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What is the minimum value of 􀝂 (􀝔) = 2􀝔2 + 4􀝔 − 4 ?  \nCircle correct answer:  \nA) −4 B) 0 C) −8 D) −6  \n2. Solve the simultaneous equations: { 32􀜽􀜽 − 46􀝇􀝇  1150  \nCircle correct answer:  \nA) (􀜽; 􀝇) = (5; 0) B) (􀜽; 􀝇) = (3; 1) C) (􀜽; 􀝇) = (2; 2) D) (􀜽; 􀝇) = (3; 0)  \n3. Find all solutions in degrees within the interval (0°; 180°) .  \n􀝏􀝅􀝊2􀝔 = 􀜿􀝋􀝏 (3􀝔 − 􀟨2)  \nCircle correct answer:  \nA) 􀰗5 ; 3􀰗5 ; 2􀰗5~~ ~~ B) 2􀰗5 ; 5􀰗5~~ ~~ C) 3􀰗5 ; 3􀰗5 ; 􀟨 D) 􀰗5 ; 3􀰗5  \n4. Solve the equation: 􀝔 2 − 15􀝔 + 50 = 0  \nCircle correct answer:  \nA) 􀝔1 = 5, 􀝔2 = 11 B) 􀝔1 = 4, 􀝔2 = 7 C) 􀝔1 = 5, 􀝔2 = −4 D) 􀝔1 = 10, 􀝔2 = 5  \n5. Solve the equation: log~~4 ~~(52􀯫+3) = 12  \nCircle correct answer:  \nA) 􀝔 = 14 B) 􀝔 = 3 C) 􀝔 = 15 D) 􀝔 = 1  \n6. Simplify the expression: 3􀯣632􀯤 ∙ 􀯣~~ ~~32􀯣􀯤2 : 􀯣~~ ~~2􀯣􀯤  \nCircle correct answer:  \nA) 3􀝌 B) 19 C) 􀝌 − 􀝍 D) 1  \n7. In the figure, the two horizontal lines are parallel, and the two transversal lines are also parallel. If the angles are as shown, find the value of 􀝔 + 􀝕 .  \nCircle correct answer:  \nA) 45° B) 90° C) 100° D) 50°  \n8. A pedestrian walks 7.8 km in 3 hours.  \nWhat distance (in km) will this person walk at the same speed in 4 hours?  \nCircle correct answer:  \nA) 10.6 B) 10.4 C) 10.8 D) 10.5  \n9. Find the equation of the function:  \nCircle correct answer:  \nA) 􀝕 = 2􀝔2 + 8􀝔 − 6  \nC) 􀝕 = −􀝔2 + 8􀝔 − 3  \nB) 􀝕 = −2􀝔2 + 4􀝔 − 5  \nD) 􀝕 = −􀝔2 + 6􀝔 − 5  \n10. Solve the inequality: 4 − 􀝔 2 > 6􀝔 . How many integer numbers satisfy the inequality?  \nCircle correct answer:  \nA) 3 B) 4 C) 6 D) 7  \n11. Given the linear function where 􀝂(3) = 7 and 􀝂(5) = 9, find 􀝂(􀝔) .  \nCircle correct answer:  \nA) 􀝂(􀝔) = 2􀝔 + 3 B) 􀝂(􀝔) = 􀝔 + 4 C) 􀝂(􀝔) = 3􀝔 D) 􀝂(􀝔) = 􀝔 + 3  \n12. Find the area of the shaded region if the side of square ABCD is 6√2 .  \nCircle correct answer:  \nA) 18 B) 36√2 C) 36 D) 36√3  \n13. Solve the equation: 4􀝔√2􀝔 − 1 = 10􀝔 − 5  \nCircle correct answer:  \nA) 􀝔1 = 12 , 􀝔2 = 58 , 􀝔3 = 52 B) 􀝔1 = 12 , 􀝔2 = 57 , 􀝔3 = 32  \nC) 􀝔1 = 13 , 􀝔2 = 78 , 􀝔3 = 52 D) 􀝔1 = 14 , 􀝔2 = 38 , 􀝔3 = 32  \n14. Find the real value of 􀝔 such that √􀯫􀯫−34 = 0  \nCircle correct answer:  \nA) 􀝔 = 1 B) 􀝔 = 2 C) 􀝔 = 3 D) 􀝔 = 4  \n15. A store sold 12 notebooks and 8 pens for 136,000 sums.  \nOn the next day, the store sold 7 notebooks and 10 pens for 122,000 sums.  \nFind the price of one notebook and one pen.  \nCircle correct answer:  \nA) Notebook – 8,000 sums; Pen – 5,000 sums B) Notebook – 6,000 sums; Pen – 8,000 sums  \nC) Notebook – 10,000 sums; Pen – 2,000 sums D) Notebook – 7,000 sums; Pen – 6,000 sums  \n 34􀳙   1  \n16. Solve for 􀝊: 272􀳙 = 9  \nCircle correct answer:  \nA) 􀝊1 = 2, 􀝊2 = 3 B) 􀝊1 = 1, 􀝊2 = 2 C) 􀝊1 = 0, 􀝊2 = 1 D) 􀝊1 = 3, 􀝊2 = 4  \n17. Simplify: 6􀯫􀯫1−1  \nCircle correct answer:  \nA) 7􀝔 + 2 B) 􀝔 + 2 C) 􀝔 + 4 D) 6􀝔 + 1  \n18. The vertex of parabola is at (4; 2) . The parabola opens downward and passed through the points (3; −1) and (5; −1) . Write the equation of the parabola.  \nCircle correct answer:  \nA) 􀝕 = −3(􀝔 − 4)2 + 2 B) 􀝕 = −2(􀝔 + 2)2 + 3 C) 􀝕 = −(􀝔 − 3)2 + 2 D) 􀝕 = − 32 (􀝔 + 2)2 − 3  \n19. Find the value of 􀝔  \nCircle correct answer:  \nA) 10 B) 12 C) 813 D) 313  \n20. Factorize 3􀝔2 + 13􀝔 − 10  \nCircle correct answer:  \nA) (􀝔 + 4)(3􀝔 − 2) B) (􀝔 + 5)(3􀝔 − 2) C) (􀝔 − 3)(2􀝔 − 1) D) (2􀝔 − 1)(􀝔 + 1)  \n21. Find the distance between the two points:  \nA(−2; 0) B (−4; 4)  \nCircle correct answer:  \nA) √5 B) 2√5 C) 3 D) 4  \n22. A uniform wire of length 80 meters is divided into three parts in the ratio 5: 7: 13 (by length) .  \nFind the length (in meters) of the part with the smallest mass.  \nCircle correct answer:  \nA) 16 B) 17 C) 16.6 D) 16.4  \n23. Solve the equation: 33􀯫+2 ∙ 3􀯫+2 = 27􀯫+4  \nCircle correct answer:  ","cbCaipt52tH1Dt98","https://ap.wps.com/l/cbCaipt52tH1Dt98","pdf",294941,"English","# Mathematics Entrance Examination\n## Instructions and exam settings\n## Multiple-choice questions (1-28)","[{\"question\":\"What are the exam instructions regarding work shown and devices?\",\"answer\":\"Read each question carefully and provide the final answer only without showing all your work. Calculators, phones, or any devices are not allowed.\"},{\"question\":\"How long is the Mathematics Entrance Examination First Mock?\",\"answer\":\"The time allowed is one hour and ten minutes.\"},{\"question\":\"What types of mathematical topics are included in the mock?\",\"answer\":\"The mock covers algebra (equations, inequalities, factorization, logarithms), functions, and geometry (distance, area, angle relations in parallel lines), including problems that form equations from given conditions.\"}]","Mathematics Entrance Examination - First Mock | PDF"]