Higher Maths Stars
Order
Ruby Emerald Amethyst Sapphire Opal Diamond Plutonium
Ruby Star 15 minutes Name ______6 1 (9 x 3) + 6 28 /7 of 35 4 2 (8 x 4) + 8 29 /7 of 28 2 3 (6 – 4) x 9 30 /3 of 27 2 4 8 + (7 x 8) 31 /9 of 18 2 5 23 – (3 x 6) 32 /5 of 25 4 6 (7 x 7) – (4 x 3) 33 /9 of 36 4 7 82 – (7 x 6) 34 /11 of 44 8 34 – (5 x 3) 35 852 ÷ 6 9 (4 x 9) + 52 36 1974 ÷ 6 10 (3 x 8) - ? = 14 37 3808 ÷ 8 11 (9 x 6) - 13 38 2133 ÷ 9 12 (8 x 4) + (3 x 6) 39 3822 ÷ 7 13 4 - 7 40 14 x 5 14 9 - ? = - 12 41 16 x 6 15 5 - 11 42 17 x 4 16 14 – 30 43 12 x 6 17 1 ½ - 2 ½ 44 19 x 7 18 9 – 12.5 45 13 x 6 19 3 - 19 46 24 x 5 20 5 – 3 - 4 47 16 x 8 21 13 - ? = -18 48 26 x 3 22 -5 + 12 = 49 43 x 4 23 -3 +22 = 50 64 x 5 24 -4 + ? = 16 2 25 /7 of 21 3 26 /5 of 15 27 ¾ of 16
Ruby Star 15 minutes
Key skills
Calculations that use brackets Adding and subtracting using negative numbers Calculating fractions of numbers Multiplying numbers greater than 10 Dividing large numbers by numbers less than 10
(Revised 3/2018)
Ruby Star 15 minutes (answers) Name ______6 1 (9 x 3) + 6 33 28 /7 of 35 30 4 2 (8 x 4) + 8 40 29 /7 of 28 16 2 3 (6 – 4) x 9 18 30 /3 of 27 18 2 4 8 + (7 x 8) 64 31 /9 of 18 4 2 5 23 – (3 x 6) 5 32 /5 of 25 10 4 6 (7 x 7) – (4 x 3) 37 33 /9 of 36 16 4 7 82 – (7 x 6) 40 34 /11 of 44 16 8 34 – (5 x 3) 19 35 852 ÷ 6 142 9 (4 x 9) + 52 88 36 1974 ÷ 6 329 10 (3 x 8) - ? = 14 10 37 3808 ÷ 8 476 11 (9 x 6) - 13 41 38 2133 ÷ 9 237 12 (8 x 4) + (3 x 6) 50 39 3822 ÷ 7 546 13 4 - 7 -3 40 14 x 5 70 14 9 - ? = - 12 21 41 16 x 6 96 15 5 - 11 -6 42 17 x 4 68 16 14 – 30 -16 43 12 x 6 72 17 1 ½ - 2 ½ -1 44 19 x 7 133 18 9 – 12.5 -3.5 45 13 x 6 78 19 3 - 19 -16 46 24 x 5 120 20 5 – 3 - 4 -2 47 16 x 8 128 21 13 - ? = -18 31 48 26 x 3 78 22 -5 + 12 = 7 49 43 x 4 172 23 -3 +22 = 19 50 64 x 5 320 24 -4 + ? = 16 20 2 25 /7 of 21 4 3 26 /5 of 15 9 27 ¾ of 16 12 Emerald Star 20 minutes Name ______9 1 The range of 28 /7 of 35 65, 37, 84 8 2 The range of 29 /7 of 28 26, 3, 19, 25 5 3 The range of 30 /3 of 27 69, 25, 41, 28 8 4 The range of 31 /5 of 15 7, 6, -8, 12 5 The mean of 32 Split 25 in the ratio 32, 12, 25 2:3 6 The mean of 33 Split 49 in the ratio 53, 14, 29 3:4 7 The mean of 34 Split 72 in the ratio 12, 7, 17 5:7 8 The mean of 35 Split 81 in the ratio 45, 7, 32 7:2 9 The mode of 36 Split 64 in the ratio 2,1,3,5,6,4,1 5:3 10 The mode of 37 82 - 32 0,3,5,1,5,1,3,3 11 62 38 52 - 22 12 92 39 62 - √81 13 112 40 152 - √64 14 √144 41 122 - √49 15 √64 42 92 - √121 16 √16 43 33 17 √1 44 What are the factors of 25? 18 √400 45 What are the factors of 19? 19 The median of 46 What are the 12,15, 18,21,24 factors of 64? 20 The median of 47 What are the 6,4,9,7,8 factors of 24? 21 The median of 48 What are the 2,29,31,17,4 factors of 54? 22 The median of 49 What are the 45,55,35,25,65,15 factors of 36? 23 20% of 30 50 What are the factors of 68? 24 60% of 80 25 40% of 25 26 45% of 50 27 80% of 70
