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  1. Problems
  2. /IB

IB problems

495 problems for IB practice, each with a worked solution. Try each one on paper first, then check your answer.

Other examsJEE MainJEE AdvancedNEETBITSATWBJEEBoard ExamOlympiadSATAPA-LevelGaokaoPCEP (Python Institute)PCAP (Python Institute)

Choose a topic to see its subtopics.

46 problems
Type:
1.
How many 3-digit numbers have three different digits? How many of them are odd? New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
2.
How many 4-digit even numbers can be made from the digits 0, 1, 2, 3, 4 and 5, if no digit is used… New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
3.
In how many ways can the letters of the word MISSISSIPPI be arranged? New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
4.
Kavya has 4 red, 3 blue and 2 green tiles. New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
5.
The word ALLAHABAD has 9 letters. How many arrangements of its letters are there? New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
6.
Seven friends take seven seats in a row at the cinema. New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Easy
7.
In how many ways can the letters of the word ORANGE be arranged so that the vowels stand only in… New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
8.
Four digit numbers are made from the digits 0, 1, 2, 3, 4, 5, with no digit repeated. New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
9.
A committee of 5 is chosen from 6 men and 5 women. How many committees have at least 2 women? New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
10.
A team of 11 is picked from 15 players, who include Kiran and Joseph. New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
11.
How many 4-letter words, with or without meaning, can be made from the letters of EDUCATION, if… New
High School (11–12) · Permutations and CombinationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
12.
For which real number k is (2 + ki)/(1 + 3i) a real number? What is its value then? New
High School (11–12) · Complex NumbersBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
13.
Find |((3 - 4i)(8 + 6i))/((1 + i)²)| without multiplying out any brackets. New
High School (11–12) · Complex NumbersBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
14.
Find the square roots of -15 + 8i. New
High School (11–12) · Complex Numbers, Quadratic EquationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
15.
The equation x² + px + q = 0 has real p and q. New
High School (11–12) · Complex Numbers, Quadratic EquationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IBStemPy LabStemPy Lab
Hard
16.
How many terms of 5, 9, 13, … must be taken so that their sum is 275? New
High School (9–10), General · Sequences and SeriesBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
17.
The sum of the first n terms of an arithmetic progression is 4n² - n. New
High School (9–10), General · Sequences and SeriesBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
18.
How many terms of 21, 18, 15, … must be added to get 81? Explain why there are two answers. New
High School (9–10), General · Sequences and SeriesBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
19.
Find the values of k for which (k + 1)x² - 2(k - 1)x + 1 = 0 has two equal roots. New
High School (9–10), General · Quadratic EquationsBoard Exam, SAT, A-Level, IBStemPy LabStemPy Lab
Medium
20.
Show that there is no real number k for which x² + 2(k + 3)x + 9k = 0 has two equal roots. New
High School (9–10), General · Quadratic EquationsBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
21.
Find the exact value of sin 105°. Then give it to three decimal places. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IBStemPy LabStemPy Lab
Easy
22.
sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IBStemPy LabStemPy Lab
Medium
23.
Prove that tan(π/4 + x) = (1 + tan x)/(1 - tan x). New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, A-Level, IBStemPy LabStemPy Lab
Medium
24.
A and B are acute angles with tan A = 1/2 and tan B = 1/3. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, A-Level, IBStemPy LabStemPy Lab
Hard
25.
cos x = -5/13, and x lies between π/2 and π. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IBStemPy LabStemPy Lab
Medium
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