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IGCSE Maths 4MA1 Year 11 starter questions: weeks 1–12

48 short questions to open a lesson for Edexcel IGCSE Maths A (4MA1) Higher, Year 11, weeks 1–12 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 1

Question 1: Factors & Primes
List the prime numbers between 20 and 40.
Question 2: Basic Probability
A bag contains 4 red, 7 blue and 9 green counters. One counter is taken at random. Find the probability that it is not blue.
Question 3: Fractions
Work out 3/5 × 2/3 + 2/5 × 1/4.
Question 4: Expected Frequency
The probability that a biased coin lands on heads is 0.35. The coin is thrown 240 times. Work out an estimate for the number of heads.

Week 2

Question 1: Set Notation
E = 1, 2, …, 12, A = multiples of 3, B = even numbers. List the members of A ∩ B and of A ∪ B.
Question 2: Complement
For the sets above, find n(A').
Question 3: Theoretical Probability
A fair spinner has sections numbered 1 to 8. Find the probability that it lands on a prime number.
Question 4: Mutually Exclusive Events
The probabilities that a counter is red, blue or yellow are 0.3, 2x and x. These are the only colours. Find x.

Week 3

Question 1: Relative Frequency
A dice is rolled 150 times and lands on 6 a total of 42 times. Work out the relative frequency of a 6 and comment on whether the dice is fair.
Question 2: Tree Diagrams
P(rain on Monday) = 0.4 and, independently, P(rain on Tuesday) = 0.3. Find the probability that it rains on exactly one of the two days.
Question 3: Venn Diagrams
In a class of 30, 18 study French, 12 study Spanish and 5 study both. How many study neither?
Question 4: Probability
Two fair coins are thrown. Find the probability of at least one head.

Week 4

Question 1: Without Replacement
A bag has 5 red and 3 blue beads. Two are taken without replacement. Find the probability that both are red.
Question 2: Conditional Probability
Of 40 students, 24 play tennis; of those, 9 also play golf. 6 students play golf only. A student is chosen at random from those who play golf. Find the probability they also play tennis.
Question 3: Venn Algebra
n(E) = 50, n(A) = 3x, n(B) = 2x, n(A ∩ B) = 8, n(A ∪ B)' = 3. Find x.
Question 4: Changing the Subject
Make x the subject of y = (3x - 2)/5.

Week 5

Question 1: Subject Twice
Make x the subject of ax + 3 = bx - 7.
Question 2: Subject Twice
Make p the subject of (p + 2)/p = q.
Question 3: Translations
The point (3, -1) is translated by -5; 4. Write down the coordinates of its image.
Question 4: Reflections
The point (4, 1) is reflected in the line y = x, then in the line x = 0. Write down the final image.

Week 6

Question 1: Rotations
The point (2, 5) is rotated 90° clockwise about the origin. Write down its image.
Question 2: Enlargements
Triangle T has a vertex at (3, 2). T is enlarged by scale factor 3, centre (1, 1). Find the image of this vertex.
Question 3: Negative Enlargement
The point (4, 6) is enlarged with scale factor -1/2, centre the origin. Write down its image.
Question 4: Reflections
Write down the equation of the mirror line that maps (1, 3) onto (5, 3).

Week 7

Question 1: Similar Triangles
Triangles ABC and PQR are similar with AB = 6 cm, PQ = 15 cm and BC = 8 cm. Find QR.
Question 2: Combined Transformations
Describe fully the single transformation equivalent to a reflection in the x-axis followed by a reflection in the y-axis.
Question 3: Ratio & Proportion
5 pens cost £3.40. Work out the cost of 12 pens.
Question 4: Similarity
A photo 12 cm by 8 cm is enlarged so that the longer side is 30 cm. Find the length of the shorter side.

Week 8

Question 1: Direct Proportion
y is directly proportional to x^2. When x = 4, y = 40. Find y when x = 6.
Question 2: Inverse Proportion
P is inversely proportional to √d. When d = 9, P = 20. Find P when d = 25.
Question 3: Regions
Write down the three inequalities that define the region bounded by x = 1, y = 2 and x + y = 7 (the triangle between them), using ≥ or ≤.
Question 4: Proportion
y x and y = 21 when x = 3. Find the formula for y in terms of x.

Week 9

Question 1: Perpendicular Lines
Find the equation of the line perpendicular to y = 2x - 3 passing through (4, 1).
Question 2: Parallel Lines
Line L is parallel to 4x + 2y = 9 and passes through (0, 5). Write down the equation of L.
Question 3: Area Scale Factor
Two similar shapes have corresponding lengths 4 cm and 10 cm. The smaller has area 24 cm². Find the area of the larger.
Question 4: Volume Scale Factor
Two similar bottles have volumes 250 cm³ and 2000 cm³. The smaller is 12 cm tall. Find the height of the larger.

Week 10

Question 1: Vector Arithmetic
a = 3; -2, b = -1; 4. Find 2a - 3b.
Question 2: Magnitude
Find the magnitude of -5; 12.
Question 3: Vector Geometry
OA = a, OB = b. M is the midpoint of AB. Find OM in terms of a and b.
Question 4: Parallel Vectors
Show that 6; -9 is parallel to -2; 3.

Week 11

Question 1: Volume of a Cone
A cone has radius 6 cm and perpendicular height 10 cm. Find its volume in terms of π.
Question 2: Volume of a Sphere
A sphere has volume 288π cm³. Find its radius.
Question 3: Chord Properties
A chord of length 16 cm is 6 cm from the centre of a circle. Find the radius.
Question 4: Pythagoras
A cuboid measures 3 cm by 4 cm by 12 cm. Find the length of its space diagonal.

Week 12

Question 1: Tangent Properties
PA and PB are tangents to a circle, centre O. Angle APB = 48°. Find angle AOB.
Question 2: Surface Area
Find the curved surface area of a cone with radius 5 cm and slant height 13 cm, in terms of π.
Question 3: Sine Rule
In triangle ABC, a = 9 cm, A = 40°, B = 65°. Find b to 3 significant figures.
Question 4: Cosine Rule
In triangle PQR, PQ = 7 cm, PR = 10 cm and angle QPR = 52°. Find QR to 3 significant figures.

More starter questions

Other weeks: Weeks 1–12 · Weeks 13–24. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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