Emerald Star 20 minutes
Key skills
Mean, Mode, Range, Median Squares and square roots Percentages of whole numbers Ratio Factors
Emerald Star 20 minutes Answers 9 1 The range of 47 28 /7 of 35 45 65, 37, 84 8 2 The range of 23 29 /7 of 28 32 26, 3, 19, 25 5 3 The range of 44 30 /3 of 27 45 69, 25, 41, 28 8 4 The range of 20 31 /5 of 15 24 7, 6, -8, 12 5 The mean of 23 32 Split 25 in the ratio 10:15 32, 12, 25 2:3 6 The mean of 32 33 Split 49 in the ratio 21:28 53, 14, 29 3:4 7 The mean of 12 34 Split 72 in the ratio 30:42 12, 7, 17 5:7 8 The mean of 28 35 Split 81 in the ratio 63:18 45, 7, 32 7:2 9 The mode of 1 36 Split 64 in the ratio 40:24 2,1,3,5,6,4,1 5:3 10 The mode of 3 37 82 - 32 15 0,3,5,1,5,1,3,3 11 62 36 38 52 - 22 21 12 92 81 39 62 - √81 27 13 112 121 40 152 - √64 217 14 √144 12 41 122 - √49 137 15 √64 8 42 92 - √121 70 16 √16 4 43 33 27 17 √1 1 44 What are the 1, 5, 25 factors of 25? 18 √400 20 45 What are the 1,19 factors of 19? 19 The median of 18 46 What are the 1,2,4,8,16, 12,15, 18,21,24 factors of 64? 32,64 20 The median of 7 47 What are the 1,2,3,4,6 6,4,9,7,8 factors of 24? 8,12,24 21 The median of 17 48 What are the 1,2,3,6,9, 2,29,31,17,4 factors of 54? 18,27,54 22 The median of 40 49 What are the 1,2,3,4,6,9, 45,55,35,25,65,15 factors of 36? 12,18,36 23 20% of 30 6 50 What are the 1,2,4,17,34, factors of 68? 68 24 60% of 80 48 25 40% of 25 10 26 45% of 50 22.5 27 80% of 70 56 Amethyst Star 20 minutes Name ______4 1 30% of 90 24 /13 of 52 8 2 70% of 80 25 /14 of 42 2 3 15% of 60 26 /15 of 75 6 4 45% of 120 27 /16 of 64 5 35% of 40 28 Split 81 in the ratio 5:4 6 24% of 200 29 Split 84 in the ratio 3:4 7 53% of 300 20 Split 96 in the ratio 5:3 8 62% of 500 31 Split 132 in the ratio 5:7 9 √144 + 19 32 Split 184 in the ratio 1:7 10 33 + 42 33 13 x 14 11 105 - 43 34 41 x 16 12 √121 x 15 35 19 x 15 13 53 - 35 36 13 x 16 14 √169 x 7 37 252 ÷ 12 15 √81 x 8 38 396 ÷ 18 16 0.3 x 16 39 552 ÷ 23 17 0.7 x 14 40 I think of a number. I multiply it by 9, add 7 and halve it. My answer is 26, what is my number? 18 32 x 0.06 41 I think of a number. I divide it by 3, add 3 and multiply it by 8. The answer is 80, what is my number? 19 0.9 x 21 42 I think of a number. I double it, multiply it by 7 and then take off 45. The answer is 11. What is my number? 20 23 x 0.8 43 I have a length of ribbon that is 126 cm long. I cut it so that one piece is 14 cm longer than the short one. How long is the short piece? 21 What is the volume of 44 I have a piece of string that is a cuboid 242 cm long. I cut it so that one 3cm x 6cm x 8cm? piece is 30 cm longer than the short one. How long is the short piece? 22 What is the volume of 45 I cut a piece of ribbon into 3 a cuboid strips. One is 26 cm long, one is 4cm x 7cm x 6cm? 7cm shorter and one is the same length as the other 2 added together. How long is the longest ribbon? 23 What is the volume of a cuboid 9cm x 6cm x 11cm?
