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 (5 + 2)² x 9 + 3 x (6 2-4²) 402 2 7659 + 4808 = 12467 3 7863-544 - 37 = 7282 4 The hundreds digit of 49167 is 1 5 73 + 48 = 121 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 1 of 9
6 71 x 3 = 213 7 6278 73 = 86 8 60 5 = 12 9 Round 56955 to hundreds 57000 10 The product of 53 and 7 is 371 11 435-119 = 316 12 What is the remainder of 70 62? 8 13 What is the remainder of 830 1? 0 14 What is the remainder of 90 2? 2851 15 92-72 = 20 16 Round 61859 to tens 61860 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 2 of 9
17 Estimate (±5%) 606 + 227 792, 874 18 Estimate (±5%) 37 + 47 80, 88 19 Estimate (±5%) 31 + 53 + 84 + 137 290, 320 20 11 x 11 = 121 21 679 + 839 = 1518 22 20 x 50 = 1000 23 6² = 36 24 71² = 5041 25 What is the remainder of 942 10? 2 26 65 x 90 = 5850 27 9 x 75 = 675 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 3 of 9
28 554 x 60 = 33240 29 47 x 95 = 4465 30 31 x 323 = 10013 31 Convert 2150 to Roman MMCL 32 Convert CXLIII to Arabic 143 33 Estimate (±5%) 9778 + 781-313 9734, 10758 34 Estimate (±5%) 280 + 762-683 342, 376 35 Estimate (±5%) 5957 + 659 + 11 + 2 6298, 6960 36 77 x 49 = 3773 37 1/8 in decimal is 0.125 38 182 + 158-65 = 275 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 972π and rounded to the nearest whole number, of a sphere with the radius of 9? 40 What is the surface area of a sphere, in terms of Pi, with radius of 3? 36π 41 What is the volume of a box with width 8 by height 3 and depth 7? 168 42 What is the area of a rectangle with dimensions of 6 by 6? 36 43 What is the volume of a cylinder, in terms of Pi, with the radius of 6 and diameter of 5? 44 What is the volume, in terms of Pi, rounded to nearest whole number, of a cone with the radius of 1 and height of 1? 45 What is the area of a circle, in terms of Pi, with the radius of 5? 180π 0π 25π 46 14 x 12 = 168 47 4/14 in lowest terms is 2/7 48 If a pound of bacon cost $4, a half dozen pounds of bacon cost 24 49 70 x 26 14 = 130 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 5 of 9
50 How many inches in 8 miles? 506880 51 How many inches in 7 feet? 84 52 How many feet in 5 miles? 26400 53 At 39 inches in a meter, how many whole meters in 53 feet? 16 54 How many prime numbers are between 10 and 36? 7 55 75 x 25 = 1875 56 The GCD of 96 and 96 is 96 57 How many ounces in 8 pounds? 128 58 At 453.592 grams per pound, how many kilograms, rounded to the nearest whole number, in 28 pounds? 59 At 28.3495 grams per ounce, how many grams, rounded to the nearest whole number, in 3 ounces? 13 85 60 1/8 + 5/8 = 3/4 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 6 of 9
61 Estimate (±5%) 79 x 69 x 40 207138, 228942 62 What is the perimeter of a equalateral triangle with sides measuring 6? 63 What is the circumference of a circle, in terms of Pi, with the radius of 1? 18 2π 64 What is the perimeter of a rectangle with dimensions of 5 by 8? 26 65 7.08 x 10^4 = 70800 66 17² x 15² = 65025 67 22² - 13² = 315 68 26² + 12² = 532 69 99 x 99 = 9801 70 How many seconds in 7 weeks? 4233600 71 How many seconds in 3 hours? 10800 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 7 of 9
72 How many hours in 3 days? 72 73 How many days in 4 weeks? 28 74 Which is smaller, 2/19 or 3/7? 2/19 75 0.3-85 = -84.7 76 8 x 8.5 = 68 77 473 11 = 43 78 0.76 + 8.9 = 9.66 79 192² = 36864 80 What is the square root of 225? 15 81 What is the cube root of 125? 5 82 The LCM of 8 and 12 is 24 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 41 the number 38? 84 1187 + 765 + 63 = 2015 85 How many even numbers are between 15 and 99? 42 86 How many odd numbers are between 24 and 96? 36 87 773 x 783 = 605259 88 560 x 22 = 12320 89 The sum of the prime numbers between 9 and 87? 857 90 Estimate (±5%) the cube root of 13824 23, 25 91 Estimate (±5%) the square root of 5476 71, 77 92 Estimate (±5%) 958 x 370 336737, 372183 93 Estimate (±5%) 955577 367 2474, 2733 2018, Art of Doing Math. All rights reserved. number-sense-practice-test-part-1-20180831 - Page 9 of 9