This practice test includes typical math questions encountered in the first 40 of 80 questions in MathLeague's Number Sense tests based on the 2017-2018 competition season. In competition the Number Sense test lasts 10 minutes, giving you 7.5 seconds per question. Number Sense tests are mental math wherein you do the work mentally and only write down the answer. Scoring is 5 points for each correct answer and -4 points for each incorrect answer up to the point you stop. For practice, our goal is to learn the math, acheive proficiency in doing the math, then improving speed. In practice, try doing each question mentally, then, as needed, work through each problem on paper. If you time your test, mark your progress at 10 minutes, then continue on and complete the test, noting the overall time. Drill sheets and study recommendations are available for each of these practice test questions. Important! As you practice, don't worry about your time or number of the questions unanswered or wrong as this is a learning process and you will see improvement over time. Fold Over to Hide Answers While Working on Each Question 1 (3 + 5)² x 4 + 2 x (4 2-8²) 132 2 9664 + 9102 = 18766 3 3157-125 - 38 = 2994 4 The ten thousands digit of 26761 is 2 5 67 + 31 = 98 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 1 of 9
6 51 x 1 = 51 7 7565 89 = 85 8 186 6 = 31 9 Round 69121 to hundreds 69100 10 The product of 33 and 4 is 132 11 916-639 = 277 12 What is the remainder of 57 54? 3 13 What is the remainder of 250 1? 0 14 What is the remainder of 57 9? 562 15 89-85 = 4 16 Round 62885 to tens 62890 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 2 of 9
17 Estimate (±5%) 813 + 426 1178, 1300 18 Estimate (±5%) 59 + 62 115, 127 19 Estimate (±5%) 41 + 11 + 52 + 63 159, 175 20 85 x 11 = 935 21 748 + 155 = 903 22 89 x 50 = 4450 23 8² = 64 24 25² = 625 25 What is the remainder of 555 95? 80 26 35 x 80 = 2800 27 7 x 75 = 525 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 3 of 9
28 526 x 40 = 21040 29 81 x 65 = 5265 30 79 x 511 = 40369 31 Convert 3044 to Roman MMMXLIV 32 Convert MMDCCCLXI to Arabic 2861 33 Estimate (±5%) 4227 + 936-671 4268, 4716 34 Estimate (±5%) 780 + 796-744 791, 873 35 Estimate (±5%) 1623 + 147 + 80 + 8 1766, 1950 36 14 x 71 = 994 37 1/4 in decimal is 0.25 38 402 + 785-93 = 1094 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 4 of 9
39 What is the volume, in terms of Pi 11π and rounded to the nearest whole number, of a sphere with the radius of 2? 40 What is the surface area of a sphere, in terms of Pi, with radius of 5? 100π 41 What is the volume of a box with width 6 by height 7 and depth 9? 378 42 What is the area of a rectangle with dimensions of 4 by 3? 12 43 What is the volume of a cylinder, in terms of Pi, with the radius of 4 and diameter of 4? 44 What is the volume, in terms of Pi, rounded to nearest whole number, of a cone with the radius of 3 and height of 7? 45 What is the area of a circle, in terms of Pi, with the radius of 8? 64π 21π 64π 46 90 x 12 = 1080 47 14/42 in lowest terms is 1/3 48 If a pound of smoked gouda cost $2.07, a dozen pounds of smoked gouda cost 24.84 49 56 x 44 14 = 176 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 5 of 9
50 How many inches in 4 miles? 253440 51 How many inches in 1 feet? 12 52 How many feet in 2 miles? 10560 53 At 39 inches in a meter, how many whole meters in 59 feet? 18 54 How many prime numbers are between 12 and 40? 7 55 92 x 25 = 2300 56 The GCD of 435 and 174 is 87 57 How many ounces in 3 pounds? 48 58 At 453.592 grams per pound, how many kilograms, rounded to the nearest whole number, in 72 pounds? 59 At 28.3495 grams per ounce, how many grams, rounded to the nearest whole number, in 9 ounces? 33 255 60 3/8 + 5/16 = 13/16 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 6 of 9
61 Estimate (±5%) 51 x 53 x 63 161775, 178803 62 What is the perimeter of a hexagon with sides measuring 3? 18 63 What is the circumference of a circle, in terms of Pi, with the radius of 5? 10π 64 What is the perimeter of a rectangle with dimensions of 8 by 6? 28 65 6.35 x 10^5 = 635000 66 22² x 13² = 81796 67 23² - 11² = 408 68 27² + 16² = 473 69 66 x 99 = 6534 70 How many seconds in 4 weeks? 2419200 71 How many seconds in 2 hours? 7200 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 7 of 9
72 How many hours in 7 days? 168 73 How many days in 5 weeks? 35 74 Which is smaller, 3/7 or 7/40? 7/40 75 60-0.86 = 59.14 76 2.4 x 3 = 7.2 77 0.2992 0.44 = 0.68 78 64 + 72 = 136 79 532² = 283024 80 What is the square root of 5041? 71 81 What is the cube root of 1? 1 82 The LCM of 28 and 32 is 224 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 8 of 9
83 What is the next prime number after 17 the number 15? 84 7818 + 529 + 96 = 8443 85 How many even numbers are between 25 and 67? 21 86 How many odd numbers are between 76 and 76? 0 87 648 x 618 = 400464 88 248 x 84 = 20832 89 The sum of the prime numbers between 32 and 88? 714 90 Estimate (±5%) the cube root of 64000 38, 42 91 Estimate (±5%) the square root of 4225 62, 68 92 Estimate (±5%) 434 x 415 171105, 189115 93 Estimate (±5%) 955385 446 2036, 2249 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 9 of 9