Amethyst Star 20 minutes
Key skills
Squares and square roots Percentages of whole numbers Ratio Volume Multiplication by numbers between 10 – 20 Reasoning
Amethyst Star 20 minutes Answers 4 1 30% of 90 27 24 /13 of 52 16 8 2 70% of 80 56 25 /14 of 42 24 2 3 15% of 60 9 26 /15 of 75 10 6 4 45% of 120 54 27 /16 of 64 24 5 35% of 40 14 28 Split 81 in the ratio 5:4 45:36 6 24% of 200 48 29 Split 84 in the ratio 3:4 36:48 7 53% of 300 159 20 Split 96 in the ratio 5:3 60:36 8 62% of 500 310 31 Split 132 in the ratio 5:7 55:77 9 √144 + 19 31 32 Split 184 in the ratio 1:7 23:161 10 33 + 42 69 33 13 x 14 192 11 105 - 43 41 34 41 x 16 656 12 √121 x 15 165 35 19 x 15 285 13 53 - 35 90 36 13 x 16 208 14 √169 x 7 91 37 252 ÷ 12 21 15 √81 x 8 72 38 396 ÷ 18 22 16 0.3 x 16 4.8 39 552 ÷ 23 24 17 0.7 x 14 9.8 40 I think of a number. I multiply it 5 by 9, add 7 and halve it. My answer is 26, what is my number? 18 32 x 0.06 1.92 41 I think of a number. I divide it 21 by 3, add 3 and multiply it by 8. The answer is 80, what is my number? 19 0.9 x 21 18.9 42 I think of a number. I double it, 4 multiply it by 7 and then take off 45. The answer is 11. What is my number? 20 23 x 0.8 18.4 43 I have a length of ribbon that is 56cm 126 cm long. I cut it so that one piece is 14 cm longer than the short one. How long is the short piece? 21 What is the volume 144cm3 44 I have a piece of string that is 106cm of a cuboid 242 cm long. I cut it so that one 3cm x 6cm x 8cm? piece is 30 cm longer than the short one. How long is the short piece? 22 What is the volume 168cm3 45 I cut a piece of ribbon into 3 45cm of a cuboid strips. One is 26 cm long, one is 4cm x 7cm x 6cm? 7cm shorter and one is the same length as the other 2 added together. How long is the longest ribbon? 23 What is the volume 594cm3 of a cuboid 9cm x 6cm x 11cm?
Sapphire Star 20 minutes Name ______1 43 - 72 24 23 x 13 2 53 + 17 25 43 x 15 3 152 + 16 26 92 x 12 4 21 + √361 27 46 x 16 5 142 - 32 28 253 x 18 6 122 + 132 29 Split 42 in the ratio 2:4:1 7 182 - 24 30 Split 81 in the ratio 3:5:1 8 √169 + 28 31 Split 132 in the ratio 4:5:2 9 √289 + 39 32 Split 324 in the ratio 4:3:2 6 3 10 /7 + /5 33 Split 152 in the ratio 6:1:1 4 7 11 /5 + /9 34 What are the common factors of 42 and 18? 2 3 12 /9 + /8 35 What are the common factors of 80 and 32? 5 5 13 /12 + /14 36 What are the common factors of 54 and 21? 1 7 14 /7 + /12 37 What are the common factors of 132 and 44? 6 2 15 /19 + /15 38 What are the common factors of 31 and 124? 16 35% of 240 39 What is halfway between 113 and 77? 17 45% of 320 40 What is halfway between 125 and 63? 18 65% of 260 41 What is halfway between 163 and 59? 19 42% of 250 42 What is halfway between 109 and 38? 20 85% of 150 43 What is halfway between 153 and 48? 21 32% of 300 44 What is halfway between 918 and 286? 22 44% of 450 45 What is halfway between 515 and 377? 23 26% of 150
