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Cambridge IGCSE 0580 Extended starter questions: weeks 34–44

44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 34–44 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 34

Question 1: 2.2 Algebraic manipulation
Expand and simplify (3x - 2)(x + 5).
Question 2: 2.5 Equations
Solve 5x - 7 = 18.
Question 3: 4.4 Similarity
In triangle ABC, D is on AB and E is on AC, and DE is parallel to BC. AD = 4 cm, AB = 10 cm and DE = 6 cm. Find BC.
Question 4: 4.8 Circle theorems II
PA and PB are tangents to a circle, centre O. Angle APB = 48°. Find angle AOB.

Week 35

Question 1: 2.5 Equations
Solve 3(x + 4) = 33.
$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Simplify fully (x² - 9)/(x² + x - 6).$

Question 2: 2.3 Algebraic fractions
Simplify fully (x² - 9)/(x² + x - 6).
Question 3: 2.2 Algebraic manipulation
Factorise completely 12x²y - 18xy.
Question 4: 2.5 Equations
Make the letter in brackets the subject of each formula. (a) C = 2π r [r] (b) y = 3x + 5 [x]

Week 36

$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Write 3/(x + 2) + 2/(x - 1) as a single fraction.$

Question 1: 2.3 Algebraic fractions
Write 3/(x + 2) + 2/(x - 1) as a single fraction.
Question 2: 2.5 Equations
Solve the simultaneous equations. 2x + y = 11 x - y = 1
Question 3: 2.6 Inequalities
x is greater than -3 and at most 5. (a) Write this as a single inequality. (b) How many integers satisfy it?
Question 4: 2.8 Proportion
y is directly proportional to x^2. When x = 4, y = 40. Find y when x = 6.

Week 37

Question 1: 2.8 Proportion
P is inversely proportional to √d. When d = 9, P = 20. Find P when d = 25.
Question 2: 2.10 Graphs of functions
Complete the table of values for y = x² - 2x - 3. x -2 -1 0 1 2 3 4; y
$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Solve 3/(x - 1) - 2/(x + 1) = 1.$

Question 3: 2.3 Algebraic fractions
Solve 3/(x - 1) - 2/(x + 1) = 1.
Question 4: 2.5 Equations
Solve (2x - 3)/4 = 5.

Week 38

Question 1: 2.10 Graphs of functions
Complete the table of values for y = 12/x. x 1 2 3 4 6 12; y
Question 2: 2.11 Sketching curves
The graph of y = x² - 9 is sketched. Write down (a) the coordinates of the points where it crosses the x-axis (b) the coordinates of the point where it crosses the y-axis (c) the equation of its line of symmetry.
Question 3: 2.9 Graphs in practical situations
A travel graph shows Sam's walk. He leaves home at 10 00 and walks 3 km in 45 minutes. He stops for 30 minutes, then walks home in 1 hour. (a) Find his speed on the way out, in km/h. (b) At what time does he arrive home?
Question 4: 2.8 Proportion
y x and y = 21 when x = 3. Find the formula for y in terms of x.

Week 39

Question 1: 2.13 Functions
f(x) = 3x² - 2. Find f(-2).
Question 2: 2.10 Graphs of functions
(a) Complete the table of values for y = x² - 5x + 4. x 0 1 2 3 4 5; y (b) The graph of y = x² - 5x + 4 is drawn from this table. Use the table to write down the solutions of x² - 5x + 4 = 0.
Question 3: 2.11 Sketching curves
Sketch the graph of y = (x - 1)(x - 5). On your sketch, show the coordinates of the points where the graph meets the axes. Write down the equation of the line of symmetry.
Question 4: 2.9 Graphs in practical situations
The graph of a taxi fare against distance is a straight line from (0, 3) to (10, 21), where the distance is in km and the fare is in dollars. (a) Write down the fixed charge. (b) Work out the charge per kilometre.

Week 40

Question 1: 2.12 Differentiation
Find the gradient of the chord joining the points on y = x² where x = 2 and x = 5.
Question 2: 2.13 Functions
g(x) = 5/(x - 4). Which value of x must be excluded from the domain of g?
Question 3: 2.12 Differentiation
Find dy/dx when y = 4x³ - 5x² + 7x - 2.
Question 4: 2.13 Functions
f(x) = 2x + 1 and g(x) = x^2. Find fg(3) and gf(3).

Week 41

Question 1: 6.3 Exact trigonometric values
Without using a calculator, write down the exact value of (a) tan 60^∘ (b) sin 90^∘ (c) cos 0^∘.
Question 2: 6.4 Trigonometric functions
Solve sin x = 0.5 for 0° ≤ x ≤ 360°.
Question 3: 6.5 Non-right-angled triangles
In triangle ABC, a = 9 cm, A = 40°, B = 65°. Find b to 3 significant figures.
Question 4: 2.12 Differentiation
Find the gradient of y = x² + 8/x at the point where x = 2.

Week 42

Question 1: 6.5 Non-right-angled triangles
In triangle PQR, PQ = 7 cm, PR = 10 cm and angle QPR = 52°. Find QR to 3 significant figures.
Question 2: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid measures 3 cm by 4 cm by 12 cm. Find the length of its space diagonal.
Question 3: 6.3 Exact trigonometric values
Without using a calculator, find the exact value of sin 30^∘ + cos 60^∘.
Question 4: 6.4 Trigonometric functions
Write down the period of y = tan x and the equations of its asymptotes for 0° ≤ x ≤ 360°.

Week 43

Question 1: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid measures 6 cm by 8 cm by 5 cm. Find the length of the space diagonal to 3 s.f.
Question 2: 6.2 Right-angled triangles
In a right-angled triangle, one angle is 35^∘ and the hypotenuse is 12 cm. Find the side opposite the 35^∘ angle. Give your answer correct to 3 significant figures.
Question 3: 6.5 Non-right-angled triangles
Find the area of a triangle with sides 8 cm and 11 cm and included angle 36°. Give your answer to 3 s.f.
Question 4: 2.12 Differentiation
Find the x-coordinates of the turning points of y = x³ - 12x + 5.

Week 44

Question 1: 4.4 Similarity
Two bottles are similar. Their heights are 18 cm and 27 cm. The diameter of the base of the smaller bottle is 6.4 cm. Find the diameter of the base of the larger bottle.
Question 2: 5.3 Circles, arcs and sectors
A sector of a circle has radius 6 cm and angle 90^∘. Find its area in terms of π.
Question 3: 5.5 Compound shapes and parts of shapes
A cube of edge 4 cm is placed on top of a cuboid measuring 6 cm by 6 cm by 2 cm. Find the total volume of the solid.
Question 4: 4.3 Scale drawings
The bearing of B from A is 070^∘. Work out the bearing of A from B.

More starter questions

Other weeks: Weeks 1–11 · Weeks 12–22 · Weeks 23–33 · Weeks 34–44 · Weeks 45–55. Answers and mark schemes are in the teacher tools.