AA SL Q/A

Sample question

Solve 2x² − 5x − 3 = 0 using the quadratic formula. Give answers in exact form.

Sample question

Solve log₃(x + 2) + log₃(x − 2) = 1 for real values of x.

Sample question

The 5th term of an AP is 12. The sum of the first 8 terms is 100. Find d.

Sample question

Find the sum to infinity of 12, 4, 4/3, … and explain why this series converges.

Sample question

Given f(x) = 2x + 3 and g(x) = x² − 1, find (f ∘ g)(x) and the inverse f⁻¹(x).

Sample question

Sketch y = −2 f(x − 3) + 1 given the graph of y = f(x). Identify each transformation.

Sample question

A bacterial culture doubles every 3 hours. Initial population 500. Find the size after 10 hours.

Sample question

In triangle ABC, a = 8 cm, b = 10 cm, C = 70°. Find side c and the area of the triangle.

Sample question

A sector has radius 6 cm and angle 75°. Find the arc length and sector area in exact form.

Sample question

Solve 2 cos²x − cos x − 1 = 0 for 0 ≤ x ≤ 2π. Give answers in exact form.

Sample question

A water level varies as h(t) = 3 sin(πt/6) + 8. Find amplitude, period and the maximum height.

Sample question

From the frequency table given, find the mean, standard deviation, and identify any outliers.

Sample question

Two cards are drawn without replacement from a standard deck. Find P(both kings).

Sample question

P(success) = 0.4. In 12 independent trials, find P(X ≥ 5) and the expected value.

Sample question

Heights ~ N(170, 8²). Find the percentage of people taller than 180 cm and the 90th percentile.

Sample question

Differentiate y = x² · sin(3x) using the product rule, then simplify your answer.

Sample question

Find the equation of the tangent and normal to y = x³ − 2x at the point (1, −1).

Sample question

A box with square base has total surface area 100 cm². Find dimensions that maximise volume.

Sample question

Find ∫ (3x² − 4x + 2)/√x dx, simplifying your answer fully.

Sample question

Find the area enclosed between y = x² and y = x + 2, giving your answer as an exact fraction.

Sample question

A particle’s velocity is v(t) = 3t² − 12. Find total distance travelled for 0 ≤ t ≤ 4.