Sapphire Star 20 minutes
Key skills
Squares and square roots of numbers up to 20 Finding the common denominator of fractions Percentages of whole numbers Ratio Common factors Finding half the difference between numbers
Sapphire Star 20 minutes Answers 1 43 - 72 15 24 23 x 13 299 2 53 + 17 142 25 43 x 15 645 3 152 + 16 241 26 92 x 12 1104 4 21 + √361 40 27 46 x 16 736 5 142 - 32 164 28 253 x 18 4554 6 122 + 132 313 29 Split 42 in the ratio 12:24: 2:4:1 6 7 182 - 24 300 30 Split 81 in the ratio 27:45:9 3:5:1 8 √169 + 28 41 31 Split 132 in the ratio 48:60: 4:5:2 24 9 √289 + 39 56 32 Split 324 in the ratio 144:108: 4:3:2 72 6 3 10 /7 + /5 51/35 33 Split 152 in the ratio 114:19: 6:1:1 19 4 7 11 /5 + /9 71/45 34 What are the common 1,2,3,6 factors of 42 and 18? 2 3 12 /9 + /8 43/72 35 What are the common 1,2,4,8, factors of 80 and 32? 16 5 5 13 /12 + /14 130/168 36 What are the common 1,3 factors of 54 and 21? 1 7 14 /7 + /12 61/84 37 What are the common 1,2,4,11, factors of 132 and 44? 44 6 2 15 /19 + /15 128/285 38 What are the common 1,31 factors of 31 and 124? 16 35% of 240 84 39 What is halfway 95 between 113 and 77? 17 45% of 320 144 40 What is halfway 94 between 125 and 63? 18 65% of 260 169 41 What is halfway 111 between 163 and 59? 19 42% of 250 105 42 What is halfway 73.5 between 109 and 38? 20 85% of 150 127.5 43 What is halfway 100.5 between 153 and 48? 21 32% of 300 96 44 What is halfway 602 between 918 and 286? 22 44% of 450 198 45 What is halfway 446 between 515 and 377? 23 26% of 150 39 Opal Star 20 minutes Name ______1 962 - 365 16 0.5 x 0.08 2 428 - 130 17 0.7 x 0.8 3 857 - 568 18 0.09 x 0.4 4 2137 - 1140 19 1.5 x 0.06 5 9006 - 896 20 0.5 x 0.018 6 564 + 378 21 -7 x 62 7 265 + 438 22 36 x -6 8 706 + 239 23 15 x -12 9 658 + 897 24 -24 x -16 10 769 + 389 25 -41 x -66 11 21.06 + 0.056 26 -702 ÷ 13 12 31.9 + 274.56 27 -624 ÷ 16 13 1.838 – 0.0028 28 -1548 ÷ -18 14 510.6 – 235. 8 29 1292 ÷ -17 15 11.92 – 5.8 30 -1786 ÷ -19
2 Start /7 of x 7 ÷3 +107 Square -15 x 2 + 47 Your with this root answer 21 of
Start Times -98 ÷2 x 5 -65 ÷100 +4.2 x15 Your with by answer 14 itself
5 Start Multiply 30% Multiplied - 60 Divide /11 -9 x24 Your with by 8 of by itself by 3 of answer 7.5
Now solve this Futoshiki problem. Every row and every column has to have the numbers 1, 2, 3 and 4. Some numbers have been put in for you. Also you have some clues from the > and < signs.
> 2 v < <
1 >
3
Finally this Sudoku problem. Every row and every column has to have the numbers 1 – 6. Also every block of 6 numbers has to have the numbers 1 – 6.
