IB Practice

【G5-MAA-54】 Q1 · IB Math AA HL · Calculus · Medium

Find the maximum value of f(x) = x³ - 6x² + 9x + 2 on the interval [0, 4].

A) 6
B) 2
C) 4
D) 9

Answer: A) 6. f'(x) = 3x² - 12x + 9 = 0 → x=1 or x=3. f(1)=6, f(3)=2, f(0)=2, f(4)=6. Maximum is 6 at x=1.

【G5-MAA-51】 Q4 · IB Math AA HL · Algebra · Medium

Given log₂(x) + log₂(x-2) = 3, find x.

A) 4
B) -2
C) 4 or -2
D) 8

Answer: A) 4. log₂(x(x-2))=3, x(x-2)=8, x²-2x-8=0, (x-4)(x+2)=0, x=4 (x=-2 rejected since log of negative is undefined).

【G5-MAA-52】 Q5 · IB Math AA HL · Functions · Hard

If f(x) = 2x + 1 and g(x) = x² - 3, find g(f(2)).

A) 22
B) 12
C) 6
D) 9

Answer: A) 22. f(2)=2(2)+1=5, g(5)=5²-3=22.

【G5-MAA-51】 Q11 · IB Math AA HL · Algebra · Easy

Solve: 2^x = 32.

A) 3
B) 4
C) 5
D) 6

Answer: C) 5. 2^5 = 32.

【G5-MAA-54】 Q12 · IB Math AA HL · Calculus · Medium

Find dy/dx if y = 3x⁴ - 2x² + 5.

A) 12x³ - 4x
B) 12x³ - 2
C) 3x³ - 2x
D) 12x⁴ - 4x²

Answer: A) 12x³ - 4x. Power rule: 4·3x³ - 2·2x = 12x³ - 4x.

【G5-MAA-55】 Q13 · IB Math AA HL · Statistics · Medium

In a normal distribution with mean 50 and SD 10, what percentage of data lies between 40 and 60?

A) 68%
B) 95%
C) 34%
D) 99.7%

Answer: A) 68%. 40 and 60 are ±1 SD from mean, covering ~68% of data.

【G5-MAA-53】 Q14 · IB Math AA HL · Vectors · Hard

Given u = (3, 4), find |u|.

A) 7
B) 12
C) 5
D) 25

Answer: C) 5. |u| = √(9+16) = √25 = 5.

【G5-MAA-51】 Q21 · IB Math AA HL · Sequences · Easy

Find the 10th term of the arithmetic sequence 3, 7, 11, 15, ...

A) 39
B) 43
C) 41
D) 47

Answer: A) 39. a_n = a_1 + (n-1)d = 3 + 9×4 = 39.

【G5-MAA-51】 Q22 · IB Math AA HL · Binomial Theorem · Medium

Find the coefficient of x³ in the expansion of (1 + 2x)⁵.

A) 10
B) 40
C) 80
D) 32

Answer: C) 80. C(5,3)·(2x)³ = 10·8x³ = 80x³, so the coefficient is 80.

【G5-MAA-51】 Q23 · IB Math AA HL · Complex Numbers · Medium

Find the modulus of the complex number z = 3 + 4i.

A) 7
B) 5
C) 25
D) 1

Answer: B) 5. |z| = √(3² + 4²) = √25 = 5.

【G5-MAA-54】 Q24 · IB Math AA HL · Integration · Hard

Evaluate ∫ x·e^x dx.

A) x·e^x + C
B) e^x(x - 1) + C
C) e^x(x + 1) + C
D) (1/2)x²·e^x + C

Answer: B) e^x(x - 1) + C. Using parts with u=x, dv=e^x dx: ∫x·e^x dx = x·e^x - ∫e^x dx = x·e^x - e^x = e^x(x-1) + C.

【G5-MAI-510】 Q25 · IB Math AI HL · Probability Distributions · Medium

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

A) 5/32
B) 10/32
C) 1/8
D) 3/16

Answer: B) 10/32. P(X=3) = C(5,3)·(1/2)⁵ = 10/32 = 5/16.

【G5-MAA-51】 Q26 · IB Math AA HL · Matrices · Hard

Given matrix A = [[2, 1], [1, 3]], find A² (the matrix product A·A).

A) [[5, 5], [5, 10]]
B) [[4, 3], [3, 10]]
C) [[5, 4], [4, 10]]
D) [[4, 1], [1, 9]]

Answer: A) [[5, 5], [5, 10]]. Row-by-column: row 1 = [2·2+1·1, 2·1+1·3] = [5, 5]; row 2 = [1·2+3·1, 1·1+3·3] = [5, 10].

【G5-MAA-54】 Q27 · IB Math AA HL · Limits · Medium

Evaluate lim(x→2) (x² - 4)/(x - 2).

A) 0
B) 4
C) undefined
D) 2

Answer: B) 4. Factor: (x-2)(x+2)/(x-2) = x+2 → 4 as x→2.

【G5-MAA-53】 Q28 · IB Math AA HL · Trigonometric Identities · Hard

Simplify: sin²θ + cos²θ + tan²θ.

A) 1
B) sec²θ
C) 2
D) tan²θ

Answer: B) sec²θ. Using sin²θ + cos²θ = 1, the expression becomes 1 + tan²θ = sec²θ.

【G5-MAA-51】 Q29 · IB Math AA HL · Logarithms · Medium

Solve: log(x) + log(x+3) = 1 (base 10).

A) 2
B) -5
C) 2 or -5
D) 5

Answer: A) 2. log(x(x+3))=1, x(x+3)=10, x²+3x-10=0, (x-2)(x+5)=0, x=2 (x=-5 rejected since log of negative is undefined).

【G5-MAA-54】 Q30 · IB Math AA HL · Optimization · Hard

A rectangle has perimeter 20 m. What is the maximum possible area?

A) 25 m²
B) 20 m²
C) 16 m²
D) 100 m²

Answer: A) 25 m². If length = x, width = 10-x, area = x(10-x) = 10x - x². Maximum at x = 5: area = 25 m² (square is optimal).

