Indices: Eduqas GCSE Higher June 2025 Paper 1 Q3

Higher June 2025 Paper 1 Q3

EduqasHigherCurrent spec4 marksIndices Linear Inequalities Ratio & Basic Proportion

(a) Given that \(3^{m+4} = 1\), find the value of \(m\). [1]

(b) Betty bought \(c\) cakes costing £2 each and \(d\) doughnuts costing £1.50 each.
She paid with a twenty pound note and was given some change.

Write an inequality to show this information. [2]

distance \(x\) = 15 miles
distance \(y\) = 36 kilometres
5 miles is approximately equal to 8 kilometres.

Circle the ratio that best represents
distance \(x\) : distance \(y\). [1]

3:5 5:12 3:4 2:3 2:5

Scheme	Marks	Comments
\(-4\)	B1

Mark scheme (b)

Scheme	Marks	Comments
\(2c + 1.5d \lt 20\) or \(2c + 1.5d \leqslant 19.50\) or \(20 - 2c - 1.5d \gt 0\) or \(200c + 150d \lt 2000\) oe or \(3.5 \leqslant 2c + 1.5d \lt 20\) or \(0 \lt 2c + 1.5d \lt 20\)	B2	Mark final answer B1 for one of the following: \(2c + kd \lt 20\) (\(k\ne1.5\) and \(k\ne 0\)) \(20 - 2c - kd \gt 0\) (\(k\ne1.5\) and \(k\ne 0\)) \(kc + 1.5d \lt 20\) (\(k\ne2\) and \(k\ne 0\)) \(20 - kc - 1.5d \gt 0\) (\(k\ne2\) and \(k\ne 0\)) \(2c + 1.5d\) ‘\(\gt\) or \(\geqslant\) or \(\leqslant\)’ 20 (not = 20) \(2c + 1.5d \leqslant 19(.99)\) \(c\) and \(d\) reversed \(2d + 1.5c \lt 20\) other letters rather than \(c\) and \(d\) in a correct inequality e.g. \(2x + 1.5y \lt 20\) inclusion of ‘x’ signs e.g. cx2 + dx1.50 < 20 c2 + d1.5 < 20 Penalise -1 if mixed units are used e.g. \(200c + 150d \lt 20\) B2-1 (1 mark) \(200c + 1.5d \lt 2000\) B2-1 (1 mark) \(2c + 150d \gt 20\) B1-1 (0 marks) Possible B1 if using double inequality but with similar errors in notation as mentioned from B1s above (e.g. 3.5 ≤ c2 + d1.5 < 20)

Scheme

Marks

Comments

\(2c + 1.5d \lt 20\)
or \(2c + 1.5d \leqslant 19.50\)
or \(20 - 2c - 1.5d \gt 0\)
or \(200c + 150d \lt 2000\) oe
or \(3.5 \leqslant 2c + 1.5d \lt 20\)
or \(0 \lt 2c + 1.5d \lt 20\)

Mark final answer

B1 for one of the following:

\(2c + kd \lt 20\) (\(k\ne1.5\) and \(k\ne 0\))
\(20 - 2c - kd \gt 0\) (\(k\ne1.5\) and \(k\ne 0\))
\(kc + 1.5d \lt 20\) (\(k\ne2\) and \(k\ne 0\))
\(20 - kc - 1.5d \gt 0\) (\(k\ne2\) and \(k\ne 0\))
\(2c + 1.5d\) ‘\(\gt\) or \(\geqslant\) or \(\leqslant\)’ 20 (not = 20)
\(2c + 1.5d \leqslant 19(.99)\)
\(c\) and \(d\) reversed \(2d + 1.5c \lt 20\)
other letters rather than \(c\) and \(d\) in a correct inequality e.g. \(2x + 1.5y \lt 20\)
inclusion of ‘x’ signs e.g. cx2 + dx1.50 < 20
c2 + d1.5 < 20

Penalise -1 if mixed units are used e.g.

\(200c + 150d \lt 20\) B2-1 (1 mark)
\(200c + 1.5d \lt 2000\) B2-1 (1 mark)
\(2c + 150d \gt 20\) B1-1 (0 marks)

Possible B1 if using double inequality but with similar errors in notation as mentioned from B1s above (e.g. 3.5 ≤ c2 + d1.5 < 20)

Corrected by Westie's Workshop

The board's mark scheme printed “2c + 150d > 20 B1-1 B1-1 (0 marks)”. Changed to “B1-1 (0 marks)” because the mark code was printed twice by mistake; it only applies once.

Original: see the board's mark scheme PDF (link above).