Mathematics 0580/33 October/November 2019: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) Write as a decimal.
4
…… [1]
36
(b) Write as a fraction in its lowest terms.
124
…… [1]
5
(c) Work out of 128.
8
…… [1]
(d) Write down all the factors of 24.
…… [2]
(e) Find the highest common factor (HCF) of 24 and 108.
…… [2]
(f) Write down an irrational number between 3 and 9.
…… [1]
(g) Write down the value of 25 0 .
…… [1]
(h) $8400 is invested for 2 years at a rate of 3.5% per year compound interest.
Work out the total amount of interest earned by the end of the 2 years.
$ …… [3]
1 4
(i) Without using a calculator, work out 2 + .
3 5
You must show all your working and give your answer as a mixed number in its simplest form.
…… [3]
Mark scheme
1(a) [0].25 1
1(b) 9 1
cao
13
1(c) 80 1
1(d) 1, 2, 3, 4, 6, 8, 12, 24 2 B1 for 6 or 7 correct factors and no extras
or 8 correct factors and at most one extra
1(e) 12 2 B1 for 2, 3, 4 or 6 as final answer
or 2 × 2 × 3
or for 2 × 2 × 2 × 3 and 2 × 2 × 3 × 3 × 3
1(f) Accept any irrational number between 1
3 and 9
1(g) 1 1
1(h) 598.29 cao 3 3.5
2
M2 for 8400 × 1 + oe
100
OR
2
3.5
M1 for 8400 × 1 + oe
100
A1 for 8998.29
1(i) 5 12 35 B1 allow denominators with multiples of 15
or or 35k 5k
15 15 15 e.g. ,
15k 15k
5 12 35 12 M1 allow other common denominators
[ 2] [+] or [+]
15 15 15 15
17 47 2 A1 with no errors or omissions seen
[2] or leading to 3 cao
15 15 15
(a) Emma records the number of letters in each word in a sentence.
7 1 5 4 2 4 5 3 3 1 2 4
Find
(i) the median,
…… [2]
(ii) the mode,
…… [1]
(iii) the range.
…… [1]
(b) Jack records the number of letters in 25 words.
Number of Number of letters in a word words
1 3
2 1
3 5
4 8
5 6
6 2
(i) Calculate the mean.
…… [3]
(ii) Priti picks one of Jack’s words at random.
Find the probability that this word has 4 or more letters.
…… [2]
(c) The table shows information about the first 90 words in a book.
(i) Complete the table.
Length of word Frequency Pie chart angle
Very short 6 24°
Short 34
Medium 41
Long 9
[2]
(ii) Complete the pie chart to show this information.
Very short
[2]
Mark scheme
2(a)(i) 3.5 2 B1 for 1, 1, 2, 2, 3, 3, 4
or 3, 4, 4, 4, 5, 5, 7
or 3 and 4 identified
2(a)(ii) 4 1
2(a)(iii) 6 1
2(b)(i) 3.76 3 M2 for (1 × 3 + 2 × 1 + 3 × 5 + 4 × 8 +
5 × 6 + 6 × 2) ÷ 25
or M1 for 1 × 3 + 2 × 1 + 3 × 5 + 4 × 8 +
5 × 6 + 6 × 2 or 94
2(b)(ii) 16 2 B1 for 16
oe
25
2(c)(i) 136 2 B1 for one correct
164
36
2(c)(ii) Correct pie chart 2 FT for 1 or 2 marks provided their 3
angles add to 336°
B1 for one correct sector
y
6
5
C 4
3
2
A
1
–6 –5 –4 –3 –2 –1 0 x
1 2 3 4 5 6
–1
–2
–3
B
–4
–5
–6
(a) Describe fully the single transformation that maps triangle A onto triangle B.
…… [2]
(b) Describe fully the single transformation that maps triangle A onto triangle C.
…… [3]
-2
(c) On the grid, draw the image of triangle A after a translation by the vector e o . [2]
-3
(d) On the grid, draw the image of triangle A after a rotation of 180° about (2, 1). [2]
Mark scheme
3(a) Reflection 2 B1 for each
y = −1
3(b) Rotation 3 B1 for each
[centre] (0, 0) oe
90° [anticlockwise] oe
3(c) Correct triangle vertices (0, −2), (3, −2) 2 −2 k
and (3, 0) B1 for translation of or
k −3
3(d) Correct triangle vertices (2, 1), (−1, 1) 2 B1 for a correct 180° rotation with
and (−1, −1) incorrect centre
(a) A plane leaves Karachi at 15 30 to fly to Bangkok.