【G5-MAA-54】 Q31 · IB Math AA HL · Differential Equations · Hard

Solve dy/dx = 2x, given y(0) = 3.

A) y = x² + 3
B) y = 2x² + 3
C) y = x² + C
D) y = 2x + 3

Answer: A) y = x² + 3. Integrate: y = x² + C. Use y(0)=3: C = 3. So y = x² + 3.

【G5-MAA-53】 Q32 · IB Math AA HL · Vector Geometry · Medium

Find the dot product of vectors a = (2, -1, 3) and b = (4, 2, -1).

A) 3
B) 8
C) 5
D) -3

Answer: A) 3. a·b = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.

【G4-Phy-42】 Q2 · IB Physics HL · Mechanics · Easy

A ball is thrown vertically upward at 20 m/s. What is the maximum height reached? (g = 10 m/s²)

A) 10 m
B) 20 m
C) 40 m
D) 5 m

Answer: B) 20 m. v² = u² - 2gh, 0 = 400 - 20h, h = 20 m.

【G4-Phy-44】 Q6 · IB Physics HL · Waves · Medium

A wave has frequency 500 Hz and speed 340 m/s. What is its wavelength?

A) 0.34 m
B) 0.68 m
C) 1.47 m
D) 170000 m

Answer: B) 0.68 m. λ = v/f = 340/500 = 0.68 m.

【G4-Phy-43】 Q7 · IB Physics HL · Thermodynamics · Hard

An ideal gas at 300 K has its temperature doubled to 600 K at constant volume. If the initial pressure was 100 kPa, what is the new pressure?

A) 50 kPa
B) 100 kPa
C) 200 kPa
D) 400 kPa

Answer: C) 200 kPa. At constant volume, P/T = constant. P₂ = P₁ × T₂/T₁ = 100 × 600/300 = 200 kPa.

【G4-Phy-42】 Q15 · IB Physics HL · Mechanics · Easy

A car decelerates from 30 m/s to 0 in 6 seconds. What is the deceleration?

A) 5 m/s²
B) -5 m/s²
C) 30 m/s²
D) 180 m/s²

Answer: B) -5 m/s². a = Δv/Δt = (0-30)/6 = -5 m/s².

【G4-Phy-45】 Q16 · IB Physics HL · Electricity · Medium

A 12V battery drives 3A through a circuit. What is the resistance?

A) 36Ω
B) 4Ω
C) 9Ω
D) 0.25Ω

Answer: B) 4Ω. R = V/I = 12/3 = 4Ω.

【G4-Phy-47】 Q17 · IB Physics HL · Modern Physics · Hard

What is the energy of a photon with frequency 5×10¹⁴ Hz? (h = 6.6×10⁻³⁴ J·s)

A) 3.3×10⁻¹⁹ J
B) 7.6×10⁻²⁰ J
C) 1.3×10⁻⁴⁸ J
D) 5×10¹⁴ J

Answer: A) 3.3×10⁻¹⁹ J. E = hf = 6.6×10⁻³⁴ × 5×10¹⁴ = 3.3×10⁻¹⁹ J.

【G4-Phy-46】 Q33 · IB Physics HL · Circular Motion · Easy

A car goes around a circular track of radius 50 m at constant speed 10 m/s. What is its centripetal acceleration?

A) 1 m/s²
B) 2 m/s²
C) 5 m/s²
D) 0 m/s²

Answer: B) 2 m/s². a_c = v²/r = 100/50 = 2 m/s².

【G4-Phy-44】 Q34 · IB Physics HL · SHM · Medium

A mass on a spring has period 2π s. If the spring constant k = 10 N/m, what is the mass? (Take π² ≈ 10)

A) 0.1 kg
B) 1 kg
C) 10 kg
D) 100 kg

Answer: C) 10 kg. T = 2π√(m/k). With T = 2π: √(m/k) = 1, so m = k = 10 kg.

【G4-Phy-45】 Q35 · IB Physics HL · Electromagnetic Induction · Medium

A magnetic flux through a coil changes from 0.05 Wb to 0.15 Wb in 0.2 s. The coil has 50 turns. What is the magnitude of the induced EMF?

A) 5 V
B) 25 V
C) 2.5 V
D) 50 V

Answer: B) 25 V. EMF = N·|ΔΦ|/Δt = 50 × (0.10)/0.2 = 25 V.

【G4-Phy-47】 Q36 · IB Physics HL · Nuclear Physics · Hard

A radioactive isotope has a half-life of 6 hours. If you start with 80 g, how much remains after 18 hours?

A) 10 g
B) 20 g
C) 40 g
D) 5 g

Answer: A) 10 g. 18 hours = 3 half-lives. 80 → 40 → 20 → 10 g.

【G4-Phy-44】 Q37 · IB Physics HL · Optics · Medium

A converging lens has focal length 20 cm. An object is placed 60 cm from the lens. At what distance from the lens is the image formed?

A) 15 cm
B) 30 cm
C) 20 cm
D) 12 cm

Answer: B) 30 cm. 1/v = 1/f - 1/u = 1/20 - 1/60 = 2/60 = 1/30, so v = 30 cm.

【G4-Phy-45】 Q38 · IB Physics HL · Capacitors · Medium

A 10 μF capacitor is charged by a 12 V battery. What charge is stored?

A) 120 μC
B) 1.2 μC
C) 12 μC
D) 1200 μC

Answer: A) 120 μC. Q = CV = 10 × 12 = 120 μC.

【G4-Phy-45】 Q39 · IB Physics HL · Magnetism · Hard

A wire of length 0.5 m carries current 4 A perpendicular to a magnetic field of 0.2 T. What is the force on the wire?

A) 0.4 N
B) 0.04 N
C) 4 N
D) 2 N

Answer: A) 0.4 N. F = BIL = 0.2 × 4 × 0.5 = 0.4 N.

