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Learn/ O Level Mathematics/ Past Papers/ 2021/ Oct/Nov 2021 /Paper 1 (Variant 1)

Paper 1 — Variant 1

O Level Mathematics · 4024/11 · Oct/Nov 2021

Question Paper

PDF · 1.2 MB · 20 pages

Mark Scheme

PDF · 307 KB · 7 pages

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Questions

17 of 24 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1
1(a) [1]
Work out 78−14\frac{7}{8} - \frac{1}{4}.
1(b) [1]
Work out 0.08×0.20.08 \times 0.2.
2 [2]
Write these numbers in order of size, starting with the smallest. 34\frac{3}{4}, 0.830.83, 1720\frac{17}{20}, 82%82\%, 0.80.8
3 [2]
Work out 45%45\% of 3030.
4
4(a) [1]
Shade one more small square so the diagram has rotational symmetry of order 44.
4(b) [1]
Shade two more small squares so the diagram has 22 lines of symmetry.
5 [1]
Simplify 3a−a+2a3a - a + 2a.
7
7(a) [1]
Evaluate 404^{0}.
7(b) [1]
Simplify m3×m5m^{3} \times m^{5}.
8
8(a) [1]
Write 63006300 m in kilometres.
8(b) [1]
Convert 11 cm2\text{cm}^{2} to mm2\text{mm}^{2}.
9 [2]
The interior angle of a regular polygon is 156∘156^\circ. Find the number of sides of this regular polygon.
10 [3]
A triangle has one angle of 55∘55^\circ. The other two angles in the triangle are in the ratio 3:23 : 2. Calculate the size of the smallest angle in the triangle.
11 [2]
By writing each number correct to 1 significant figure, estimate the value of 58.2432.5×0.126\frac{58.24}{32.5 \times 0.126}.
12 [3]
Solve the simultaneous equations. Show all your working. 2x−y=122x - y = 12 7x+3y=297x + 3y = 29
14
14(a) [2]
Express 6060 as the product of its prime factors.
14(b) [3]
A school buys packs of pens and packs of rulers. There are 6060 pens in each pack of pens. There are 4242 rulers in each pack of rulers. The school wants to buy exactly the same number of pens and rulers. Work out the smallest number of each pack the school should buy.
15
The point AA has position vector (3−7)\begin{pmatrix} 3 \\ -7 \end{pmatrix} and AB→=(−512)\overrightarrow{AB} = \begin{pmatrix} -5 \\ 12 \end{pmatrix}.
15(a) [2]
Find the coordinates of point BB.
15(b) [2]
Find ∣AB→∣|\overrightarrow{AB}|.
17
17(a) [1]
Factorise. 4b2−c24b^{2} - c^{2}
17(b) [2]
Factorise. x2+5x−6x^{2} + 5x - 6
20
These are the first five terms of a sequence. 4, 8, 16, 32, 644, \ 8, \ 16, \ 32, \ 64
20(a) [1]
Find the next number in the sequence.
20(b)
The nnth term of the sequence above is 2n+12^{n+1}. Write down an expression, in terms of nn, for the nnth term of these sequences.
20(b)(i) [1]
1, 5, 13, 29, 61, …1, \ 5, \ 13, \ 29, \ 61, \ \ldots
20(b)(ii) [2]
10, 19, 32, 53, 90, …10, \ 19, \ 32, \ 53, \ 90, \ \ldots
21
f(x)=62−x\mathrm{f}(x) = \frac{6}{2 - x}
21(a) [1]
Find f(−1)\mathrm{f}(-1).
21(b) [3]
Find f−1(x)\mathrm{f}^{-1}(x).
21(c) [3]
f(t)=f(5t+2)\mathrm{f}(t) = \mathrm{f}(5t + 2) Find the value of tt.
23
23(a) [2]
Expand and simplify. (x+5)(x−2)(x + 5)(x - 2)
23(b) [3]
Write as a single fraction in its simplest form. 3x−4+2x+5\frac{3}{x - 4} + \frac{2}{x + 5}

Published by Cambridge Assessment International Education. Reproduced for study use.