The distance is 3840 km.
The plane flies at an average speed of 720 km/h.
The local time in Bangkok is 2 hours ahead of the local time in Karachi.
Find the local time in Bangkok when the plane arrives.
…… [4]
(b) In Bangkok a watch costs 2610 baht.
The exchange rate is $1 = 34.8 baht.
Find the cost of the watch in dollars.
$ …… [2]
(c) The price of another watch increases from $18 to $19.17 .
Find the percentage increase in the price of this watch.
…… % [3]
(d) Raoul makes a profit when he sells his watch for $36.
The ratio of the price Raoul paid for the watch and the profit he makes is price paid : profit = 7 : 2.
Work out the profit that Raoul makes.
$ …… [2]
Mark scheme
4(a) 22 50 4 M1 for 3840 ÷ 720
A1 for 5[h] 20[m]
M1dep for 15 30 + their 5[h] 20[m] [+2]
or 17 30 + their 5[h] 20[m]
4(b) 75 2 M1 for 2610 ÷ 34.8
4(c) 6.5 3 19.17 − 18
M2 for [× 100] oe
18
19.17
or − 1 [× 100] oe
18
19.17
or × 100 [– 100] oe
18
19.17
or M1 for or 19.17 – 18
18
4(d) 8 2 36
M1 for
2+7
(a) Simplify.
9x - 2y - 5x - y
…… [2]
(b) P = 4ab + 3b 2
Work out the value of a when P = 35 and b = 5.
a = …… [3]
(c) Solve.
(i) 10x = 5
x = …… [1]
(ii) 7x - 3 = 2x + 11
x = …… [2]
(iii) 3 (2x - 1) = 27
x = …… [3]
(d) Rearrange T = 5 (p + 2) to make p the subject.
p = …… [2]
(e) Solve the simultaneous equations.
You must show all your working.
3x - y = 22 x + 2y = 5
x = ……
y = …… [3]
Mark scheme
5(a) 4x – 3y final answer 2 B1 for 4x or – 3y
or 4x – 3y not as final answer
5(b) −2 3 M1 for 35 = 4 × a × 5 + 3 × 52 or better
M1 for 35 – their 3 × 52 = their 4 × 5 × a
or better
or
M1 for P − 3b 2 = 4ab or better
M1 for 35 – 3 × 52 = 4 × 5 × a or better
5(c)(i) 1 1
[0].5 or
2
5(c)(ii) 2.8 oe 2 M1 for 7x − 2x = 11 + 3 or better
5(c)(iii) 5 3 M1 for correct first step
i.e. 6x – 3 [= 27] or 2x – 1 = 9
M1 for correct second step leading to
ax = b
5(d) T T − 10 2 T
[p =] − 2 or final answer M1 for = p + 2 oe or T = 5p + 10
5 5 5
5(e) Correct method to eliminate one variable M1
[x =] 7 A1
[y =] −1 A1 If 0 scored, SC1 for two values that
satisfy one of the original equations or
SC1 if no working shown, but 2 correct
answers given
(a) The scale drawing shows the positions of town A and town B.
The scale is 1 centimetre represents 12 kilometres.
North
A North
B
Scale : 1 cm to 12 km
(i) Measure the bearing of town B from town A.
…… [1]
(ii) Find the actual distance from town A to town B.
…… km [2]
(iii) Town C is on a bearing of 064° from town A and 028° from town B.
On the scale drawing, mark the position of town C. [2]
(b) The bearing of town D from town E is 245°.
Work out the bearing of town E from town D.
…… [2]
(c) The diagram shows three towns, P, Q and R.
North
Q
P
NOT TO
SCALE
R
The bearing of town Q from town P is 090°.
(i) Complete the statement.
Town …… is due west of town …… . [1]
(ii) PQ and QR are two sides of a regular decagon.
Work out angle PQR.
Angle PQR = …… [3]
Mark scheme
6(a)(i) 115 1
6(a)(ii) 63.6 2 B1 for 5.3 [cm]
6(a)(iii) Correct position of town C 2 B1 for indication on diagram of
either a bearing of 064° from A
or a bearing of 028° from B
6(b) [0]65 2 M1 for 245 – 180 oe
or for a complete diagram with North
lines at D and E and 245° marked
correctly at E and 65° marked correctly at
D
6(c)(i) P Q 1
6(c)(ii) 144 3 M2 for 180 – (360 ÷ 10) oe
180 × (10 − 2 )
or
10
M1 for 360 ÷ 10
or 180 × (10 – 2) oe
(a) The diagram shows a shape made from two rectangles.