【G4-Phy-47】 Q40 · IB Physics HL · Quantum · Medium

In the photoelectric effect, if light of frequency below the threshold frequency is shone on a metal, what happens?

A) Electrons are emitted with low KE
B) No electrons are emitted
C) Electrons are emitted with high KE
D) The metal becomes positively charged

Answer: B) No electrons are emitted. Below the threshold frequency, no electrons are emitted regardless of intensity.

【G4-Phy-43】 Q41 · IB Physics HL · Thermodynamics · Easy

How much heat is needed to raise the temperature of 2 kg of water by 5°C? (Specific heat capacity of water = 4200 J/kg·°C)

A) 42000 J
B) 4200 J
C) 8400 J
D) 21000 J

Answer: A) 42000 J. Q = mcΔT = 2 × 4200 × 5 = 42000 J.

【G4-Phy-49】 Q42 · IB Physics HL · Fluids · Medium

What is the pressure at a depth of 10 m in water? (Density of water = 1000 kg/m³, g = 10 m/s²)

A) 10000 Pa
B) 100000 Pa
C) 1000 Pa
D) 100 Pa

Answer: B) 100000 Pa. P = ρgh = 1000 × 10 × 10 = 100000 Pa = 100 kPa.

【G3-Econ-31】 Q3 · IB Economics HL · Microeconomics · Easy

Which of the following will cause a shift of the demand curve to the right?

A) A decrease in the price of the good
B) An increase in consumer income (normal good)
C) A decrease in the price of a substitute good
D) An improvement in production technology

Answer: B). Income increase shifts demand right for normal goods. A is movement along curve, C shifts left, D shifts supply.

【G3-Econ-32】 Q8 · IB Economics HL · Macroeconomics · Medium

Which of the following is an example of expansionary fiscal policy?

A) Increasing interest rates
B) Increasing government spending
C) Selling government bonds
D) Increasing reserve requirements

Answer: B). Expansionary fiscal policy involves increasing government spending or decreasing taxes to stimulate aggregate demand.

【G4-Chem-415】 Q9 · IB Chemistry HL · Equilibrium · Hard

For the reaction N₂ + 3H₂ ⇌ 2NH₃, what happens to the equilibrium when pressure is increased?

A) Shifts left
B) Shifts right
C) No change
D) Reaction stops

Answer: B) Shifts right. Increasing pressure shifts equilibrium toward the side with fewer moles of gas. Products have 2 moles vs 4 moles of reactants.

【G3-BM-38】 Q10 · IB Business Management HL · Marketing · Easy

Which of the following is NOT one of the 4 Ps of the marketing mix?

A) Price
B) Promotion
C) Position
D) Product

Answer: C) Position. The 4 Ps are Product, Price, Place, Promotion.

【G3-Econ-31】 Q18 · IB Economics HL · Microeconomics · Easy

If the price of coffee rises, what happens to demand for tea (a substitute)?

A) Decreases
B) Increases
C) No change
D) Becomes zero

Answer: B) Increases. Substitutes: when coffee price rises, consumers switch to tea.

【G3-Econ-32】 Q19 · IB Economics HL · Macroeconomics · Medium

What is the primary tool used by central banks to control inflation?

A) Tax rates
B) Government spending
C) Interest rates
D) Exchange rates

Answer: C) Interest rates. Central banks adjust interest rates to control money supply and inflation.

【G3-BM-39】 Q20 · IB Business Management HL · Finance · Medium

A company's revenue is $500,000 and costs are $350,000. What is the profit margin?

A) 25%
B) 30%
C) 70%
D) 42.9%

Answer: B) 30%. Profit = $150,000. Margin = 150,000/500,000 = 30%.

【G3-Econ-31】 Q43 · IB Economics HL · Market Failure · Medium

Which of the following is an example of a negative externality?

A) Vaccination programs
B) Pollution from a factory
C) Public parks
D) Education subsidies

Answer: B). Negative externalities impose costs on third parties. Pollution is a classic example. The other options are positive externalities or public goods.

【G3-Econ-32】 Q44 · IB Economics HL · Monetary Policy · Easy

To combat inflation, a central bank should:

A) Lower interest rates
B) Increase interest rates
C) Buy government bonds
D) Decrease reserve requirements

Answer: B) Increase interest rates. Contractionary monetary policy raises rates to reduce money supply and aggregate demand.

【G3-Econ-33】 Q45 · IB Economics HL · Exchange Rates · Medium

If the US dollar appreciates against the Japanese yen, what happens to US exports to Japan?

A) They become cheaper for Japanese buyers
B) They become more expensive for Japanese buyers
C) They remain the same price
D) They become zero

Answer: B) They become more expensive for Japanese buyers. A stronger USD means Japanese buyers need more yen to purchase the same US goods.

【G3-BM-39】 Q46 · IB Business Management HL · Accounting · Medium

A company has current assets of $200,000 and current liabilities of $100,000. What is the current ratio?

A) 0.5
B) 2
C) 1.5
D) 3

Answer: B) 2. Current ratio = Current assets / Current liabilities = 200,000 / 100,000 = 2.

【G3-BM-37】 Q47 · IB Business Management HL · HRM · Easy

According to Maslow's hierarchy of needs, which need is at the highest level?

A) Safety
B) Physiological
C) Self-actualization
D) Esteem

Answer: C) Self-actualization. Maslow's hierarchy from lowest to highest: physiological, safety, love/belonging, esteem, self-actualization.

【G4-Chem-414】 Q48 · IB Chemistry HL · Kinetics · Medium

Which factor does NOT increase the rate of a chemical reaction?

A) Increasing temperature
B) Increasing concentration
C) Adding a catalyst
D) Decreasing surface area

Answer: D) Decreasing surface area. Decreasing surface area reduces the rate of reaction by lowering collision frequency.

【G4-Chem-415】 Q49 · IB Chemistry HL · Equilibrium · Hard

For the exothermic reaction N₂ + 3H₂ ⇌ 2NH₃, what happens to the equilibrium when temperature is increased?

