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IGCSE Maths 4MA1 Year 10 starter questions: weeks 12–22

44 short questions to open a lesson for Edexcel IGCSE Maths A (4MA1) Higher, Year 10, weeks 12–22 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 12

Question 1: Changing the Subject
Make t the subject of v = u + at.
Question 2: Changing the Subject
Make r the subject of V = 4/3π r^3.
Question 3: Linear Inequalities
Solve 7 - 2x > 3x - 8.
Question 4: Integer Solutions
n is an integer. List all the values of n such that -6 ≤ 3n < 9.

Week 13

Question 1: nth Term
Find an expression for the nth term of the sequence 5, 11, 17, 23, …
Question 2: Sequences
The nth term of a sequence is 4n + 7. Is 95 a term of this sequence? Give a reason.
Question 3: Gradient
Find the gradient of the line through (-2, 7) and (4, -5).
Question 4: y = mx + c
Write down the gradient and y-intercept of the line 3x + 2y = 10.

Week 14

Question 1: Equation of a Line
Find the equation of the line through (1, 3) and (5, 11). Give your answer in the form y = mx + c.
Question 2: Simultaneous Equations
Solve the simultaneous equations 3x + 2y = 16 and 5x - 2y = 32.
Question 3: Simultaneous Equations
Adult tickets cost £a and child tickets cost £c. 2 adult and 3 child tickets cost £47. 1 adult and 4 child tickets cost £41. Find a and c.
Question 4: Length of a Line Segment
Work out the length of the line segment joining A(-1, 2) and B(5, 10).

Week 15

Question 1: Regions
The region R satisfies y ≥ 1, x + y ≤ 6 and y ≤ 2x. Write down the coordinates of the vertex of R where y = 2x meets x + y = 6.
Question 2: Factorising
Factorise x² + 11x + 24.
Question 3: Linear Equations
Solve (2x - 3)/4 = x - 5.
Question 4: Angle Facts
Two angles on a straight line are in the ratio 2: 7. Work out the size of the smaller angle.

Week 16

Question 1: Polygons
Each exterior angle of a regular polygon is 24°. (a) How many sides does the polygon have? (b) Work out the size of each interior angle.
Question 2: Angle Sums
Work out the sum of the interior angles of a nonagon (9 sides).
Question 3: Parallel Lines
Two parallel lines are crossed by a transversal. One of the co-interior angles is (3x + 12)° and the other is (2x - 7)°. Find x.
Question 4: Triangles
In triangle ABC, AB = AC and angle BAC = 38°. Side BC is extended to D. Work out the exterior angle ACD.

Week 17

Question 1: Congruence
State the four conditions that can be used to prove two triangles are congruent.
Question 2: Scale Drawings
A map has a scale of 1: 25 000. Two villages are 9.2 cm apart on the map. Work out the real distance between them in kilometres.
Question 3: Bearings
The bearing of B from A is 064°. Work out the bearing of A from B.
Question 4: Polygons
The interior angle of a regular polygon is 162°. How many sides does it have?

Week 18

Question 1: Area of a Trapezium
A trapezium has parallel sides of 7.4 cm and 11.6 cm and a perpendicular height of 5 cm. Work out its area.
Question 2: Compound Area
An L-shape is made by removing a 3 cm by 4 cm rectangle from the corner of a 10 cm by 8 cm rectangle. Work out (a) its area, (b) its perimeter.
Question 3: Loci
Describe the locus of points that are equidistant from two fixed points A and B.
Question 4: Constructions
Which construction would you use to find all points equidistant from two intersecting lines l_1 and l_2?

Week 19

Question 1: Circles
A circle has area 50 cm². Work out its radius. Give your answer to 3 significant figures.
Question 2: Arcs & Sectors
A sector has radius 9 cm and angle 80°. Work out the perimeter of the sector. Give your answer to 3 significant figures.
Question 3: Volume
A cylinder has radius 4 cm and height 10 cm. Work out its volume, giving your answer in terms of π.
Question 4: Surface Area
Work out the total surface area of a closed cylinder with radius 3 cm and height 7 cm. Give your answer in terms of π.

Week 20

Question 1: Unit Conversions
Convert 2.4 m² into cm².
Question 2: Unit Conversions
A tank holds 0.36 m³ of water. How many litres is this? (1 litre = 1000 cm³)
Question 3: Pythagoras
A right-angled triangle has shorter sides 8.5 cm and 12.3 cm. Work out the length of the hypotenuse to 3 significant figures.
Question 4: Pythagoras
A ladder of length 6.5 m leans against a vertical wall. The foot of the ladder is 2.5 m from the wall. How far up the wall does the ladder reach?

Week 21

Question 1: Trigonometry
In triangle ABC, angle B = 90°, AC = 14 cm and angle A = 35°. Work out the length of BC to 3 significant figures.
Question 2: Trigonometry
In a right-angled triangle, the side opposite angle x is 5.2 cm and the adjacent side is 7.9 cm. Work out x to 1 decimal place.
Question 3: Trigonometry
The hypotenuse of a right-angled triangle is x cm. The side adjacent to a 62° angle is 9 cm. Work out x to 3 significant figures.
Question 4: Pythagoras
A rectangle has diagonal 17 cm and width 8 cm. Work out its area.

Week 22

Question 1: Angle of Elevation
A tower is 45 m tall. From a point 80 m from its base on level ground, work out the angle of elevation of the top of the tower. Give your answer to 1 decimal place.
Question 2: Bearings & Trigonometry
A ship sails 12 km on a bearing of 050°. How far east of its starting point is it? Give your answer to 3 significant figures.
Question 3: Factorising
Factorise x² - 9x + 20.
Question 4: Factorising
Factorise 2x² - 7x - 15.

More starter questions

Other weeks: Weeks 1–11 · Weeks 12–22 · Weeks 23–33. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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