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Calculus  \nA. Basic properties (such as increasing/decreasing, positive/negative, zeros) and graphs of polynomial functions, rational functions, irrational (root) functions  \nB. Absolute value function  \nC. One-to-one functions and their inverses  \nD. Basic properties (such as increasing/decreasing, positive/negative, zeros) and graphs of exponential and logarithmic functions  \nE. Limits and continuity  \nF. Vertical, horizontal and oblique asymptotes  \nG. Definition of a derivative, intuitive definition of a derivative derivatives of basic functions, chain rule  \nH. Applications of derivatives: extreme values, concave upward/downward, l’Hospital rule  \nI. Equation of the tangent line to the curve of a graph at a certain point  \nJ. Definition of an antiderivative, antiderivatives of basic functions  \nK. Connection between derivatives and antiderivatives  \nL. Definite integrals  \nM. Techniques of integration: substitution rule, integration by parts, partial fractions  \nB. Algebra  \nA. Division of polynomials  \nB. Binomium of Newton  \nC. Solving of equations and inequalities involving polynomial, rational, irrational, exponential, logarithmic functions  \nD. Solving of systems of equations  \nC. Trigonometry  \nA. Degrees and radians  \nB. Trigonometric functions sine, cosine, tangent, cotangent and their graphs  \nC. Fundamental identity, addition and subtraction formulas, double-angle formulas, half-angle formulas, product-to-sum formulas, sum-to-product formulas  \nD. Proving of trigonometric identities  \nE. Trigonometric equations  \nF. Trigonometry of right triangles  \nD. Geometry  \nA. Points, coordinates and equations  \nB. Equation of a circle  \nC. Equation of a line  \nD. Parallel and perpendicular lines  \nMathematics Practice Test  \n1. Consider the function 􀝂: ℝ → ℝ: 􀝔 ↦ 􀝔 cos(􀝔2 ) . Evaluate the derivative of 􀝂 at the point√2􀟨⁄2.    \na. 􀝂 ′ (√2􀟨⁄2) = − 􀟨  \nb. 􀝂 ′ (√2􀟨⁄2) = − √2􀟨  \nc. 􀝂 ′ (√2􀟨⁄2) = √2 􀟨  \nd. 􀝂 ′ (√2􀟨⁄2) = 0  \ne. 􀝂 ′ (√2􀟨⁄2) = 1 − √2􀟨  \n2. Consider a natural number 􀝉 ≠ 0. Evaluate lim  􀯡􀯠   \n􀯡 → ∞ 􀯠−􀯡 .  \na. 1  \nb. 􀝉  \nc. 1  \nd. −1  \ne. – 􀝉  \n3. Consider the circle with equation 􀝕 2 − 2􀝕 + 􀝔 2 + 6􀝔 − 15 = 0. If 􀜯 = (􀜽, 􀜾) is its center and 􀜴 its radius, then 2􀜽 + 􀜾 + 􀜴 2 is equal to  \na. 10  \nb. 14  \nc. 20  \nd. 24  \ne. 30  \n4. Evaluate ∫ 􀯘 √􀳣 􀝀􀝔  \n√􀯫 .  \na. 􀝁 √􀯫  + constant  \nb. 2􀝁√􀯫 + constant  \nc. 􀝁 −√􀯫 + constant  \nd. √􀝔  􀝁 √􀯫 + constant e. 12 􀝁 √􀯫 + constant  \n5. The trigonometric expression cos~~ ~~􀯫1tan~~ ~~􀯫 − sin 􀝔 equals[a.](a. si)[ si](a. si)1n~~ ~~􀯫  \nb. stinan􀯫􀯫  \nc. (scino􀯫s~~ ~~􀯫)2 d. cosisn􀯫􀯫  \ne. (cos 􀯫)2 sin 􀯫  \n6. A function 􀝂: 􀜣 → 􀜤: 􀝔 ↦ 􀝂(􀝔) is a one-to-one function is for all 􀝔, 􀝕 ∈ 􀜣 it holds that: if 􀝔 ≠ 􀝕 , then 􀝂(􀝔) ≠ 􀝂(􀝕) . Determine which of the following functions is one-to-one.  \na. 􀝂: ℕ × ℕ → ℕ: (􀝊, 􀝉) ↦ 􀝉 + 􀝊  \nb. 􀝂: ℕ × ℕ → ℕ: (􀝊, 􀝉) ↦ 􀝉􀝊  \nc. 􀝂: ℕ × ℕ → ℕ: (􀝊, 􀝉) ↦ 3􀯠 5􀯡  \nd. 􀝂: ℕ × ℕ → ℕ: (􀝊, 􀝉) ↦ 􀝉􀯡  \ne. 􀝂: ℕ × ℕ → ℕ: (􀝊, 􀝉) ↦ 2􀯠+􀯡  \n7. Consider the function 􀝂: ℝ ⟶ ℝ: 􀝔 ↦ 􀝔 − √􀝔2 + 5􀝔 . Which of the following statements is true?  \na. 􀝂 is increasing on its domain.  \nb. 􀝂 is decreasing on its domain.  \nc. 􀝂 has two distinct zeros.  \nd. 􀝂 (􀝔) ≤ 0 for all 􀝔 in its domain.  \ne. 􀝂 has both negative as positive values on its domain  \n8. Suppose 􀜽, 􀜾 , 􀜿 and 􀝀 are real numbers such that 􀜽􀜾 \u003C 􀜿􀝀 and 0 \u003C 􀜽 \u003C 􀜿 . Which of the following statements is definitely true?  \na. 􀜽 \u003C 􀜿􀝀  \nb. 􀜾 \u003C 􀝀  \nc. 􀜽 \u003C 􀯖􀯗􀯕  \nd. If 􀝀 \u003C 0 , then 􀜾 \u003C 0.  \ne. If 􀜾 \u003C 0 , then 􀝀 \u003C 0.  \n9. The function 􀝏􀝃􀝊 is defined as follows: 􀝏􀝃􀝊 (􀝔) = {~~ ~~|􀯫􀯫0| ,,∫04 􀝔 􀝏􀝃􀝊(2 − 􀝔) 􀝀􀝔 .  \na. 8  \nb. 4  \nc. 0  \nd. −4  \ne. −8  \n􀝔 ≠ 0  \n. Evaluate 􀝔 = 0  \n10. Suppose 􀝂: ℝ ⟶ ℝ is a differentiable function such that 􀝂(􀝔) ≥ 0 for all 􀝔 ∈ ℝ and 􀜲 (5,9) is a point on the graph of 􀝂 . The tangent line to the curve of 􀝂 at 􀜲 intersects the x-axis at the point 􀜳 (1, 0) . If a function ℎ is defined as ℎ: ℝ ⟶ ℝ: 􀝔 ↦ √􀝂 (􀝔) , then ℎ′(5) equals:  \na. 38  \nb. 32 ","cbCaispr1IzaRQla","https://ap.wps.com/l/cbCaispr1IzaRQla","pdf",793696,12,"English","# Mathematics Practice Test\n## Calculus and derivatives\n## Limits and continuity\n## Algebra and functions\n## Trigonometry\n## Geometry\n# Chemistry Topics and Practice","[{\"question\":\"What mathematics topics are included in the practice section?\",\"answer\":\"It covers calculus (derivatives, limits, continuity, integrals, asymptotes), algebra for solving polynomial/rational/exponential/logarithmic forms and systems, plus trigonometry (identities and formulas) and basic geometry (points, lines, circles).\"},{\"question\":\"Which chemistry fundamentals are listed for review?\",\"answer\":\"The chemistry review includes elements and mixtures, Lavoisier’s law, atomic/molecular representations, oxidation numbers and ions, acid–base and reaction equation types, pH and titration, atomic models, energy levels and bonding, Lewis notation, intermolecular forces, nomenclature, and stoichiometry.\"},{\"question\":\"What kinds of questions appear in the Chemistry Practice Test?\",\"answer\":\"The practice test includes reaction-based numerical problems, such as using a given chemical reaction for rocket propellants to calculate the volume of nitrogen gas produced under specified conditions.\"}]","Online Aptitude Test Sample | PDF",1790764553]