A) Equilibrium shifts right
B) Equilibrium shifts left
C) No change
D) Reaction stops

Answer: B) Equilibrium shifts left. For an exothermic reaction, increasing temperature shifts equilibrium toward the reactants (the endothermic direction).

【G4-Chem-416】 Q50 · IB Chemistry HL · Acids & Bases · Medium

What is the pH of a solution with [H⁺] = 1×10⁻⁴ M?

A) 4
B) 10
C) 0.0001
D) 14

Answer: A) 4. pH = -log[H⁺] = -log(10⁻⁴) = 4.

【G4-Bio-421】 Q51 · IB Biology HL · Cell Biology · Easy

Which organelle is primarily responsible for ATP production in eukaryotic cells?

A) Nucleus
B) Ribosome
C) Mitochondrion
D) Golgi apparatus

Answer: C) Mitochondrion. Mitochondria carry out aerobic cellular respiration, producing ATP via oxidative phosphorylation.

【G4-Bio-421】 Q52 · IB Biology HL · Molecular Biology · Easy

In DNA replication, which enzyme synthesizes the new complementary DNA strand?

A) Helicase
B) DNA polymerase
C) Ligase
D) RNA primase

Answer: B) DNA polymerase. DNA polymerase adds nucleotides in the 5'→3' direction using the template strand. Helicase unwinds; ligase joins Okazaki fragments.

【G4-Bio-423】 Q53 · IB Biology HL · Genetics · Medium

A heterozygous tall plant (Tt) is crossed with a homozygous short plant (tt). What is the expected ratio of tall to short offspring?

A) 3 : 1
B) 1 : 1
C) 1 : 0
D) 1 : 2 : 1

Answer: B) 1 : 1. Punnett square: Tt × tt yields 50% Tt (tall) and 50% tt (short).

【G4-Bio-424】 Q54 · IB Biology HL · Human Physiology · Medium

Which hormone is secreted by the pancreas in response to high blood glucose levels?

A) Glucagon
B) Insulin
C) Thyroxine
D) ADH

Answer: B) Insulin. Insulin lowers blood glucose by promoting uptake into cells and storage as glycogen. Glucagon raises blood glucose.

【G4-Bio-423】 Q55 · IB Biology HL · Ecology · Easy

Which of the following best describes a group of individuals of the same species living in the same area?

A) Community
B) Ecosystem
C) Population
D) Biome

Answer: C) Population. A population is a group of conspecific individuals; a community includes multiple species; an ecosystem includes biotic + abiotic.

【G4-Bio-425】 Q56 · IB Biology HL · Evolution · Medium

The forelimbs of humans, bats, and whales have similar bone structures despite different functions. This is an example of:

A) Analogous structures
B) Homologous structures
C) Vestigial structures
D) Convergent evolution

Answer: B) Homologous structures. Homology indicates shared ancestry. Analogous structures result from convergent evolution (similar function, different origin).

【G4-Bio-422】 Q57 · IB Biology HL · Cell Biology · Hard

During which stage of meiosis does crossing over (recombination) between homologous chromosomes occur?

A) Prophase I
B) Metaphase I
C) Prophase II
D) Anaphase I

Answer: A) Prophase I. Synapsis and crossing over occur in prophase I of meiosis, producing recombinant chromatids and increasing genetic variation.

【G4-Bio-422】 Q58 · IB Biology HL · Molecular Biology · Hard

Which process converts the genetic information in mRNA into a sequence of amino acids?

A) Replication
B) Transcription
C) Translation
D) Reverse transcription

Answer: C) Translation. Translation at the ribosome uses tRNA and codon-anticodon pairing to synthesize the polypeptide. Transcription makes mRNA from DNA.

【G4-Bio-423】 Q59 · IB Biology HL · Genetics · Medium

In humans, color blindness is an X-linked recessive trait. A carrier mother and unaffected father have a son. What is the probability he is colorblind?

A) 0%
B) 25%
C) 50%
D) 100%

Answer: C) 50%. Mother (XᴮXᵇ) × Father (XᴮY): sons inherit Y from father and either Xᴮ or Xᵇ from mother → 50% chance of XᵇY (colorblind).

【G4-Bio-425】 Q60 · IB Biology HL · Human Physiology · Hard

In the nephron, most reabsorption of glucose, amino acids, and water occurs in which structure?

A) Bowman's capsule
B) Proximal convoluted tubule
C) Loop of Henle
D) Distal convoluted tubule

Answer: B) Proximal convoluted tubule. The PCT reabsorbs ~70–80% of filtrate including all glucose (via cotransport), amino acids, salts, and water.

【G5-MAA-54】 Q61 · IB Math AA HL · Calculus · Easy

Find the derivative of f(x) = sin(x) + cos(x).

A) cos(x) − sin(x)
B) −cos(x) + sin(x)
C) sin(x) + cos(x)
D) tan(x)

Answer: A) cos(x) − sin(x). d/dx sin(x) = cos(x); d/dx cos(x) = −sin(x); sum gives cos(x) − sin(x).

【G5-MAA-54】 Q62 · IB Math AA HL · Calculus · Hard

Evaluate ∫₀¹ (2x + 3) dx.

A) 3
B) 4
C) 5
D) 2

Answer: B) 4. Antiderivative: x² + 3x. At x=1: 1 + 3 = 4; at x=0: 0. Definite integral = 4 − 0 = 4.

【G5-MAA-53】 Q63 · IB Math AA HL · Vectors · Medium

Vectors a = (1, 2) and b = (3, k) are perpendicular. Find k.

A) −3/2
B) 3/2
C) −6
D) 0

Answer: A) −3/2. Perpendicular ⇒ dot product = 0: 1·3 + 2·k = 0 → 3 + 2k = 0 → k = −3/2.

【G5-MAI-510】 Q64 · IB Math AI HL · Probability · Easy

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

A) 1/3
B) 1/2
C) 2/3
D) 1/6

Answer: A) 1/3. Numbers > 4 on a die are {5, 6}: 2 favorable outcomes out of 6, so P = 2/6 = 1/3.

