4024/21 May/Jun 2024, Question 8: Exponential Functions

Part (ai) · 1 mark

Complete the table of y values for y = 2ˣ/5 at x = 0 to 5, finding the missing value at x = 5.

1. 1x = 5: y = 2⁵/5 = 32/5 = 6.4

Answer6.4

Part (aii) · 3 marks

Draw the graph of y = 2ˣ/5 on the grid for x from 0 to 5.

1. 1Plot (0, 0.2), (1, 0.4), (2, 0.8), (3, 1.6), (4, 3.2), (5, 6.4)
2. 2Join with a smooth increasing curve, getting steeper to the right

AnswerCorrect smooth curve

Part (aiiia) · 2 marks

1. 12ˣ⁺³ = 2ˣ × 2³ = 8 × 2ˣ
2. 28 × 2ˣ = 100, so 2ˣ = 100/8 = 12.5
3. 32ˣ/5 = 12.5/5 = 5/2

Answer2ˣ/5 = 5/2 shown

Part (aiiib) · 2 marks

Sketch y = 2ˣ/5, then draw a suitable line on the grid to solve 2ˣ⁺³ = 100.

1. 1From (iii)(a), solve 2ˣ/5 = 2.5
2. 2Draw the horizontal line y = 2.5
3. 3It meets the curve at x ≈ 3.6

Answer3.5 to 3.8

Part (b) · 3 marks

From the sketch of y = a + bx − x² crossing the x-axis at integer values, find a and b.

1. 1y-intercept is 7, so a = 7
2. 2Roots are integers with product −7 (one negative, one positive further right): x = −1 and x = 7
3. 3y = −(x + 1)(x − 7) = −(x² − 6x − 7) = 7 + 6x − x²
4. 4b = 6

Answera = 7, b = 6

More past-paper questions on exponential functions

• 4024/12 May/Jun 2026 Q22 · 4 marks
• 4024/22 Oct/Nov 2025 Q17 · 4 marks
• 4024/22 May/Jun 2023 Q4 · 12 marks
• 4024/22 Oct/Nov 2023 Q6 · 10 marks
• 4024/21 Oct/Nov 2021 Q7 · 11 marks
• 4024/22 May/Jun 2020 Q7 · 14 marks