Mathematics 0580/43 October/November 2021: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 4 (Extended), October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
The diagram shows three triangles, T, A, and B, drawn on a 1 cm2 grid.
y
8
7
B
6
5
4
A
3
T
2
1
0 1 2 3 4 5 6 7 8 x
(a) Describe fully the single transformation that maps triangle T onto triangle A.
…… [3]
(b) (i) Describe fully the single transformation that maps triangle T onto triangle B.
…… [2]
(ii) Calculate the distance that each point of triangle T moves when it is mapped onto triangle B.
…… cm [2]
Mark scheme
1(a) Rotation 3 B1 for each
90° clockwise oe
[centre] (5, 2)
1(b)(i) Translation 2 B1 for each
−1
4
1(b)(ii) 4.12 or 4.123... 2 M1 for (their (–1))2 + (their 4)2
(a)
A
NOT TO
SCALE
38° O
B
P
A, B and P are points on a circle, centre O and angle OBA = 38° .
Find angle APB.
Angle APB = …… [3]
(b)
F
E
NOT TO
SCALE
T D
50°
C
U
CDEF is a cyclic quadrilateral and FC = FE.
TU is a tangent to the circle at C and angle TCF = 50°.
Find
(i) angle EFC,
Angle EFC = …… [2]
(ii) angle CDE.
Angle CDE = …… [1]
Mark scheme
2(a) 52° 3 M1 for 180 – 2 × 38, implied by 104
M1 for their AOB ÷ 2
2(b)(i) 80° 2 B1 for FEC =50 or FCE = 50
2(b)(ii) 100° 1 FT 180 – their (i)
(a)
5 cm NOT TO
SCALE
C 4 cm
D
A 10 cm B
The diagram shows a prism.
The cross-section of the prism is a trapezium with CD parallel to AB and AC = BD.
AB = 10 cm, CD = 4 cm and the height of the trapezium is 5 cm.
The volume of the prism is 525 cm3.
(i) The prism is made of iron.
1 cm3 of iron has a mass of 7.8 g.
Calculate the mass of the prism.
Give your answer in kilograms.
…… kg [2]
(ii) Calculate the length of the prism.
…… cm [3]
(iii) Calculate the total surface area of the prism.
…… cm 2 [6]
(iv) In a mathematically similar prism, the height of the trapezium is 10 cm.
Calculate the volume of this prism.
…… cm 3 [3]
(b) A cuboid measures 10 cm by 4 cm by 6 cm.
Each side is measured correct to the nearest centimetre.
Complete the inequality for the volume, V, of this cuboid.
…… cm 3 G V 1 …… cm 3 [3]
Mark scheme
3(a)(i) 4.095 2 B1 for figs 4095
525 × 7.8
or M1 for
1000
3(a)(ii) 15 3 B2 for 35
OR
1
M2 for (10 + 4) × 5 × L = 525 oe
2
1
M1 for (10 + 4) × 5 oe
2
3(a)(iii) 455 or 454.9... 6 M3 for their [BD =] 32 + 52 × (their 15)
[× 2]
or
B2 for 34 or 5.83 or 5.830 to 5.831
2
1
or M1 for 52 + (10 − 4 )
2
and
M1 for their 35 × 2
M1 for (their 15) × 10 and (their 15) × 4
3(a)(iv) 4200 3 10
3
M2 for 525 × oe
5
3 3
10 5
or M1 for or oe
5 10
3(b) 182.875 ... 307.125 final answer 3 B2 for either seen
or M1 for 10 ± 0.5 or 6 ± 0.5 or 4 ± 0.5
oe
(a) Solve the simultaneous equations.
You must show all your working.
2p - q = 7
3p + 2q = 7
p = ……
q = …… [3]
(b) Solve the equation. x 2x
+ =1
4 3
x = …… [2]
(c) - 8 1 3x - 2 G 7
(i) Solve the inequality.
…… [3]
(ii) Find the integer values of x that satisfy the inequality.
…… [1]
(d) Factorise completely.
16a - 4a 2
…… [2]
(e) Write each of the following as a single fraction, in its simplest form.