【G5-MAI-510】 Q65 · IB Math AI HL · Probability · Hard

Events A and B are independent. P(A) = 0.4, P(B) = 0.5. What is P(A ∪ B)?

A) 0.9
B) 0.7
C) 0.2
D) 0.1

Answer: B) 0.7. Independent ⇒ P(A∩B) = 0.4×0.5 = 0.2. P(A∪B) = P(A)+P(B)−P(A∩B) = 0.4+0.5−0.2 = 0.7.

【G5-MAI-510】 Q66 · IB Math AI HL · Statistics · Medium

The data set {2, 4, 6, 8, 10} has mean 6. What is the standard deviation (population, ungrouped)?

A) 2
B) √8
C) 4
D) √10

Answer: B) √8. Squared deviations: (−4)², (−2)², 0², 2², 4² = 16, 4, 0, 4, 16. Variance = (40)/5 = 8. σ = √8.

【G5-MAA-51】 Q67 · IB Math AA HL · Complex Numbers · Easy

Simplify: i² + i⁴, where i = √−1.

A) 0
B) 2
C) −2
D) 2i

Answer: A) 0. i² = −1, i⁴ = (i²)² = (−1)² = 1. Sum: −1 + 1 = 0.

【G5-MAA-51】 Q68 · IB Math AA HL · Complex Numbers · Medium

Write z = 1 + i in polar form (modulus–argument form).

A) √2 (cos π/4 + i sin π/4)
B) 2 (cos π/4 + i sin π/4)
C) √2 (cos π/2 + i sin π/2)
D) 1 (cos π/4 + i sin π/4)

Answer: A) √2 (cos π/4 + i sin π/4). |z| = √(1+1) = √2; arg(z) = arctan(1/1) = π/4.

【G5-MAA-51】 Q69 · IB Math AA HL · Matrices · Easy

Given A = [[1, 2], [3, 4]], find the determinant det(A).

A) −2
B) 10
C) 2
D) −10

Answer: A) −2. For 2×2 [[a,b],[c,d]], det = ad − bc = (1)(4) − (2)(3) = 4 − 6 = −2.

【G5-MAA-51】 Q70 · IB Math AA HL · Matrices · Hard

Which condition must hold for a square matrix A to have an inverse A⁻¹?

A) det(A) = 0
B) det(A) ≠ 0
C) A is symmetric
D) All entries are positive

Answer: B) det(A) ≠ 0. A square matrix is invertible (non-singular) iff its determinant is nonzero. Singular matrices have det = 0.

【G5-MAA-54】 Q71 · IB Math AA HL · Calculus · Medium

Find the slope of the tangent to y = x³ at x = 2.

A) 6
B) 8
C) 12
D) 3

Answer: C) 12. dy/dx = 3x². At x = 2: 3(4) = 12. So the tangent slope is 12.

【G5-MAI-510】 Q72 · IB Math AI HL · Probability · Medium

In a normal distribution with μ = 100 and σ = 15, what z-score corresponds to x = 115?

A) 0
B) 1
C) −1
D) 2

Answer: B) 1. z = (x − μ)/σ = (115 − 100)/15 = 15/15 = 1.

【G5-MAA-53】 Q73 · IB Math AA HL · Vectors · Hard

Find the cross product a × b where a = (1, 0, 0) and b = (0, 1, 0).

A) (0, 0, 1)
B) (0, 0, −1)
C) (1, 1, 0)
D) (0, 0, 0)

Answer: A) (0, 0, 1). Standard basis cross product: î × ĵ = k̂ = (0, 0, 1), perpendicular to both with |a||b| sin 90° = 1.

【G5-MAI-510】 Q74 · IB Math AI HL · Statistics · Easy

Find the median of: 3, 7, 2, 9, 5.

A) 5
B) 5.2
C) 7
D) 2

Answer: A) 5. Ordered: 2, 3, 5, 7, 9. With n = 5 (odd), median is the (n+1)/2 = 3rd value = 5.

【G4-Phy-42】 Q75 · IB Physics HL · Mechanics · Medium

A 2 kg object experiences a net force of 10 N. What is its acceleration?

A) 0.2 m/s²
B) 5 m/s²
C) 20 m/s²
D) 12 m/s²

Answer: B) 5 m/s². Newton's second law: F = ma ⇒ a = F/m = 10 / 2 = 5 m/s².

【G4-Phy-42】 Q76 · IB Physics HL · Mechanics · Hard

A block of mass 5 kg slides down a frictionless incline of angle 30°. What is its acceleration down the slope? (g = 10 m/s²)

A) 10 m/s²
B) 5 m/s²
C) 8.66 m/s²
D) 0 m/s²

Answer: B) 5 m/s². Parallel component: a = g sin θ = 10 · sin 30° = 10 × 0.5 = 5 m/s² (mass cancels on frictionless incline).

【G4-Phy-45】 Q77 · IB Physics HL · Electricity · Easy

Two resistors, 3 Ω and 6 Ω, are in parallel. What is the equivalent resistance?

A) 9 Ω
B) 2 Ω
C) 4.5 Ω
D) 18 Ω

Answer: B) 2 Ω. 1/Rₚ = 1/3 + 1/6 = 1/2 ⇒ Rₚ = 2 Ω (parallel: equivalent resistance is less than the smallest resistor).

【G4-Phy-45】 Q78 · IB Physics HL · Electricity · Hard

A 12 V battery with internal resistance 1 Ω is connected to a 3 Ω load. What is the terminal voltage across the load?

A) 9 V
B) 12 V
C) 3 V
D) 4 V

Answer: A) 9 V. Total R = 1 + 3 = 4 Ω ⇒ I = 12/4 = 3 A. Terminal V = I × R_load = 3 × 3 = 9 V (or 12 − I×1 = 9 V).

【G4-Phy-45】 Q79 · IB Physics HL · Magnetism · Easy

Which of the following materials is NOT ferromagnetic?

