Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematics 1 (1) Fill in the empty boxes. 1 2 (2) 4+3 = (3) 10 - 9 = (4) 2x6 = (5) 15 3 = (6) 859 x 3 = (9) (11) 258 188 + 387 ___ 4 6 (7) (10) a) 4 + = 7 b) 4 - =2 c) 3 x = 9 d) 20 =5 7 150 5 = 9 10 13 (8) 3.14 + 6.2 = 537 - 318 ___ If pupil has completed the above, move on to NC Level Questions 1 Mathematics Assessment 2 Level 3 (A) You can make six numbers using these digit cards: Complete the list to show the six different numbers. Answer of 100 (B) Fill in the missing numbers. 68 + 20 × 300 .............. .............. .............. = 100 = 100 = 100 2 65 (C) × – 2 .............. = 100 Sums Calculate: 52 – 38 = ………... 259 + 386 = ………... 36 × 4 = ………..... 135 ÷ 5 = ………..... Level 4 (D) Forty-five (a) Fill in the missing numbers so that the answer is always 45. The first one is done for you. 5 40 + ...... 142 – .......... 50% of .......... = 45 450 1 of .......... 4 3 (E) Multiplication Work out 32 × 21 Show your working. ..................................... (F) Missing numbers Fill in the missing numbers. (G) 3.7 + 2.9 + 2.5 = = 4 Fractions (a) Look at these fractions: 1 2 1 3 5 6 Mark each fraction on the number line. The first one is done for you. 0 1 1 2 4 (H) Equations Solve these equations. a + 12 = 24 a = …………………. b – 12 = 24 b = ………………… Level 5 (I) Each diagram below was drawn on a square grid. (a) Write what percentage of each diagram is shaded. The first one is done for you. 75 ............... % ............... % ............... % 5 (J) Percentages (Use a Calculator) Calculate: 8% of £26.50 = £ 12½ % of £98 = £ (K) Solving (a) When x = 5, work out the values of the expressions below. 2x + 13 = ......................... 5x – 5 = ........................... 3 + 6x = ........................... Level 6 (L) Calculate Calculate 57.3 × 2.1 Show your working. . . . . . . . . ……………. 6 (M) Thinking fractions Calculate 5 3 6 5 Show your working. Write your answer as a fraction in its simplest form. ……………………….. (N) Solve these equations. Show your working. 8k 1 = 15 k = ............................ 2m + 5 = 10 m = ............................ 3t + 4 = t + 13 t = ............................ 7 Level 7 (o) Multiplication grids Write the missing numbers in these multiplication grids. × 8 9 72 –6 × 3 30 0.2 1.2 6 3 marks (p) Finding y Solve these equations. Show your working. (a) 4 – 2y 10 – 6y y ......................... 2 marks 8 (b) 5y + 20 3(y – 4) y ......................... 2 marks (c) 9y 9 2y 1 y ......................... 2 marks 9 (d) 9 y2 y2 y ......................... or ......................... 2 marks (q) Algebra (a) Find the values of a and b when p 10 a 3 p3 2 a ......................... 1 mark b 2 p 2 p – 3 7p b ......................... 1 mark 10 (b) Simplify this expression as fully as possible: 3cd 2 5cd 1 mark (c) Multiply out and simplify these expressions: 3(x – 2) – 2 (4 – 3x) 1 mark (x + 2)(x + 3) 1 mark (x + 4)(x – 1) 1 mark (x – 2)2 1 mark 11 Level 8 (r) Writing Numbers 1 is equal to 0.0004 2500 (a) Write 0.0004 in standard form. ............................... 1 mark (b) Write 1 in standard form. 25000 ............................... 1 mark (c) Work out 1 1 2500 25000 Show your working, and write your answer in standard form. ............................... 