1 3
(i) '
2a 4b
…… [2]
x
(ii) 2- x-1
…… [2]
Mark scheme
4(a) Correctly eliminate one variable M1
p=3 A2 A1 for each
q = –1 If M0, SC1 for 2 values satisfying one of
original equations
If 0 scored SC1 for correct answers with
no working
4(b) 1 12 2 3x 8 x
1 or 1.09 or 1.090 to 1.091 M1 for + = 1 or better
11 11 12 12
4(c)(i) –2 < x ⩽ 3 3 B2 for –2 < x or x ⩽ 3
or M1 for –8 + 2 < 3x or 3x ⩽ 7 + 2
4(c)(ii) –1, 0, 1, 2, 3 1 FT dep on –ve and +ve values in their
(c)(i)
4(d) 4a (4 − a ) final answer 2 B1 for any correct partial factorisation
4(e)(i) 2b 2 1 4b
final answer M1 for × or better
3a 2a 3
4(e)(ii) x−2 2 B1 for 2(x – 1) – x oe seen.
final answer nfww
x −1
(a) $500 is invested at a rate of 3% per year.
Calculate the total interest earned at the end of 7 years when
(i) simple interest is paid,
$ …… [2]
(ii) compound interest is paid.
$ …… [3]
(b) The value of a car decreases exponentially by 10% each year.
The value now is $6269.40 .
Calculate the value of the car 3 years ago.
$ …… [3]
Mark scheme
5(a)(i) 105 2 3
M1 for × 500 [×7 ]
100
5(a)(ii) 115 or 114.9... 3 3
7
M2 for 500 × 1 + [ −500]
100
k
3
or M1 for 500 × 1 + , k integer ⩾ 2
100
5(b) 8600 3 6269.4
M2 for 3
oe
10
1 −
100
3
10
or M1 for C × 1 − = 6269.4 oe
100
D
100° NOT TO
SCALE
50° C
A 12 cm
8 cm
11 cm
B
(a) Calculate AD.
AD = …… cm [3]
(b) Calculate angle BAC and show that it rounds to 40.42°, correct to 2 decimal places.
[4]
(c) Calculate the area of the quadrilateral ABCD.
…… cm2 [3]
(d) Calculate the shortest distance from B to AC.
…… cm [3]
Mark scheme
6(a) 9.33 or 9.334... 3 12sin 50
M2 for
sin100
sin100 sin 50
or M1 for = oe
12 AD
6(b) 112 + 122 − 82 M2 M1 for
[cos =]
2 × 11 × 12 82 = 112 + 122 − 2 × 11 × 12cos( BAC )
40.415... A2 201 67
A1 for 0.761... or or
264 88
6(c) 70.8 or 70.77 to 70.79... 3 M1 for
1
× 12 × their (a) × sin(180 − 100 − 50)
2
1
M1 for × 12 × 11× sin(40.42)
2
6(d) 7.13 or 7.131 to 7.132... 3 dist
M2 for = sin(40.42)
11
or M1 for recognition that shortest
distance is perpendicular to AC
(a) Amir buys 3 cakes that cost c cents each and 2 loaves of bread that cost (2c - 11) cents each.
He spends a total of $5.87 .
Find the value of c.
c = …… [3]
(b) A bottle of water costs $w.
A bottle of juice costs $(w + 1).
Alex spends $22 on bottles of water and $42 on bottles of juice.
The number of bottles of water is equal to the number of bottles of juice.
Find the value of w.
w = …… [3]
(c) Alicia walks a distance of 9 km at a speed of x km/h.
She then runs a distance of 5 km at a speed of (2x + 1) km/h.
The total time Alicia takes is 2.5 hours.
(i) Show that 10x 2 - 41x - 18 = 0 .
[4]
(ii) Work out Alicia’s running speed.
You must show all your working.