A) Iron
B) Nickel
C) Copper
D) Cobalt

Answer: C) Copper. Fe, Ni, Co are classic ferromagnetic materials. Cu is weakly diamagnetic and not strongly attracted to magnets.

【G4-Phy-45】 Q80 · IB Physics HL · Magnetism · Medium

A charged particle moves parallel to a uniform magnetic field B. The magnetic force on the particle is:

A) Maximum
B) Zero
C) Depends on charge sign only
D) Equal to qB

Answer: B) Zero. Lorentz force F = qv × B, magnitude qvB sin θ. When v ∥ B, θ = 0° and sin 0° = 0 ⇒ F = 0.

【G4-Phy-44】 Q81 · IB Physics HL · Waves · Easy

Two waves of equal amplitude and frequency arrive perfectly out of phase at a point. What occurs?

A) Constructive interference
B) Destructive interference
C) Standing wave only
D) Resonance

Answer: B) Destructive interference. Out of phase by 180° gives A + (−A) = 0 total amplitude → destructive (node).

【G4-Phy-44】 Q82 · IB Physics HL · Waves · Hard

A string of length L fixed at both ends vibrates in its first harmonic (fundamental mode). What is the wavelength?

A) L/2
B) L
C) 2L
D) 4L

Answer: C) 2L. Fixed at both ends ⇒ nodes at each end. Fundamental = one loop: half a wavelength fits, so λ/2 = L ⇒ λ = 2L.

【G4-Phy-43】 Q83 · IB Physics HL · Thermodynamics · Medium

The first law of thermodynamics is a restatement of which principle?

A) Conservation of momentum
B) Conservation of energy
C) Conservation of mass
D) Entropy increase

Answer: B) Conservation of energy. ΔU = Q − W (or Q = ΔU + W) formalizes energy conservation for thermal systems.

【G4-Phy-43】 Q84 · IB Physics HL · Thermodynamics · Easy

What is absolute zero on the Celsius scale?

A) 0°C
B) −100°C
C) −273°C
D) 273°C

Answer: C) −273°C. Absolute zero = 0 K = −273.15°C, the theoretical minimum temperature where molecular motion is at minimum.

【G4-Phy-47】 Q85 · IB Physics HL · Quantum · Medium

Which phenomenon demonstrates the particle nature of light?

A) Young's double-slit interference
B) Photoelectric effect
C) Diffraction through a slit
D) Refraction by a prism

Answer: B) Photoelectric effect. Einstein explained the PE effect by quantized light (photons) delivering energy E = hf to eject electrons, showing particle behavior.

【G4-Phy-47】 Q86 · IB Physics HL · Quantum · Hard

Which principle states that the position and momentum of a particle cannot both be known precisely at the same time?

A) Pauli exclusion principle
B) Heisenberg uncertainty principle
C) Aufbau principle
D) Hund's rule

Answer: B) Heisenberg uncertainty principle. Δx · Δp ≥ ℏ/2, a fundamental limit of quantum mechanics. Pauli: no two fermions share identical quantum numbers.

【G4-Chem-412】 Q87 · IB Chemistry HL · Bonding · Easy

Which type of bond is formed between two atoms with a large difference in electronegativity?

A) Nonpolar covalent
B) Polar covalent
C) Ionic
D) Metallic

Answer: C) Ionic. Large ΔEN (typically > 1.7) leads to electron transfer and formation of ions (e.g., Na⁺Cl⁻).

【G4-Chem-412】 Q88 · IB Chemistry HL · Bonding · Medium

Using VSEPR theory, what is the electron domain geometry and molecular shape of NH₃?

A) Tetrahedral; trigonal pyramidal
B) Trigonal planar; trigonal pyramidal
C) Tetrahedral; tetrahedral
D) Linear; bent

Answer: A) Tetrahedral; trigonal pyramidal. 4 electron domains (3 bonds + 1 lone pair) ⇒ electron geometry tetrahedral; lone pair repels more ⇒ molecular shape trigonal pyramidal.

【G4-Chem-413】 Q89 · IB Chemistry HL · Energetics · Medium

A reaction has ΔH = −85 kJ mol⁻¹. This reaction is:

A) Endothermic, absorbing heat
B) Exothermic, releasing heat
C) At equilibrium
D) Non-spontaneous at any T

Answer: B) Exothermic, releasing heat. Negative ΔH means enthalpy of products < reactants; heat is released to the surroundings.

【G4-Chem-413】 Q90 · IB Chemistry HL · Energetics · Hard

Which combination of ΔH and ΔS guarantees a reaction is spontaneous at all temperatures?

A) ΔH > 0, ΔS > 0
B) ΔH < 0, ΔS < 0
C) ΔH < 0, ΔS > 0
D) ΔH > 0, ΔS < 0

Answer: C) ΔH < 0, ΔS > 0. Gibbs: ΔG = ΔH − TΔS. For ΔH negative and ΔS positive, ΔG is always negative at any T → always spontaneous.

【G4-Chem-415】 Q91 · IB Chemistry HL · Redox · Easy

In the reaction Zn + Cu²⁺ → Zn²⁺ + Cu, which species is reduced?

A) Zn
B) Cu²⁺
C) Zn²⁺
D) Cu

Answer: B) Cu²⁺. Reduction = gain of electrons (oxidation state decreases): Cu²⁺ + 2e⁻ → Cu. Zn is oxidized (loses electrons).

【G4-Chem-415】 Q92 · IB Chemistry HL · Redox · Hard

What is the oxidation number of Cl in KClO₃?

A) −1
B) +1
C) +5
D) +7

Answer: C) +5. K = +1, each O = −2. Let Cl = x: +1 + x + 3(−2) = 0 ⇒ x = +5.

