Edexcel IAL Maths Year 1 starter questions: weeks 27–40
42 short questions to open a lesson for Edexcel International A Level Maths Year 1, weeks 27–40 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; answers and mark schemes stay with teachers.
Week 27
Question 1: Conditional probability
P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.2. Find P(A | B) and P(B | A).
Question 2: Conditional probability
A bag has 5 red and 3 blue counters. Two are taken without replacement. Find the probability that the second is blue given that the first is red.
Question 3: Correlation & regression
A scatter diagram of hours revised against test score shows points close to a straight line sloping upwards. Describe the correlation and interpret it in context.
Week 28
Question 1: Correlation & regression
Given S_xy = 48, S_xx = 64 and S_yy = 49, find the product moment correlation coefficient.
Question 2: Correlation & regression
Given S_xy = 30, S_xx = 12, x = 4 and y = 15, find the regression line of y on x.
Question 3: Discrete random variables
A discrete random variable has P(X = x) = kx for x = 1, 2, 3, 4. Find k and P(X ≥ 3).
Week 29
Question 1: Discrete random variables
X takes the values 0, 1, 2 with probabilities 0.2, 0.5, 0.3. Find E(X) and Var(X).
Question 2: Discrete random variables
E(X) = 4 and Var(X) = 3. Find E(2X - 5) and Var(2X - 5).
Question 3: Discrete random variables
X has a discrete uniform distribution over 1, 2, …, 8. Find P(X > 5) and E(X).
Week 30
Question 1: The normal distribution
X N(50, 4²). Find P(X < 56).
Question 2: Standardising & z-values
X N(20, 5²). Find P(15 < X < 30).
Question 3: Standardising & z-values
X N(μ, 10²) and P(X > 80) = 0.0228. Find μ.
Week 31
Question 1: Coding
Data are coded with y = 2x + 3. Given x = 7 and σ_x = 1.5, find y and σ_y.
Question 2: Probability & Venn diagrams
In a year group 60% study French, and 30% of those also study Spanish. Of the students not studying French, 50% study Spanish. Find the probability that a randomly chosen student studies Spanish.
Question 3: The normal distribution
Plant heights are N(30, 4²) cm. Find the proportion of plants taller than 25 cm.
Week 32
Question 1: Algebraic division & the factor theorem
Divide x³ + 2x² - 5x - 6 by (x + 1).
Question 2: Coordinate geometry: circles
Find the points where the line y = 2x meets the circle (x - 1)² + (y - 2)² = 5.
Question 3: The normal distribution
X N(100, 15²). Find P(X > 130).
Week 33
Question 1: Increasing/decreasing functions & stationary points
Find the maximum value of y = 12x - x³ for x > 0.
Question 2: Graph transformations
Describe the transformation that maps y = f(x) onto y = f(x - 2) + 3.
Question 3: Composite & inverse functions
Given f(x) = 2x + 1 and g(x) = x², find fg(3) and gf(3).
Week 34
Question 1: Surds
Expand and simplify (3 + √2)(3 - √2).
Question 2: Arithmetic sequences & series
The 3rd term of an arithmetic sequence is 11 and the 8th term is 31. Find the first term and the common difference.
Question 3: Probability & Venn diagrams
A and B are independent, P(A) = 0.3 and P(B) = 0.5. Find P(A ∪ B).
Week 35
Question 1: Differentiating polynomials
Find dy/dx when y = 2/(x²), and its value when x = 2.
Question 2: Laws of logarithms & solving equations
Solve 2^(x+1) = 3^x, giving x to 3 significant figures.
Question 3: Measures of location & spread
Find the interquartile range of 3, 5, 6, 8, 9, 11, 14.
Week 36
Question 1: The discriminant
Find the set of values of k for which x² + 4x + k = 0 has no real roots.
Question 2: Radian measure, arc & sector
A chord subtends an angle of (π)/3 radians at the centre of a circle of radius 6 cm. Find the exact area of the minor segment.
Question 3: Correlation & regression
The regression line of y on x is y = 12 + 0.8x, from data with 10 ≤ x ≤ 50. Estimate y when x = 30, and say why an estimate at x = 90 would be unreliable.
Week 37
Question 1: Coordinate geometry: straight lines
Find the equation of the perpendicular bisector of A(2, 1) and B(6, 9).
Question 2: Sum to infinity
A geometric series has first term 10 and sum to infinity 25. Find the common ratio.
Question 3: Standardising & z-values
IQ scores are modelled as N(100, 15²). Find the score exceeded by 10% of people, to 1 decimal place.
Week 38
Question 1: Further differentiation
An open box has a square base of side x cm and surface area A = x² + 128/x. Find the value of x that minimises A.
Question 2: Integration of polynomials
Find ∫ (x³ + 4)/(x²) dx.
Question 3: Discrete random variables
X takes the values 1, 2, 3, 4 with probabilities 0.3, p, 0.2, q, and E(X) = 2.5. Find p and q.
Week 39
Question 1: Binomial expansion (positive integer n)
Use the first three terms of the expansion of (1 + 2x)⁸ to estimate 1.02⁸, to 4 decimal places.
Question 2: Trig identities & equations
Prove that (sin²θ)/(1 - cosθ) ≡ 1 + cosθ.
Question 3: Conditional probability
P(A) = 0.4, P(B | A) = 0.25 and P(B | A') = 0.5. Find P(B) and P(A | B).
Week 40
Question 1: Tangents & normals
The curve y = x² - 5x + 6 has a tangent parallel to the line y = 3x. Find the point of contact.
Question 2: Definite integrals & area
Find the area enclosed between the curve y = x² and the line y = 2x.
Question 3: The normal distribution
X N(μ, σ²) with P(X < 35) = 0.8413 and P(X < 25) = 0.1587. Find μ and σ.
More starter questions
Other weeks: Weeks 1–13 · Weeks 14–26 · Weeks 27–40. Answers and mark schemes are in the starter tasks for teachers.