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IB Mathematics: Applications and Interpretation HL · 12.4: Solving Equations with Technology · 12.4.8

Solving Equations with Technology: exam review Exam review Answers

Section A: short questions

1. (a) $2x + y - 3z = 11$, $x - 2y + z = -2$, $4x - y + 2z = 8$
2. (b) $x = 3,\ y = 2,\ z = −1$
1. (a) $2x^2 - 9x + 5 = 0$
2. (b) $x = 0.649$ or $x = 3.85$
3. (c) $x = −1.40$
1. (a) $x = 0.667$ (a repeated root)
2. (b) The solver gives $x = 2 \pm 2.24i$. Both solutions contain $i$, so there are no real solutions
3. (c) $x = −2.25, −0.555, 0.802, 2$
1. (a) $x = −1.85, 0, 4.85$
2. (b) $x = −2.42, 0.917, 4.51$
3. (c) $c = −27$ or $c = 5$
1. (a) $k = 10$
2. (b) The lines are parallel (both have gradient $\frac{3}{2}$) and different, so they never meet
1. (a) $x + y + z = 24$, $y = 7$, $z - x = 9$
2. (b) $x = 4,\ y = 7,\ z = 13$
1. (a) $4a + 2b = 6$, $4a + b = 7$
2. (b) $a = 2,\ b = −1$
3. (c) PQ = 7.75

Section B: long questions

1. (a) $p + q + r = 24000$
2. (b) $0.02p + 0.035q + 0.05r = 870$
3. (c) $-p + q = 4000$
4. (d) $8 000
5. (e) 46.0%
1. (a) $300c + 120s + 60b = 10800$, $10c + 6s + 8b = 590$, $15c + 6s + 9b = 720$
2. (b) 30
3. (c) $9.60
1. (a) $V = 4x^3 - 112x^2 + 720x$
2. (b) The width is $20 - 2x$. It must be positive, so $x < 10$
3. (c) $x = 1.93$ or $x = 6.70$
4. (d) Length 32.1 cm, width 16.1 cm
1. (a) $u_1 = 7,\ d = 4$
2. (b) $n = 20$
3. (c) $r = 1.5$ or $r = −2.5$
4. (d) $r = 1.5$
1. (a) 27.7 and 108 tickets
2. (b) 28 tickets and 108 tickets
3. (c) greatest profit $812, from 68 tickets
4. (d) 48 to 88 tickets
1. (a) 2 m
2. (b) 12 m after 1.43 s
3. (c) 2.99 s
4. (d) 2.21 s

jmaths.xyz · AI HL · 12.4.8 Unit review