【G4-Chem-416】 Q93 · IB Chemistry HL · Acids & Bases · Easy

According to the Brønsted–Lowry definition, a base is:

A) A proton donor
B) A proton acceptor
C) An electron-pair donor
D) A hydroxide producer only

Answer: B) A proton acceptor. Brønsted–Lowry: acid = H⁺ donor, base = H⁺ acceptor. (Lewis: acid = e⁻ pair acceptor; base = e⁻ pair donor.)

【G4-Chem-416】 Q94 · IB Chemistry HL · Acids & Bases · Hard

What is the pH of a 0.001 M NaOH solution (assume full dissociation)?

A) 3
B) 11
C) 13
D) 1

Answer: B) 11. [OH⁻] = 0.001 M ⇒ pOH = 3. At 25°C: pH + pOH = 14 ⇒ pH = 11.

【G4-Chem-418】 Q95 · IB Chemistry HL · Organic Chemistry · Easy

Which of the following is an alkane?

A) C₂H₄
B) C₂H₆
C) C₂H₂
D) C₆H₆

Answer: B) C₂H₆. Alkanes have general formula CₙH₂ₙ₊₂ (single bonds only). C₂H₄ = alkene; C₂H₂ = alkyne; C₆H₆ = benzene (aromatic).

【G4-Chem-418】 Q96 · IB Chemistry HL · Organic Chemistry · Medium

What type of isomerism is shown by CH₃CH₂OH (ethanol) and CH₃OCH₃ (methoxymethane)?

A) Geometric (cis–trans)
B) Optical
C) Functional group
D) Chain (structural)

Answer: C) Functional group. Both have molecular formula C₂H₆O but different functional groups (alcohol vs ether) → functional group isomerism (class of structural isomerism).

【G4-Chem-418】 Q97 · IB Chemistry HL · Organic Chemistry · Hard

Which reaction type converts ethene (C₂H₄) into ethanol (C₂H₅OH) by adding water across the double bond?

A) Substitution
B) Elimination
C) Hydration (addition)
D) Esterification

Answer: C) Hydration (addition). Addition of H₂O across C=C (acid-catalyzed hydration): the double bond breaks; −H and −OH add to each carbon → ethanol.

【G4-Chem-414】 Q98 · IB Chemistry HL · Kinetics · Hard

A catalyst increases the rate of a chemical reaction primarily by:

A) Increasing the temperature
B) Increasing the concentration of reactants
C) Providing an alternative reaction pathway with lower activation energy
D) Shifting the equilibrium position toward products

Answer: C) Providing an alternative reaction pathway with lower Eₐ. Lower Eₐ means more particles have sufficient energy to react; catalysts do not affect ΔH or equilibrium position.

【G3-Econ-31】 Q99 · IB Economics HL · Microeconomics · Medium

If a 10% increase in price causes a 5% decrease in quantity demanded, the price elasticity of demand (PED) is:

A) −0.5 (demand is inelastic)
B) −2 (demand is elastic)
C) −0.5 (demand is elastic)
D) −2 (demand is inelastic)

Answer: A) −0.5 (demand is inelastic). PED = %ΔQd / %ΔP = −5%/10% = −0.5. Since |PED| < 1, demand is inelastic.

【G3-Econ-31】 Q100 · IB Economics HL · Microeconomics · Hard

Which market structure is characterized by many firms, differentiated products, and relatively easy entry/exit?

A) Perfect competition
B) Monopoly
C) Monopolistic competition
D) Oligopoly

Answer: C) Monopolistic competition. Key: many firms + product differentiation (unlike perfect competition's homogeneous goods) and free entry/exit (unlike oligopoly/monopoly).

【G3-Econ-31】 Q101 · IB Economics HL · Externalities · Medium

A government imposes a per-unit Pigouvian tax on a good with negative production externalities. The intended outcome is:

A) Shift the supply curve right and raise output
B) Shift the supply curve left and lower output toward the social optimum
C) Shift demand right to internalize the externality
D) Eliminate the good entirely from the market

Answer: B) Shift supply left, lower output toward social optimum. The tax raises producers' MPC closer to MSC, reducing overproduction and moving equilibrium closer to the socially efficient quantity.

【G3-Econ-32】 Q102 · IB Economics HL · Macroeconomics · Easy

Which of the following is included in the expenditure approach to calculating GDP?

A) Intermediate goods purchases
B) Government transfer payments
C) Investment spending (I)
D) Used car resale

Answer: C) Investment spending (I). Expenditure GDP = C + I + G + (X − M). Intermediate goods, transfers, and used-goods sales are excluded.

【G3-Econ-32】 Q103 · IB Economics HL · Macroeconomics · Medium

Which type of unemployment arises from a mismatch between workers' skills and available jobs?

A) Frictional unemployment
B) Structural unemployment
C) Cyclical (demand-deficient) unemployment
D) Seasonal unemployment

Answer: B) Structural unemployment. Structural = skills/location mismatch (e.g., declining industry). Frictional = between jobs; cyclical = recession-related.

【G3-Econ-32】 Q104 · IB Economics HL · Fiscal Policy · Medium

In a recession, an appropriate discretionary fiscal policy response would be to:

A) Raise taxes and cut government spending
B) Lower interest rates
C) Increase government spending and/or cut taxes
D) Sell government bonds on the open market

Answer: C) Expansionary fiscal policy: higher G and/or lower T increases AD to close a recessionary gap. B and D are monetary policy tools (central bank), not fiscal.

【G3-Econ-33】 Q105 · IB Economics HL · International Trade · Easy

A country has a comparative advantage in producing a good when it can do so:

A) With the absolute lowest labor cost
B) At a lower opportunity cost than its trading partner
C) Using fewer raw materials
D) With a higher price than other countries

Answer: B) At a lower opportunity cost. Comparative advantage is based on opportunity cost, not absolute productivity. Gains from trade arise from specializing per CA.

【G3-Econ-33】 Q106 · IB Economics HL · Exchange Rates · Hard

In a floating exchange-rate system, an increase in demand by foreigners for a country's exports will tend to cause the country's currency to:

A) Appreciate
B) Depreciate
C) Remain unchanged
D) Experience hyperinflation

Answer: A) Appreciate. Foreign buyers need the domestic currency to pay for exports ⇒ demand for domestic currency rises ⇒ the currency appreciates (higher exchange value).

