Western Province Grade 11 Maths Term 3 Test 2021

Cash discount versus instalment plan; interest per instalment

Answer: (i) Rs 28 500 (ii) Rs 2640 (iii) Rs 264

💡 What it's asking: Compare paying cash (with a discount) and paying by instalments. The extra paid on instalments is the interest.

1. 1(i) 5% discount on Rs. 30 000 = 1500, so cash price = Rs. 28 500.
2. 2(ii) Instalment total = 6000 + 10 × 2664 = 6000 + 26 640 = Rs. 32 640.
3. 3(ii) Extra over the marked price = 32 640 − 30 000 = Rs. 2640.
4. 4(iii) The loan is 30 000 − 6000 = 24 000, repaid in 10 instalments, and the extra 2640 is the interest.
5. 5(iii) Following the marking scheme, interest per instalment = 2640 ÷ 10 = Rs. 264.

✅ Each instalment 2664 = 2400 (loan ÷ 10) + 264 (interest). It adds up.

Graph of y = x(x - 2) - 3; turning point, roots, behaviour

Answer: (i) -3 (iii) (1, -4) (iv) x = -1, 3

💡 What it's asking: Draw the curve y = x(x − 2) − 3 from a table, then read its lowest point, where it crosses the x-axis, and how y changes.

1. 1(i) x = 2: y = 2(2 − 2) − 3 = 0 − 3 = −3.
2. 2(ii) Plot (−2, 5), (−1, 0), (0, −3), (1, −4), (2, −3), (3, 0), (4, 5) and join with a smooth U-shaped curve.
3. 3(iii) The lowest point (turning point) is (1, −4).
4. 4(iv) x² − 2x − 3 = 0 is the same as y = 0, so read where the curve crosses the x-axis: x = −1 and x = 3.
5. 5(v) From x = −1 to x = 1, y goes down from 0 to −4 (its minimum).

✅ Substitute x = 3: 9 − 6 − 3 = 0 ✓; x = −1: 1 + 2 − 3 = 0 ✓.