2 1 4 6
4 1 3 2
5 3 1 4 6 4 5
Key skills
Adding and subtracting large numbers mentally Adding and subtracting decimals Multiplying decimals Multiplying and dividing using negative numbers Mathematical reasoning (Revised 7/2018) Opal Star 20 minutes Answers 1 962 - 365 597 16 0.5 x 0.08 0.04 2 428 - 130 298 17 0.7 x 0.8 0.56 3 857 - 568 289 18 0.09 x 0.4 0.036 4 2137 - 1140 997 19 1.5 x 0.06 0.090 5 9006 - 896 8110 20 0.5 x 0.018 0.0090 6 564 + 378 942 21 -7 x 62 -434 7 265 + 438 703 22 36 x -6 -216 8 706 + 239 945 23 15 x -12 -180 9 658 + 897 1555 24 -24 x -16 384 10 769 + 389 1158 25 -41 x -66 2706 11 21.06 + 0.056 21.116 26 -702 ÷ 13 -54 12 31.9 + 274.56 306.46 27 -624 ÷ 16 -39 13 1.838 – 1.8352 28 -1548 ÷ -18 86 0.0028 14 510.6 – 235. 8 274.8 29 1292 ÷ -17 -76 15 11.92 – 5.8 6.12 30 -1786 ÷ -19 94
2 Start /7 of x 7 ÷3 +107 Square -15 x 2 + 47 Your with this root answer of 21 6 42 14 121 11 -4 -8 39 39 Start Times -98 ÷2 x 5 -65 ÷100 +4.2 x15 Your with by answer itself 14 196 98 49 245 180 1.8 6 90 90 5 Start Multiply 30% Multiplied - 60 Divide /11 -9 x11 Your with by 8 of by itself by 3 of answer
7.5 60 18 324 264 88 40 31 341 341
Now solve this Futoshiki problem. Every row and every column has to have the numbers 1, 2, 3 and 4. Some numbers have been put in for you. Also you have some clues from the > and < signs.
4 > 3 1 2 v 1 < 2 3 < 4
2 1 4 > 3
3 4 2 1
Finally this Sudoku problem. Every row and every column has to have the numbers 1 – 6. Also every block of 6 numbers has to have the numbers 1 – 6.
3 2 6 5 4 1 4 5 1 6 3 2
2 4 5 3 1 6 1 6 3 4 2 5
5 3 2 1 6 4 6 1 4 2 5 3
Key skills
Adding and subtracting large numbers mentally Adding and subtracting decimals Multiplying decimals Multiplying and dividing using negative numbers Mathematical reasoning Diamond Star 20 minutes Name ______
Multiplication of two and three digit numbers Percentages of numbers Multiplying and dividing fractions Squares and square roots Dividing large numbers by numbers less than 20 Mathematical reasoning
1 36 x 8 17 35% of 80 2 87 x 9 18 45% of 120 3 523 x 6 19 32% of 550 4 616 x 7 20 62% of 350 5 5107 x 6 The next 4 have decimal answers 6 23 x 18 21 73% of 230 7 36 x 32 22 24% of 610 8 67 x 29 23 57% of 740 9 327 x 36 24 83% of 920 3 7 10 417 x 59 25 /5 x /9 6 8 11 322 ÷ 14 26 /11 ÷ /7 7 5 12 916 ÷ 16 27 /9 ÷ /7 11 17 13 1332 ÷ 18 28 /14 x /19 16 4 14 1254 ÷ 19 29 /9 ÷ /3 15 6 15 799 ÷ 17 30 /17 x /11 16 1692 ÷ 18
Start 3/7 Times ÷25 +174 2/3 +74 Square - X3 - Your with of by of root of 3.5 19.3 answer 35 this itself
Start -40 Times -17 3/8 X8 +97 Square X 5 + ÷ 11 Your with by of root of 47 answer 31 itself
Solve these Sujiko puzzles. You need to arrange the numbers 1 – 9 in the boxes so that the 4 numbers surrounding each circle add to make the number in the circle.
(Revised 3/2018)
Diamond Star 20 minutes Answers
Mental multiplication of two and three digit numbers Percentages of numbers Multiplying and dividing fractions Squares and square roots Mathematical reasoning
1 36 x 8 288 17 35% of 80 28 2 38 x 7 266 18 45% of 120 54 3 53 x 6 318 19 32% of 550 176 4 87 x 9 783 20 62% of 350 217 5 76 x 4 304 The next 4 have decimal answers 6 523 x 6 3138 21 73% of 230 167.9 7 616 x 7 4312 22 24% of 610 146.4 8 3024 x 8 24192 23 57% of 740 421.8 9 5107 x 6 30642 24 83% of 920 763.6 3 7 10 23 x 18 414 25 /5 x /9 21/45 6 8 11 36 x 32 1152 26 /11 ÷ /7 42/88 or 21/44 7 5 14 24 x 35 840 27 /9 ÷ /7 49/45 11 17 15 67 x 29 1943 28 /14 x /19 187/266 16 4 16 327 x 36 11772 29 /9 ÷ /3 48/36 or 4/3 15 6 30 /17 x /11 90/187
Start 3/7 Times ÷25 +174 2/3 +74 Square -3.5 X3 - Your with of by of root of 19.3 answer 35 this itself 15 225 9 183 122 196 14 10.5 31.5 12.2 12.2 Start -40 Times -17 3/8 X8 +97 Square X 5 +47 ÷ 11 Your with by of root of answer 31 itself -9 81 64 24 192 289 17 85 132 12 12
Solve these Sujiko puzzles. You need to arrange the numbers 1 – 9 in the boxes so that the 4 numbers surrounding each circle add to make the number in the circle.