2 marks 12 (s) Graphs Match each graph to the correct equation. A B y C y x D y x E y x y x x Graph ................ shows the equation y 2x – 6 Graph ................ shows the equation y 6x3 Graph ................ shows the equation y 6 – x Graph ................ shows the equation y x2 – 6 Graph ................ shows the equation y 1 6x 2 marks 13 Mathematics 1 (Answers) (1) Fill in the empty boxes. 1 2 (2) 4+3 = (4) (6) (9) 3 4 6 7 7 (3) 10 - 9 = 1 2x6 = 12 (5) 15 3 = 5 859 x 3 = 2577 150 5 = 30 258 188 + 387 833 5 (7) (10) 8 9 10 (8) 11 12 3.14 + 6.2 = 13 9.34 537 - 318 219 Fill in the blanks using words: (11) a) 3 b) 2 c) 3 d) 4 14 Mathematics Assessment 2 (Answers) Level 3 (A) You can make six numbers using these digit cards: 3 5 7 Complete the list to show the six different numbers. 357 375 537 573 735 753 Answer of 100 (B) Fill in the missing numbers. 68 + 32 .............. = 100 20 × 5 .............. = 100 300 3 .............. = 100 15 65 (C) × 2 30 .............. – = Sums Possible methods/strategies Calculate: 4 52 – 38 52 - 38 14 100 1 10 4 = 14 38 259 + 386 = 645 36 × 4 = 144 135 ÷ 5 = 27 48 52 259 + 386 645 36 x 4 144 27 5 1335 36 x 2 = 72 72 x 2 = 144 135 10 = 13.5 13.5 x 2 = 27 16 Level 4 (D) Forty-five (a) Fill in the missing numbers so that the answer is always 45. The first one is done for you. 10 40 + 5 142 – 97 50% of 90 = 45 450 10 1 of 180 4 (E) Multiplication Work out 32 × 21 Show your working. Alternatively x 30 2 20 600 40 1 30 2 640 32 32 x 21 32 640 672 672 672 ..................................... 17 (F) Missing numbers Fill in the missing numbers. (G) 3.7 + 2.9 + 2.5 1.1 = 6.2 = 4 3.7 + 2.5 6.2 Fractions (a) Look at these fractions: 1 2 1 3 5 6 Mark each fraction on the number line. The first one is done for you. 0 1 3 5 6 1 1 2 (H) Equations Solve these equations. a + 12 = 24 a = 24 - 12 12 a = …………………. b – 12 = 24 b = 24 + 12 36 b = ………………… 18 Level 5 (I) Each diagram below was drawn on a square grid. (b) Write what percentage of each diagram is shaded. The first one is done for you. 75 ............... % 60 ............... % 60 ............... % (J) Percentages B Calculate using calculator £ 2.12 0.08 x 26.50 £ 12.25 0.125 x 98 8% of £26.50 = 12½ % of £98 = 19 (K) Solving (a) When x = 5, work out the values of the expressions below. (2x 5 + 13 = 23) 23 2x + 13 = ......................... (5x 5 – 5 = 20) 20 5x – 5 = ........................... 4 (3 + 6x 5 = 33) 33 + 6x = ........................... Level 6 0 Calculate Calculate 57.3 × 2.1 Show your working. 114.6 573 21 573 11460 12033 50 7 0.3 2 100 14 0.6 0 .1 5 0.7 0.03 5.73 120.33 . . . . . . . . ……………. (M) Thinking fractions 53 Calculate 6 5 Show your working. 15 30 1 2 or 20 1 5 62 1 3 x = 51 1 2 Write your answer as a fraction in its simplest form. 1 2 ……………………….. (N) Solve these equations. Show your working. 8k 1 = 15 8k = 16 2 k = ............................ 2m + 5 = 10 2m = 5 2.5 m = ............................ 3t + 4 = t + 13 2t = 9 4.5 t = ............................ 