Chem1911 Sample Quiz 1

Chem1911 Sample Quiz 1 (i)

• The decay product resulting from the emission of an alpha particle from 210/85At is 206/83Bi.
• To balance the nuclear reaction 235/92U + 1/0n → ? + 96/39Y + 3 1/0n, the needed nuclide is 137/53I.
• 90/38Sr is the isotope of strontium that undergoes radioactive decay by β emission.
• For hydrogen (H), the 2s and 2p orbitals have the same energy.
• The electron excitation of the hydrogen atom that requires light of the shortest wavelength is n = 2 to n = 3.
• A 5s atomic orbital has 0 planar nodes and 4 spherical nodes.
• The 1s¹2p¹ → 1s² transition of He occurs at a longer wavelength than 54 nm, given that the 1s¹3p¹ → 1s² transition is at 54 nm.
• With a half-life of 5730 years, 14C dating methods can be usefully applied to 15th-century paintings.
• The valid set of quantum numbers is n=5, l=4, ml=3, ms=+1/2.
• The algebraic expression (0.350 kg * 141 J) / (0.921 m + 68 m) = 0.72 kg J m-1 to the appropriate number of significant figures.
• Sigma orbitals having a planar node normal to the internuclear axis between the atomic nuclei is an incorrect statement about molecular orbitals for homonuclear diatomic molecules.
• In the compound represented, the hybridizations of the designated atoms are: P = sp², Q = sp², and R = sp³.
• H-O-O-H is the correct Lewis structure of H2O2 with all charges and lone pairs shown.
• There are 3 non-bonding electron pairs (lone pairs) around the Cl atom in HCl.
• The functional group labelled A in the molecule is Amine.

Chem1911 Sample Quiz 1 (ii)

• The decay product resulting from electron capture by the 144/61 Pm nuclide is 144/60Nd.
• To balance the nuclear reaction 233/92 U + 1/0 n → ? + 99/42 Mo + 3 1/0 n, the needed nuclide is 132/50 Sn.
• 65/31 Ga does not undergo radioactive decay via electron capture.
• For N6+, the 2s and 2p orbitals have the same energy.
• The electron excitation of the hydrogen atom that requires light of the longest wavelength is n = 5 to n = 100.
• A 2p atomic orbital has 1 planar node and 0 spherical nodes.
• The 1s¹2p¹ → 1s² transition of He occurs at a longer wavelength than 54 nm, given that the 1s¹3p¹ → 1s² transition is at 54 nm.
• With a half-life of 5730 years, 14C dating methods can be usefully applied to 15th-century paintings.
• The valid set of quantum numbers is n=2, l=1, ml=0, ms=-1/2.
• The algebraic expression (3.69 kg * 30 J) / (87.1 m + 98.5 m) = 0.60 kg J m-1 to the appropriate number of significant figures.
• Pi orbitals having a planar node normal to the internuclear axis between the atomic nuclei is an incorrect statement about molecular orbitals for homonuclear diatomic molecules.
• In the compound represented, the hybridizations of the designated atoms are: P = sp, Q = sp², and R = sp³.
• :C≡N: is the correct Lewis structure of CN- with all charges and lone pairs shown.
• There are 0 non-bonding electron pairs (lone pairs) around the B atom in BF3.
• The functional group labelled B in the molecule is Alcohol.

MATH1061: Mathematics 1A

• R ⊂ Q is not true.
• For f(x) = 1 – x² and g(x) = ln(x), the domain of g o f is [-1,1], and the range is (-∞,0].
• For tanh(x) = (ex - e-x) / (ex + e-x), the limit as x→∞ of tanh(x) is 1.
• If f(x) = x⁶ sin(x) + cosh(6x), then f'(x) = x⁶ cos(x) + 6x⁵ sin(x) + 6 sinh(6x).
• If f(x) = (2x)x, then f'(x) = (2x)x(1+ln(2x)).
• The three-term Taylor polynomial about x = 0 for f(x) = 1 / (1-2x) is -1 + 2x - 4x².
• If z = 1 – 3i and w = 2 + i, then wz = 5 - 5i.
• For lines u = [1,2,1], v = [b,a,2], and w = [a,b,-4], a = -9 and b = 3 where 6u - v + w = 0.
• A parametric equation for the line in R² that passes through (1,1) and is perpendicular to [3,2] is l: [1, 1] + t[-2,3], t∈R.
• A parametric equation for the line in R³ that passes through (1,2,5) and is perpendicular to both [1,1,1] and [2,0,0] is l: [1,2,5] + t[0,2, -2], t∈ R.
• The line [x, y, z] = [1, 2, -2] + t[2, 1,2], t ∈ R intersects the plane x + 2y + 3z = 19 at (5,1,4).
• sin(4θ) = cos⁴(θ) - 6 cos² (θ) sin²(θ) + sin⁴(θ).

PRACTICE EXAM A SEMESTER 1 2024

• For f(x) = cosh(x) from R→ [1,∞), f is surjective but not injective.

• The limit as x→1 of (2x - 2x-1)/(x² - 2x + 1) is 1.

• For f(x) = 2x³ - 3x² - 12x + 4, the minimum value for f(x) is -16.

• d/dx (x/cos(x)) = 1/cos(x) + (x tan(x))/cos(x)

• Given g(x) = ke-x when x ≤ π and g(x) = sin(2x) when x > π, the value of k that makes this a continuous function is 1.

• The first three nonzero terms in the Taylor series for ∫x0 e^(-s²) ds about x = 0 is x - x³/3 + x⁵/10.

• The plot representing f(x), f'(x), and f"(x) is: f(x): Plot 3, f'(x): Plot 2, f"(x): Plot 1.

• ∫ cos(x) / √(1 + 2sin(x)) dx = √(1+2sin(x)) + C.

• The length of the curve y = cosh(x) from x = 0 to x = ln(2) is 3/4.

• The volume generated by rotating the curve √x around the x-axis from 0 to 4 is 8π.

• For the set S = {z ∈ C : Rez ≥ 0 and Im z ≤ 0}, then {iz : z ∈ S} would be represented by the 1st quadrant.

• For v = [2, 6, -1] and w = [-3, α, 3/2], v and w are parallel if α = -9.

• Given non-zero vectors u, v, w ∈ R² with u · v = 0, it is not necessarily true that proju(w) - projv(w) = 0.

• The lines x = 3 + t, y = -5 + 2t, z = 5 - t and x = -3 - 2s, y = -2 - 4s, z = 1 + 2s do not intersect.

• [2, -1, 5] is parallel to the plane 2x - y + 5z = 3.

• Given matrix A is 3x3 and B is 3x2 and C is 2x3, A² + BC is a 3 × 3 matrix.

• Given A = [1 1 0 \ 1 1 1 \ 0 1 1], A-1 = [0 1 -1 \ 1 -1 1 \ -1 1 0] is true.

• If B is a square matrix with det(B) = 2 and det((-1/√2)B) = 1/2, B is a 4 x 4 matrix.

• If A₁ = PD₁P⁻¹ and A₂ = PD₂P⁻¹, with D₁ = [1 0 \ 0 2], D₂ = [3 1 \ 0 1], and P = [1 1 \ 1 0], then (A₁A₂)⁵ = [2⁵ 3⁵-2⁵ \ 0 3⁵ ].

• For a 3 × 3 matrix A with three distinct eigenvalues, A is invertible is not necessarily true.