Nationella prov (Sweden) · Mathematics
Algebra, Equations, Exponents and Sequences
35 practice questions, each with the answer and an explanation.
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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.
All 35 questions
- Solve the linear equation for x: 7x - 15 = 3x + 21.
- Solve the quadratic equation x^2 - 8x + 12 = 0 using the quadratic formula or factoring.
- Simplify the exponential expression (3x^3 y^2)^3.
- Evaluate the logarithmic expression log_2(64) + log_3(81).
- Find the 15th term of the arithmetic progression with first term a_1 = 4 and common difference d = 3.5.
- Factor the algebraic expression 9x^2 - 49y^2 completely.
- Solve the system of equations: 2x + 3y = 19 and 5x - y = 5. What is the value of x + y?
- Solve the rational equation: 4/(x - 2) = 3/(x + 1).
- Simplify the expression with rational exponents: (16x^4 / y^8)^(3/4) for positive x and y.
- Determine the sum of the first 8 terms of the geometric progression: 3, 6, 12, 24, ...
- Solve for x: lg(x) + lg(x - 3) = 1, where lg denotes the common logarithm base 10.
- Find all real solutions to the equation |2x - 7| = 13.
- Solve the inequality: 3x - 4 < 5x + 8.
- Find the discriminant of the quadratic equation 3x^2 - 5x + 4 = 0 and determine the nature of its roots.
- Simplify the algebraic fraction: (x^2 - 9) / (2x^2 + 5x - 3).
- If 2^(x+1) + 2^x = 48, what is the value of x?
- The sum of three consecutive odd integers is 111. What is the value of the largest of the three integers?
- Solve for x in the equation: sqrt(3x + 1) = x - 3.
- Simplify the expression: (2 / (x - 1)) - (3 / (x + 2)).
- Determine the value of k such that the polynomial P(x) = 2x^3 - kx^2 + 5x - 6 is divisible by (x - 2).
- Expand and simplify the product: (2x - 3y)(4x^2 + 6xy + 9y^2).
- Solve the rational inequality: (2x - 5)/(x + 3) <= 0.
- If the sum of an infinite geometric series with first term a = 12 is 36, what is the common ratio r?
- Evaluate the summation: sum_{k=1}^{20} (4k - 3).
- Express the radical expression in simplest form: sqrt(72) - sqrt(18) + sqrt(50).
- Solve for x in the exponential relation: 3^(2x - 1) = 27^(x - 2).
- What is the remainder when the polynomial f(x) = 3x^4 - 2x^2 + 5x - 7 is divided by (x + 1)?
- Rationalize the denominator of the fraction: 6 / (3 - sqrt(3)).
- Given log_b(2) = 0.356 and log_b(5) = 0.827, determine the numerical value of log_b(20).
- A deposit of 50,000 SEK grows at 3% annual compound interest. How many years are required for the balance to surpass 65,000 SEK? (log(1.3) approx 0.1139, log(1.03) approx 0.0128)
- Solve the equation: 1/x + 1/(x + 2) = 5/12.
- Simplify the algebraic fraction: ((1/x) - (1/y)) / ((1/x^2) - (1/y^2)).
- Solve the absolute value inequality: |3x - 5| <= 10.
- If the polynomial P(x) = x^3 - 7x^2 + 14x - 8 has known roots at 1 and 4, find the remaining root.
- Find all real solutions for x in: 4^x - 5 * 2^x + 4 = 0.
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