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  1. Problems
  2. /Number Systems

Number Systems

Mathematics
+ Upload a Problem
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42 problems
Type:
1.
A square garden has an area of 18 m². Find its side, its perimeter and its diagonal. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
2.
Find √3 + √5 to three decimal places. Prove that √3 + √5 is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
3.
Find the whole number m for which (3 + √m)(3 - √m) = 4. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
4.
Prove that 5 - 3√2 is irrational. You may use the fact that √2 is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
5.
Prove that the cube root of 2, the number whose cube is 2, is irrational. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
6.
Among all fractions p/q with a bottom q from 1 to 10, which one is closest to √3 = 1.7320508…? New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
7.
6 is not a prime, but √6 is still irrational. Prove it by contradiction, using only the prime 2. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Hard
8.
Prove that √7 is irrational. Give a reason for every step. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
9.
Prove that if 6 divides a², then 6 divides a. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
10.
Prove that if n² is a multiple of 3, then n is a multiple of 3. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Medium
11.
Kabir works out n² - n + 11 for n = 1, 2, 3, … and finds 11, 13, 17, 23, 31 and so on, all primes. New
High School (9–10), General · Rational and Irrational NumbersStemPy LabStemPy Lab
Easy
12.
Find the smallest number that leaves a remainder of 5 when divided by 12, by 15 and by 20. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Hard
13.
Use Euclid's division method to find the HCF of 1517 and 902. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Medium
14.
Three tanks hold 238 litres, 357 litres and 476 litres of water. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Medium
15.
On a road, one traffic light turns green every 40 seconds and another every 56 seconds. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Easy
16.
Two numbers have an HCF of 12 and an LCM of 360. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Hard
17.
Neha is told that the HCF of 234 and 390 is 78. Find their LCM without factorising. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Medium
18.
Find the HCF and the LCM of 28, 42 and 70. Is HCF × LCM equal to 28 × 42 × 70? New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Medium
19.
Find the HCF and the LCM of 132 and 198 from their prime factorisations. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Easy
20.
Let n = 2³ × 3² × 5. How many factors does n have, counting 1 and n? New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Hard
21.
For which of these numbers is there a natural number n that makes the number end in the digit 0? New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Medium
22.
Write 3150 as a product of prime powers. New
High School (9–10), General · Divisibility, HCF and LCMStemPy LabStemPy Lab
Easy
23.
Simplify, using the laws of exponents. 5^(3/4) × 5^(1/4); (6^(1/3))⁶; 2^(1/2) × 18^(1/2)
High School (9–10), General · Exponents and RadicalsStemPy LabStemPy Lab
Medium
24.
Find the value of 27^(4/3), 243^(2/5) and 625^(-1/4).
High School (9–10), General · Exponents and RadicalsStemPy LabStemPy Lab
Medium
25.
Find the value of 169^(1/2), 1000^(1/3), 243^(1/5) and 256^(1/4).
High School (9–10), General · Exponents and RadicalsStemPy LabStemPy Lab
Easy
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