【G3-BM-38】 Q107 · IB Business Management HL · Marketing · Medium

Which pricing strategy involves setting a very low initial price to quickly gain market share?

A) Price skimming
B) Penetration pricing
C) Cost-plus pricing
D) Loss leader

Answer: B) Penetration pricing. Skimming = high initial price; penetration = low initial price to penetrate the market rapidly and build volume.

【G3-BM-310】 Q108 · IB Business Management HL · Operations Management · Easy

Which production method produces a single, unique product to customer specifications (e.g., custom furniture)?

A) Job production
B) Batch production
C) Flow (mass) production
D) Mass customization

Answer: A) Job production. Job = one-off custom unit; batch = groups of identical units; flow = continuous standardized units on a line.

【G3-BM-310】 Q109 · IB Business Management HL · Operations · Medium

Which operations management tool identifies the bottleneck activities and critical path of a project?

A) SWOT analysis
B) Ansoff matrix
C) Critical path analysis (CPA)
D) Boston Consulting Group (BCG) matrix

Answer: C) Critical path analysis. CPA (with network diagrams) calculates EST, LFT, float, and the critical path of tasks determining minimum project duration.

【G3-BM-39】 Q110 · IB Business Management HL · Finance · Easy

Which financial statement shows a firm's assets, liabilities, and equity at a point in time?

A) Income statement (P&L)
B) Balance sheet (statement of financial position)
C) Cash flow statement
D) Funds flow statement

Answer: B) Balance sheet. Balance sheet = snapshot of financial position (A = L + E) at a date. Income statement covers a period's revenues and expenses.

【G3-BM-39】 Q111 · IB Business Management HL · Finance · Hard

A company's net profit after tax is $50,000, total equity is $250,000, and it pays $10,000 in dividends. Calculate return on equity (ROE).

A) 4%
B) 20%
C) 25%
D) 16%

Answer: B) 20%. ROE = (Net profit after tax / Equity) × 100% = (50,000 / 250,000) × 100% = 20%. Dividends do not reduce net profit used for ROE.

【G3-BM-37】 Q112 · IB Business Management HL · Human Resource Management · Medium

In Herzberg's two-factor theory, which is a motivating factor (satisfier) rather than a hygiene factor?

A) Salary
B) Working conditions
C) Achievement / recognition
D) Company policy

Answer: C) Achievement / recognition. Herzberg motivators (intrinsic): achievement, recognition, responsibility, advancement. Hygiene (extrinsic context): pay, conditions, policies—prevent dissatisfaction but do not strongly motivate.

【G3-BM-36】 Q113 · IB Business Management HL · Strategy · Hard

In the BCG matrix, a product with high market share in a low-growth market is classified as a:

A) Star
B) Cash cow
C) Question mark (problem child)
D) Dog

Answer: B) Cash cow. BCG: Star = high share, high growth; Cash Cow = high share, low growth (cash-generating mature products); Question mark = low share, high growth; Dog = low share, low growth.

【G3-BM-36】 Q114 · IB Business Management HL · Strategy · Easy

Which Ansoff matrix strategy involves existing products in existing markets?

A) Market development
B) Product development
C) Market penetration
D) Diversification

Answer: C) Market penetration. Ansoff: Penetration = existing product/existing market (lowest risk); Diversification = new product/new market (highest risk).

【G4-CS-431】 Q115 · IB Computer Science SL · System Fundamentals · Easy

Which of the following best describes an algorithm?

A) A programming language
B) A finite sequence of well-defined steps to solve a problem
C) A hardware component
D) A type of data structure

Answer: B) A finite sequence of well-defined steps to solve a problem. Algorithms are unambiguous, have clear inputs/outputs, and terminate (typically).

【G4-CS-434】 Q116 · IB Computer Science HL · Data Structures · Medium

Which data structure uses LIFO (Last-In, First-Out) ordering?

A) Queue
B) Stack
C) Linked list
D) Binary search tree

Answer: B) Stack. Push/pop at the top ⇒ LIFO. Queue uses FIFO (First-In, First-Out).

【G4-CS-434】 Q117 · IB Computer Science HL · Algorithms · Hard

Using Big-O notation, what is the average-case time complexity of binary search on a sorted array of size n?

A) O(1)
B) O(log n)
C) O(n)
D) O(n log n)

Answer: B) O(log n). Binary search halves the search space each step; number of comparisons is proportional to log₂n ⇒ logarithmic time. Linear search is O(n).

【G3-Hist-313】 Q118 · IB Psychology HL · Criminological / Abnormal · Medium

According to the biological approach to behavior, which brain structure is most associated with the "fight or flight" fear response and emotional memory?

A) Cerebellum
B) Amygdala
C) Broca's area
D) Medulla oblongata

Answer: B) Amygdala. The amygdala (part of the limbic system) is central to fear conditioning, threat appraisal, and forming emotional (fearful) memories.

【G3-Hist-313】 Q119 · IB Psychology HL · Developmental · Medium

Piaget proposed that in the sensorimotor stage, infants develop an understanding that objects continue to exist when out of sight. This concept is called:

A) Conservation
B) Object permanence
C) Egocentrism
D) Assimilation

Answer: B) Object permanence. A key milestone of the sensorimotor stage (0–2 years), demonstrated typically by 8 months. Conservation appears in the concrete operational stage.

【G3-Hist-312】 Q120 · IB History HL · 20th-Century World History · Easy

Which treaty officially ended World War I and imposed heavy reparations on Germany?

A) Treaty of Versailles (1919)
B) Treaty of Brest-Litovsk
C) Treaty of Tordesillas
D) Treaty of Westphalia

Answer: A) Treaty of Versailles (1919). The Treaty of Versailles (June 1919) redrew Europe, created the League of Nations, and assigned "war guilt" + reparations to Germany, with long-term consequences.

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