Edexcel IAL Maths Year 1 starter questions: weeks 1–13
39 short questions to open a lesson for Edexcel International A Level Maths Year 1, weeks 1–13 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 1
Question 1: Algebraic expressions & indices
Simplify (2x³)^4.
Question 2: Algebraic expressions & indices
Factorise completely x³ - 9x.
Question 3: Surds
Simplify √50 + √18.
Week 2
Question 1: Surds
Rationalise the denominator of 6/(3-√3), giving your answer in the form a + b√3.
Question 2: Quadratic functions & graphs
Solve 2x² - 5x - 3 = 0.
Question 3: Quadratic functions & graphs
Write x² + 6x - 4 in the form (x+p)² + q.
Week 3
Question 1: The discriminant
Find the values of k for which x² + kx + 9 = 0 has equal roots.
Question 2: Quadratic functions & graphs
Find the coordinates of the turning point of y = x² - 8x + 19.
Question 3: Simultaneous equations
Solve the simultaneous equations 3x + 2y = 12 and 5x - y = 7.
Week 4
Question 1: Simultaneous equations
Solve the simultaneous equations y = x + 1 and x² + y² = 13.
Question 2: Inequalities (linear & quadratic)
Solve 5 - 2x < 11.
Question 3: Inequalities (linear & quadratic)
Find the set of values of x for which x² - x - 12 > 0.
Week 5
Question 1: Sketching polynomial graphs
Find the points where y = x(x-2)(x+3) meets the coordinate axes.
Question 2: Sketching polynomial graphs
Write down the equations of the asymptotes of y = 3/x + 2.
Question 3: Graph transformations
The curve y = x² is translated by the vector 3; -1. Write down the equation of the new curve.
Week 6
Question 1: Graph transformations
The point (4, 6) lies on y = f(x). Write down its image on y = 3f(x) and on y = f(2x).
Question 2: Coordinate geometry: straight lines
Find the equation of the line through (2, -1) and (6, 7) in the form y = mx + c.
Question 3: Coordinate geometry: straight lines
Find the gradient of a line perpendicular to 3x + 4y - 8 = 0.
Week 7
Question 1: Coordinate geometry: straight lines
Find the length of the line segment joining A(1, 2) and B(7, 10).
Question 2: Sine & cosine rules, area of a triangle
In triangle ABC, AB = 7 cm, AC = 5 cm and angle BAC = 60^∘. Find the exact length of BC.
Question 3: Sine & cosine rules, area of a triangle
Find the area of triangle PQR with PQ = 8 cm, PR = 5 cm and angle QPR = 30^∘.
Week 8
Question 1: Sine & cosine rules, area of a triangle
In triangle ABC, a = 10 cm, angle A = 30^∘ and angle B = 45^∘. Find the exact length of b.
Question 2: Trig ratios & graphs
Write down the maximum value of y = 5 - 2sin x and the value of x, 0^∘ ≤ x < 360^∘, where it occurs.
Question 3: Radian measure, arc & sector
Convert 135^∘ to radians, giving your answer in terms of π.
Week 9
Question 1: Radian measure, arc & sector
A sector has radius 6 cm and angle 0.8 radians. Find its arc length and its area.
Question 2: Radian measure, arc & sector
A sector of a circle of radius 10 cm has area 40 cm². Find the angle of the sector in radians.
Question 3: Differentiation from first principles
Find, in terms of h, the gradient of the chord joining the points on y = x² where x = 3 and x = 3 + h. What does it tend to as h → 0?
Week 10
Question 1: Differentiating polynomials
Differentiate y = 4x³ - 5x² + 7x - 2.
Question 2: Differentiating polynomials
Differentiate y = (x² + 3)/(√x).
Question 3: Tangents & normals
Find the equation of the tangent to y = x² - 4x + 1 at the point where x = 3.
Week 11
Question 1: Tangents & normals
Find the equation of the normal to y = x³ at the point (1, 1).
Question 2: Integration of polynomials
Find ∫ (6x² - 4x + 3) dx.
Question 3: Integration of polynomials
Given that dy/dx = 3x² + 2 and the curve passes through (1, 5), find y in terms of x.
Week 12
Question 1: Algebraic expressions & indices
Evaluate 27^(-2/3) without a calculator.
Question 2: Inequalities (linear & quadratic)
Solve x² < 4x.
Question 3: Trig ratios & graphs
Solve sin x = 0.5 for 0^∘ ≤ x ≤ 360^∘.
Week 13
Question 1: Algebraic division & the factor theorem
Show that (x - 2) is a factor of x³ - 3x² - 4x + 12, and factorise it fully.
Question 2: The remainder theorem
Find the remainder when 2x³ - x² + 5 is divided by (x + 1).
Question 3: Mathematical proof
Prove that the sum of any three consecutive integers is a multiple of 3.
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.