0580.E2.6.03 — 3x < 2x + 4.: past paper questions

Real questions on 0580.e2.6.03 — 3x < 2x + 4.

The newest 15 of 15 written questions. Open one to see it on the real paper.

1. 0980/41 · October/November 2024 · Q7a[2]
   A company makes scientific calculators and graphic calculators. Each day they make $x$ scientific calculators and $y$ graphic calculators. These inequalities describe the number of scientific and graphic calculators they make each day. $x<180$ $y\le 90$ $x+y\le 240$ (a) Complete these two statements. The...See it on the paper →
2. 0980/41 · October/November 2024 · Q7b[1]
   7 A company makes scientific calculators and graphic calculators. Each day they make $x$ scientific calculators and $y$ graphic calculators. These inequalities describe the number of scientific and graphic calculators they make each day. $x<180$ $y⩽90$ $x+y⩽240$ (b) Scientific calculators cost...See it on the paper →
3. 0980/41 · October/November 2024 · Q7c[13]

   13-mark question — its maths and diagrams are best seen on the paper.

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4. 0980/41 · October/November 2024 · Q7d[2]
   A company makes scientific calculators and graphic calculators. Each day they make $x$ scientific calculators and $y$ graphic calculators. These inequalities describe the number of scientific and graphic calculators they make each day. $x<180$ $y\le 90$ $x+y\le 240$ (d) Scientific calculators are sold for...See it on the paper →
5. 0980/42 · May/June 2024 · Q8a[3]
   A baker decorates $x$ small cakes and $y$ large cakes. In one day, he decorates: • not more than 16 small cakes • less than 10 large cakes • more small cakes than large cakes • a total of not more than 24 cakes. One of the inequalities that shows this information is $x\le 16$. (a) Write down the other three inequaliti...See it on the paper →
6. 0980/42 · May/June 2024 · Q8b[6]

   6-mark “Label” question — its maths and diagrams are best seen on the paper.

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7. 0980/42 · May/June 2024 · Q8c[2]
   A baker decorates $x$ small cakes and $y$ large cakes. In one day, he decorates: • not more than 16 small cakes • less than 10 large cakes • more small cakes than large cakes • a total of not more than 24 cakes. One of the inequalities that shows this information is $x⩽16$. (c) The baker earns $8 for decorati...See it on the paper →
8. 0980/21 · October/November 2023 · Q11[3]
   11 Solve. $4(2x-3)⩾43+3x$See it on the paper →
9. 0980/22 · May/June 2023 · Q8b[3]
   8 Solve. (b) $11x-3\ge 2(2x+9)$See it on the paper →
10. 0980/22 · May/June 2023 · Q9a[1]
    9 $F$ is the point $(1,-4)$, $\overrightarrow{FG}=\left(\begin{array}{c}8\\ -3\end{array}\right)$ and $\overrightarrow{GH}=\left(\begin{array}{c}-12\\ 35\end{array}\right)$. Find (a) $3\overrightarrow{FG}$See it on the paper →
11. 0980/41 · October/November 2022 · Q3b(i)[3]
    (b) $-3⩽2x+3<9$ (i) Solve the inequality.See it on the paper →
12. 0980/41 · October/November 2022 · Q3b(ii)[2]
    (b) $-3\le 2x+3<9$ (ii) Write down all the integer values of $x$ that satisfy the inequality.See it on the paper →
13. 0980/42 · May/June 2022 · Q10a[2]
    (a) Find all the positive integers which satisfy the inequality. $3n-8>5n-15$See it on the paper →
14. 0980/42 · May/June 2022 · Q10b(i)[3]
    (b) [Diagram: A coordinate grid with x-axis from -3 to 11 and y-axis from -3 to 9. A shaded region R is bounded by three lines: a vertical dashed line at $x=4$, a solid line with equation $10y+8x=80$, and a dashed line with equation $2y=x-4$. The region R is to the right of $x=4$, below the line $10y+8x=80$...See it on the paper →
15. 0980/42 · May/June 2022 · Q10b(ii)[2]
    (b) [Diagram: A coordinate grid with x-axis from 0 to 11 and y-axis from -3 to 9. A shaded region R is bounded by three lines: a vertical dashed line at $x=4$, a solid line with equation $10y+8x=80$, and a dashed line with equation $2y=x-4$. The region R is the white triangular area in the lower-left of the sha...See it on the paper →

What examiners said

This was very well attempted. The most common error was to give the wrong inequality sign, or to just give 11 as the answer, even when the fully correct answer had been seen in the working. Some candidates had difficulty when their ‘x’ term was negative and there was a need to reverse the inequality sign. Those who did not get the correct value for x, usually correctly expanded the brackets follow...

— Examiner report, October/November 2023, 0980/21 Q11 (Cambridge)

Candidates who worked simultaneously with both sides of the inequality in the format given usually reached a correct solution, although on the left-hand side the subtraction of 3 from –3 was occasionally thought to be 0. Candidates who worked with the inequality in the given format but dealt with only one side at a time were almost always unsuccessful. For example, a common first step was −3 2 x <...

— Examiner report, October/November 2022, 0980/41 Q3(b)(i) (Cambridge)

Candidates with a correct inequality in part (b)(i) often correctly listed the required integer values. The common error seen was to misinterpret the nature of the inclusivity of the inequality for example by omitting the 3 or including the –3. In addition, 0 was sometimes omitted from the otherwise correct list of integers.

— Examiner report, October/November 2022, 0980/41 Q3(b)(ii) (Cambridge)