…… km/h [4]
Mark scheme
7(a) 87 3 M2 for 3c + 4c = 587 + 22 or better
or M1 for 3c + 2(2c – 11) [= 587 or 5.87]
7(b) 1.1[0] 3 M2 for 22w + 22 = 42w or better
22 42
or M1 for = oe
w w +1
OR
B2 for number of bottles = 20
or M1 for Nw = 22 and N(w+1) = 42
7(c)(i) 9 5 M2 9 5
+ = 2.5 oe M1 for or
x 2x + 1 x 2x + 1
9(2 x + 1) + 5 x = 2.5 x(2 x + 1) oe M1 Correctly clearing fractions, or correctly
collecting into a single fraction
9(2 x + 1) + 5 x FT their expression dep on two fractions
or [= 2.5 oe] both with algebraic denominators
x(2 x + 1)
All brackets expanded leading to A1
10 x 2 − 41x − 18 = 0 with no errors or
omissions
7(c)(ii) (2 x − 9)(5 x + 2) M2 B1 for (ax + b)(cx + d )
−( −41) ± ( −41) 2 − 4(10)( −18) with ac = 10 and bd = –18 or
or ad + bc = –41
2(10)
or (−41) 2 − 4(10)(−18)
−( −41) + q −( −41) − q
or oe or oe or
2(10) 2(10)
both
2 2
41 18 41
or M1 for x − − − = 0 or
20 10 20
better
10 A2 9
A1 for [x =] oe
2
or M1 for 2 × their positive root + 1
(a) Jean asks 600 people to choose their favourite sport.
The pie chart shows some of this information.
Football
105°
60°
27°
Tennis
Rugby
(i) Show that 100 people choose tennis.
[1]
(ii) Work out how many people choose rugby.
…… [2]
(iii) 125 people choose cricket and the rest choose swimming.
Complete the pie chart to show this information.
[2]
(b) The heights of some plants are measured:
• smallest height = 0.6 cm
• range = 8.1 cm
• median = 5.2 cm
• lower quartile = 3.4 cm
• interquartile range = 4.1 cm.
On the grid, draw a box-and-whisker plot to show this information.
0 1 2 3 4 5 6 7 8 9 10
Height (cm) [3]
(c) A dice is rolled 100 times.
The frequency table shows the results.
Score 1 2 3 4 5 6
Frequency 16 25 17 19 8 15
Find
(i) the range,
…… [1]
(ii) the mode,
…… [1]
(iii) the median.
…… [1]
(d) 50 students answer a mathematics question.
The table shows the time, t seconds, taken by each student to answer the question.
Time (t seconds) 10 1 t G 20 20 1 t G 25 25 1 t G 30 30 1 t G 50 50 1 t G 80
Frequency 2 8 12 16 12
Calculate an estimate of the mean.
…… s [4]
Mark scheme
8(a)(i) 60 1
× 600 oe
360
8(a)(ii) 45 2 27
M1 for × 600 oe
360
8(a)(iii) Correct straight line on the pie chart 2 B1 for 75
8(b) Correct diagram 3 B1 for any three of 0.6, 3.4, 5.2, 7.5, 8.7
correctly placed
B1 for 7.5 and 8.7 seen
0.6 3.4 5.2 7.5 8.7
8(c)(i) 5 1
8(c)(ii) 2 1
8(c)(iii) 3 1
8(d) 39.2 4 M1 for mid-values soi
M1 for Σfx with x in correct interval
including boundaries
Σfx
M1 dep for dep on second M1
50
f (x) = x (x - 1) (x - 2)
(a) Find the coordinates of the points where the graph of y = f (x) crosses the x-axis.
( …… , …… )
( …… , …… )
( …… , …… ) [2]
(b) Show that f (x) = x 3 - 3x 2 + 2x .
[2]
(c) Find the coordinates of the turning points of the graph of y = f (x) .
Show all your working and give your answers correct to 1 decimal place.
( …… , …… )
( …… , …… ) [8]
(d) Sketch the graph of y = f (x) .
y
O x
[2]
Mark scheme
9(a) (0, 0), (1, 0), (2, 0) 2 B1 for any two correct
If 0 scored, SC1 for all three x values
clearly identified
9(b)
( ) (
x x 2 − x − 2 x + 2 or x 2 − x ( x − 2 ) ) (
2 B1 for x x 2 − x − 2 x + 2
)
or ( x − 1) ( x − 2 x ) 2
( )
or x − x ( x − 2 )
2
leading to x 3 − 3 x 2 + 2 x with no errors or (
or ( x − 1) x 2 − 2 x )
omissions
9(c) 3x 2 − 6 x + 2 B2 B1 for 2 correct terms
dy M1
their =0
dx
M2 M1 for
−( −6) ± ( −6 )2 − 4(3)(2) (−6) 2 − 4(3)(2) or for
their
2(3) p± q
p = –(–6) and r = 2(3) if in form
r
(0.4, 0.4) B3 B2 for 0.4 or 0.42... and 1.6 or 1.57 to
(1.6, –0.4) 1.58
or for one correct pair of coordinates
or B1 for 0.4 or 0.42... or 1.6 or 1.57 to
1.58
1 1
If 0 scored SC1 for 1 + and 1 –
3 3
or better or for one correct pair of
coordinates in any form
9(d) Correct sketch
2
2 FT their (c) but must be cubic
i.e. correct shape cubic through origin and
1
max and min in correct quadrants
0
.5 0 0.5 1 1.5 2 2.5
-1
B1 for cubic shape sketch
-2
(a) Sarah spins a fair four-sided spinner numbered 0, 1, 1 and 3.