Plutonium Star 20 minutes Name ______
Division by numbers up to 99. The squares and square roots of numbers up to 30. Algebra Mathematical reasoning
If a = 3, b = 5, c = 8 , 16 7686 ÷ 61 d = 11, what are 1 ab - c 17 9860 ÷ 68 2 c2 - b 18 0.83 x 0.07 3 a(b + c) 19 1.004 x 0.03 4 (c + b)(d – a) 20 21.3 x 0.041 5 bc(c + d) 21 1.78 x 0.92 6 a/(b+c) ÷ b/(d+b) 22 0.056 x 1.08 7 (ab)2 - db 23 15.12 ÷ 0.56 8 222 - 67 24 1.476 ÷ 0.36 9 √841 - 42 25 19.61 ÷ 0.53 10 √576 - √196 11 212 + √676 12 2322 ÷ 43 13 2898 ÷ 46 14 2912 ÷ 91 15 3984 ÷ 83
Start 3/5 of Times - 2/9 Square - X 3.7 Add Square X Your with this by 801 of root of 14.6 together root of 524 answer 85 itself this the digits
Start Square x 35 -17 3/8 2/3 of +393 Square X 5 + 51 ÷ 11 Your with root of of root of answer 729
You have to put the numbers 1 – 9 in the right squares to make the answers vertically and horizontally.
x + 38 - - x 1 - x -21 x - x + x 7 77 48 -9 42
4 ÷ x 20 - - + x + 58 + ÷ x 9 - ÷ 1 5 -2 42
Plutonium Star 20 minutes Answers
Division by numbers up to 99. The squares and square roots of numbers up to 30. Algebra Mathematical reasoning
If a = 3, b = 5, c = 8 , 16 7686 ÷ 61 126 d = 11, what are 1 ab - c 7 17 9860 ÷ 68 145 2 c2 - b 59 18 0.83 x 0.07 0.0581 3 a(b + c) 39 19 1.004 x 0.03 0.03012 4 (c + b)(d – a) 104 20 21.3 x 0.041 0.8733 5 bc(c + d) 760 21 1.78 x 0.92 1.6376 6 a/(b+c) ÷ b/(d+b) 48/65 22 0.056 x 1.08 0.06048 7 (ab)2 - db 170 23 15.12 ÷ 0.56 27 8 222 - 67 417 24 1.476 ÷ 0.36 4.1 9 √841 - 42 13 25 19.61 ÷ 0.53 37 10 √576 - √196 10 11 212 + √676 467 12 2322 ÷ 43 54 13 2898 ÷ 46 63 14 2912 ÷ 91 32 15 3984 ÷ 83 48
Start 3/5 of Times - 2/9 Square - X 3.7 Add Cube X 524 Your with this by 801 of root of 14.6 together root answer 85 itself this the of digits
51 2601 1800 400 20 5.4 19.98 3 1572 1572 27 Start Square x 35 -17 3/8 2/3 of +393 Square X 5 + 51 ÷ 11 Your with root of of root of answer 729 25 27 945 928 348 232 625 125 176 16 16
You have to put the numbers 1 – 9 in the right squares to make the answers vertically and horizontally.
9 x 4 + 2 38 - - x 1 - 8 x 3 -21 x - x 6 + 5 x 7 77 48 -9 42
4 ÷ 1 x 5 20 - - + 8 x 7 + 2 58 + ÷ x 9 - 3 ÷ 6 1 5 -2 42