Maths Higher Paper2 2024 Mutiple choice Revision

GCSE Maths Higher, Paper 2 (June 2024, calculator)
Q1 Circle parts: region A is a segment (between a chord and an arc). Region B is a sector (between two radii and an arc).
Q2 Reverse percentage: a 12% reduction means a multiplier of 0.88. Original mass = 2.2 million ÷ 0.88 = 2.5 × 10⁶ kg.
Q3 Inverse proportion: in D = K/B, K is the total number of blueberries. From 120 = K/2, K = 240. So B = 6 gives D = 40, and D = 30 gives B = 8.
Q4 Probability: the spinner must be 5, 5, 6, 7, 7, 8, so P(5) = 1/3. The second spinner’s table must be wrong because its probabilities add to 1.1, not 1.
Q5 Graphs: y = −2x + 6 gives C(0, 6) and D(3, 0). A quadratic’s turning point is midway between its roots: (−2 + 8) ÷ 2 = 3.
Q6 Standard form on the calculator: (2.5 × 10⁴)⁻³ = 6.4 × 10⁻¹⁴.
Q7 Relative frequency: best estimate = 52/200 = 13/50, because the most trials give the most reliable estimate.
Q8 Speed: distance ÷ time = (120 − 30) ÷ 5 = 18 m/s.
Q9 Venn diagram: P ∩ Q is the overlap.
Q10 Repeated percentage change: 90 000 × 1.03 × 1.08 = 100 116, so yes, more than 100 000.
Q11 Map scale: 15 × 20 000 = 300 000 cm = 3 km.
Q12 Congruence: three pairs of equal sides, so SSS.
Q13 Estimated mean from grouped data: use the midpoints. Σfx = 300.8, and 300.8 ÷ 40 = 7.52 m.
Q14 Substitution: for y = x² + c, c = 6, so w = 55. If the graph is actually a straight line, w can’t be found from one point.
Q15 Units: 1800 s × 10.9 kg/s = 19.62 tonnes, so no, not more than 20 tonnes. Do the working before ticking the box.
Q16 Box plot: lower quartile = upper quartile − IQR = 7 − 3 = 4. Then plot min, LQ, median, UQ and max.
Q17 Angles on a straight line: (11/12)x − 29 = 180, so x = 228. The angles are 72° and 108°, a ratio of 2 : 3.
Q18 Trigonometry: x = 23.7 cos 52° ≈ 14.6 cm.
Q19 Algebra: the expression expands and simplifies to −42. 8x² − 18x − 35 = (4x + 5)(2x − 7), found by splitting the middle term.
Q20 Rearranging into a quadratic: x² − 2x − 13 = 0, so x = (2 ± √56)/2.
Q21 Fractions and ratio: the West stand is 7/20 of the stadium. 4480 ÷ 7 = 640 per twentieth, so the total is 12 800.
Q22 Iteration: start at x₁ = 1 and press = repeatedly until the value stops changing. x ≈ 4.791 to 4 s.f.
Q23 Vectors: DE = 8a − 4b = 4 × EF. They are parallel and share point E, so D, E and F are collinear.
Q24 Modelling the cooling curve: with y = 126/x, y = 10.5 °C at x = 12. With the exponential model y = 63(⅓)^(x/6), y = 7 °C, which is less.
Q25 Similar prisms: the volume scale factor is 1125 ÷ 72 = 15.625, so the length scale factor is 2.5. The total edge length is 150 cm.