(i) What number is the spinner most likely to land on?
…… [1]
(ii) Sarah spins the spinner twice.
Find the probability that it lands on the number 1 both times.
…… [2]
(iii) Sarah spins the spinner until it lands on the number 3.
729
The probability that this happens on the nth spin is .
16384
Find the value of n.
n = …… [2]
(b) Scott takes an examination.
The examination is in two parts, a theory test and a practical test.
Both parts must be passed to pass the examination.
The probability that Scott passes the theory test is 0.9 .
The probability that Scott passes the practical test is 0.8 .
Find the probability that
(i) Scott passes the examination,
…… [2]
(ii) Scott passes the theory test or the practical test but not both.
…… [3]
Mark scheme
10(a)(i) 1 1
10(a)(ii) 1 2 2 2
oe nfww M1 for × oe
4 4 4
10(a)(iii) 7 2 3 1
k
M1 for trials with × soi
4 4
10(b)(i) 0.72 oe 2 M1 for 0.9 × 0.8
10(b)(ii) 0.26 oe 3 M2 for 0.9 × 0.2 + 0.1 × 0.8
or 1 – their (b)(i) – 0.1 × 0.2
or M1 for 0.9 × 0.2 or 0.1 × 0.8
or 1 – their (b)(i) or 1 – 0.1 × 0.2
f (x) = 2x - 1 g (x) = x 2 + 2x h (x) = 4 x j (x) = 2 x
(a) Find the value of
(i) h(3),
…… [1]
(ii) fh(3).
…… [1]
(b) Solve the equation gf (x) = 0 .
x = …… or x = …… [4]
(c) p -1 (x) = f (x)
Find p(x).
…… [2]
1
(d) h (x) j (x) =
2
Find the value of x.
x = …… [3]
Mark scheme
11(a)(i) 64 1
11(a)(ii) 127 1 FT 2 × their (a)(i) – 1
11(b) 1 4 M1 for ( 2 x − 1)2 + 2(2 x − 1)
± oe nfww
2
B1 for 4 x 2 − 2 x − 2 x + 1 or
( 2 x − 1)( 2 x − 1 + 2 )
B1 for 4 x 2 − 1 [= 0] or ( 2 x − 1)( 2 x + 1)
[= 0]
OR
M1 for x(x + 2) = 0 (solving g(x) = 0)
A1 for x = 0 or –2
B1 for 2x – 1 = 0 or 2x – 1 = –2
11(c) x +1 2 M1 for
oe final answer y 1
2 y + 1 = 2 x or = x − or x = 2 y − 1
2 2
11(d) 1 3 1
− oe nfww B2 for 3x = − oe
6 2
OR
1
x
M1 for 22 x × 2 x oe or 4 2 × 4 x oe or 8x
oe
1 1 1
− − −
M1 for 2 2 or 4 4 or 8 6 soi
Checked your answers against these? Let AI mark the whole paper, on your own working.
Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Where can I find the 0580/43 October/November 2021 mark scheme?+
On this page, free: the mark scheme for IGCSE Mathematics 0580/43, October/November 2021 (0580_w21_ms_43), and the question paper (0580_w21_qp_43), to read or download, with each question's marking points written out underneath.
How many marks is 0580/43 out of?+
Mathematics 0580/43 for October/November 2021 is out of 130 marks, with 2 hours 30 minutes to answer it.
Can I get my 0580/43 answers marked?+
Yes. Upload your answers to 0580/43/O/N/21 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.