Real numbers
number sets and set operations, intervals, equations with absolute value, divisibility and remainders, powers with integer and rational exponents, roots of any degree, logarithms, compound interest
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Find A ∩ B
A = {−4, 7, 12, 13} B = {−4, 6, 12}
Problem
The value of an investment grew every year by the same percentage. At the start it was 32 000 zloty, and after 3 years it was 55 296 zloty. By what percentage did it grow each year?
How many solutions does the equation have?
|x + 7| = 6
Problem
110 000 zloty was deposited at 3% a year, compounded annually. How many zloty will be in the account after 3 years?
Calculate
log₁₀ 100⁵
Problem
44 000 zloty was put on deposit for 1 year. The interest rate is 6% a year, compounded half-yearly. Ignore the tax on interest. How many zloty will be on the deposit after that time? Give the answer to the nearest grosz.
Rationalise the denominator
19/(2√3)
Write the interval shown on the number line
Which interval is marked on the number line?
Problem
A natural number n leaves a remainder of 1 when divided by 3. What remainder does 5n² leave when divided by 3?
List the elements of the set (here ℕ = {0, 1, 2, …})
A = {x ∈ ℕ : x < 0}
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