UTBK-SNBT (Indonesia) · Penalaran Matematika

Aritmetika dan Aljabar

18 practice questions, each with the answer and an explanation.

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If $f (x) = 2 x^{2} - 3 x + 5$ and $g (x) = x - 2$ , what is the remainder when the product polynomial $f (x) \cdot g (x)$ is divided by $(x - 3)$ ?
A trader purchased 40 crates of fruit for a total of $1,200. If 10% of the fruit spoiled and the remainder was sold at $40 per crate, what was the trader's net profit percentage?
In an arithmetic progression, the 4th term is 17 and the 10th term is 41. What is the sum of the first 15 terms of this progression?
Solve the inequality: $\frac{2 x - 5}{x + 3} \leq 1$ . What is the complete solution set?
If $2^{x + 1} + 2^{x - 1} = 20$ , what is the numerical value of $x$ ?
A water tank is filled by pipe A in 6 hours and emptied by pipe B in 9 hours. If both operate simultaneously starting with an empty tank, how many hours will it take to fill the tank completely?
If $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ , what is the real solution for $x$ ?
The roots of quadratic equation $x^{2} - (k + 2) x + (2 k + 1) = 0$ are $α$ and $β$ . If $α^{2} + β^{2} = 11$ , what is the positive value of $k$ ?
What is the determinant of matrix $M = (35 - 2 4)$ ?
A geometric sequence has first term $a = 3$ and common ratio $r = 2$ . Which term of this sequence is equal to 384?
Solve the system: $3 x + 2 y = 16$ and $2 x - y = 6$ . What is the value of $x^{2} - y^{2}$ ?
If $a + b = 7$ and $ab = 10$ , what is the numerical value of $a^{3} + b^{3}$ ?
A line passes through $(2, 5)$ and is perpendicular to $2 x - 4 y = 9$ . What is the y-intercept of this line?
The average of five distinct integers is 24. If the median is 26 and the smallest integer is 10, what is the maximum possible value of the largest integer?
If $x^{2} - 6 x + y^{2} + 8 y + 25 = 0$ , what is the value of $x + y$ ?
How many positive integer factors does the number 360 have?
A machine depreciates at a rate of 10% per year on its reducing balance. If its value after 2 years is $16,200, what was its original purchase price?
If $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$ and $x + y = 18$ , what is the numerical value of $x y$ ?

Aritmetika dan Aljabar

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