32 cm
9 cm
24 cm
NOT TO
SCALE
18 cm
(i) Work out the perimeter.
…… cm [2]
(ii) Work out the area.
…… cm2 [2]
(b) The diagram shows a triangle between two parallel lines, AB and CD.
A B
128° v° y°
NOT TO
SCALE
w° 63°
C D
Find the value of
(i) v,
v = …… [1]
(ii) w,
w = …… [1]
(iii) y.
y = …… [1]
(c) These two cuboids have the same volume.
NOT TO
SCALE
h cm
18.6 cm
8.2 cm
30.6 cm
10.2 cm
16.4 cm
Find the value of h.
h = …… [3]
(d) The diagram shows two similar triangles, ABC and DEF.
NOT TO
SCALE
E
B
6 cm 48 cm
C
F
A 8.5 cm
D
Calculate DF.
DF = …… cm [2]
Mark scheme
7(a)(i) 112 2 B1 for 14 or 15
or M1 for
9 + 32 + 24 + 18 + their 14 + their 15
or 2(24 + 32)
7(a)(ii) 558 2 M1 for 24 × 18 + 9 × their 14 oe
or 32 × 9 + 18 × their 15 oe
or 32 × 24 − their 14 × their 15 oe
7(b)(i) 52 1
7(b)(ii) 52 1 FT their (b)(i)
7(b)(iii) 65 1 FT 180 – 63 − their (b)(i)
or 180 – 63 − their (b)(ii)
7(c) 12.4 3 M2 for (18.6 × 16.4 × 10.2) ÷ (30.6 × 8.2)
oe
or M1 for 18.6 × 16.4 × 10.2 or 3111.408
or 30.6 × 8.2 × h or 250.92h
7(d) 68 nfww 2 48 6 8.5 6
M1 for or or or oe
6 48 6 8.5
(a) (i) Complete the table of values for y = x 2 - 2x .
x –2 –1 0 1 2 3 4 y 8 0 –1 0 8
[1]
(ii) On the grid, draw the graph of y = x 2 - 2x for - 2 G x G 4 .
y
9
8
7
6
5
4
3
2
1
0 x
–2 –1 1 2 3 4
–1
–2
[4]
(b) Here are the first four terms of a sequence.
3 9 15 21
(i) Find the next term.
…… [1]
(ii) Write down the rule for continuing this sequence.
…… [1]
(iii) Find the nth term of this sequence.
…… [2]
Question 9 is printed on the next page.
Mark scheme
8(a)(i) 3 3 1
8(a)(ii) Correct curve 4 B3FT for 6 or 7 points correctly plotted
or B2FT for 4 or 5 points correctly plotted
or B1FT for 2 or 3 points correctly plotted
8(b)(i) 27 1
8(b)(ii) Add 6 oe 1
8(b)(iii) 6n – 3 oe final answer 2 B1 for 6n + a or bn – 3 (b ≠ 0)
(a) By rounding each number correct to 1 significant figure, show that an estimate for this calculation is 20.
9.78 + 31.562
0.381 # 5.09
[2]
(b) Write these numbers in order, smallest first.
22 333
3.142 3.1416
7 106
…… 1 …… 1 …… 1 …… [2]
smallest
(c) The length, p cm, of a pencil is 9.8 cm, correct to 2 significant figures.
Complete the statement about the value of p.
…… G p 1 …… [2]
52163
(d) Calculate 3.142 - .
16 604
Give your answer in standard form correct to 2 significant figures.
…… [2]
Mark scheme
9(a) 10 + 30 M1
[0].4 × 5
40 A1
[= 20]
2
9(b) 333 22 2 B1 for 3.1428[…] or 3.143 and
3.1416 3.142 3.1415[…]
106 7
or for 3 in the correct order
9(c) 9.75 9.85 2 B1 for one correct or both correct and
reversed
9(d) 4.1 × 10–4 cao 2 B1 for 4.07[6…] × 10-4 or 4.08× 10-4
or figs 41
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Mathematics 0580/33 for October/November 2019 is out of 104 marks, with 2 hours to answer it.
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