1. Completes both multiplication grids correctly, ie × 8 –5 9 72 –45 –6 –48 30 3 21 × 0.2 0.4 3 0.6 1.2 15 3 6 or Completes one of the grids correctly and makes not more than one error or omission in the other grid 2 or Completes one of the grids correctly 1 or Makes not more than one error or omission in each grid ! For 2m or 1m, follow through For the first grid, accept follow through only from their –5 but note that their –5 must be negative eg –6 (error but negative) × 8 9 72 –54 –6 –48 30 follow through For the second grid, accept follow through only from their 15 eg × 0.2 0.4 3 0.6 1.2 10 (error) 2 6 follow through [3] 22 2. Finding y (a) For 2m indicates a correct value, with no evidence that the value is derived from an incorrect method, eg: 2 1.5 For only 1m correctly reduces the equation to 2 terms, eg: 4y = 6 -4y = – 6 4y – 6 = 0 y=6÷4 y= or 6 4 Solves for y with not more than one computational error, eg: 6y – 2y = 10 – 4 4y = 8 y=2 For 2m accept an improper fraction written in its simplest terms eg: 3 ‘2’ Throughout the question do not accept incorrect methods leading to a correct value eg for part (a) ‘10 + 4 = 6y + 2y, 14 = 8y, y = 1.5’ For 1m throughout the question accept decimals rounded or truncated to 1 or more d.p. Throughout the question do not accept inability to process negative values as a computational error eg, in part (a) from 4 – 2y = 10 – 6y, accept 6y – 2y and 10 – 4, but not 6y + 2y or 10 + 4, or 8y or 14 (b) For 2m indicates – 16 2 For only 1m correctly multiplies y – 4 by 3, eg: 3y – 12 seen 5y – 3y = –20 – 12 2y = –32 y=– (c) 32 2 For 2m indicates –1 2 For only 1m correctly reduces the equation to 2 terms, eg: 9y = –9 -9y = 9 23 0 = 9y + 9 or Correctly multiplies 2y + 1 by 9, eg: 18y + 9 seen or Shows a correct simplification, eg: y 1 2y 1 (d) For 2m indicates both y = 1 and y = –5 2 For only 1m shows one correct solution, with no evidence that the solution found is derived from an incorrect method. or Shows a correct simplification of 9 = (y + 2) 2, eg: 9 = y2 + 4y + 4 9 = y2 + 2y + 2y + 4 5 = y(y + 4) y+2= 9=3 3=y+2 The other solution may be incorrect or omitted. [8] 3. (a) (b) Indicates 1500 1 Indicates 20 1 Indicates a correct, fully simplified expression eg: 1 ' 3d ' 5 3 ' d' 5 3d ÷ 5 0.6d Do not accept unconventional fractions eg: ' (c) 1.5 d' 2.5 Indicates a correct, fully simplified expression for 3(x – 2) – 2(4 – 3x) eg: 1 9x – 14 –14 + 9 × x Indicates a correct simplified expression for (x + 2) (x + 3) eg: 1 x2 + 5x + 6 x2 + 6 + 5 × x 24 Indicates a correct simplified expression for (x + 4) (x – 1) eg: 1 x2 + 3x – 4 3 × x – 4 + x2 Indicates a correct simplified expression for (x – 2)2 eg: 1 x2 – 4x + 4 x2 + x × – 4 + 4 x2 + 4(-x + 1) x2 should be written with index notation, ie not as x × x or xx. However, do not penalise this error more than once within the question. Throughout the question do not accept continuation from a correct response to an incorrect response eg: ‘x2 + 5x + 6 = 5x3 + 6’ [7] 4. Writing Numbers (a) 4 × 10–4 or 4 × 10-04 ! Unconventional index from notation eg, for part (a) 0.4 × 10–3 1 4 104 Penalise the first occurrence only. Do not accept incorrect notation eg, for part (a) 4–4 (b) 4 × 10–5 ! 1 Follow through from part (a) Provided the power is negative eg, for part (a) as 2 × 10–5 2 × 10–6 (c) 4.4 × 10–4 2 or 1 Digits 44 seen eg 25 4400 0.00044 44 100000 Do not accept digits 44 seen from an incorrect method eg 4 × 10–4 + 4 × 10–5 = 44 × 10–9 [4] 5. Graphs Gives all five correct letters in the correct order, ie D C B A E 2 or Gives at least three correct letters 1 [2] 26