………..……. m [2] STS\G10\Term 2\Maths\ Booklet\CDAU\ADVETI Version 1.0 2013 16 | 16