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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: second paper Answers

Section A: short questions

1. (a) $3x + 2y - 4z = -4$, $x - y + 2z = -3$, $2x - 3y + z = -12$
2. (b) $x = −2,\ y = 3,\ z = 1$
1. (a) $3x^2 - 9x + 4 = 0$
2. (b) $x = 0.543$ or $x = 2.46$
3. (c) $x = −1.48$
1. (a) $x = 0.75$ (a repeated root)
2. (b) The solver gives $x = −3 \pm 2i$. Both solutions contain $i$, so there are no real solutions
3. (c) $x = −2.43, −0.649, 0.855, 2.22$
1. (a) $x = −4.85, 0, 1.85$
2. (b) $x = −4.51, −0.917, 2.42$
3. (c) $c = −5$ or $c = 27$
1. (a) $k = 12$
2. (b) The lines are parallel (both have gradient $−\frac{5}{2}$) and different, so they never meet
1. (a) $x + y + z = 30$, $y = 9$, $z - x = 11$
2. (b) $x = 5,\ y = 9,\ z = 16$
1. (a) $9a + 3b = 9$, $6a + b = 9$
2. (b) $a = 2,\ b = −3$
3. (c) PQ = 7.83

Section B: long questions

1. (a) $a + b + c = 300$
2. (b) $0.04a + 0.06b + 0.1c = 18.8$
3. (c) $a - b = 20$
4. (d) 80 kg
5. (e) 42.6%
1. (a) $200p + 150q + 100t = 14500$, $80p + 90q + 60t = 7100$, $4.5p + 5q + 3.5t = 400$
2. (b) 30
3. (c) $4.44
1. (a) $V = 4x^3 - 200x^2 + 2400x$
2. (b) The width is $40 - 2x$. It must be positive, so $x < 20$
3. (c) $x = 4.37$ or $x = 11.9$
4. (d) Length 51.3 cm, width 31.3 cm
1. (a) $u_1 = 4,\ d = 5$
2. (b) $n = 16$
3. (c) $r = 2$ or $r = −3$
4. (d) $r = 2$
1. (a) 29.3 and 171 tickets
2. (b) 30 tickets and 170 tickets
3. (c) greatest profit $2000, from 100 tickets
4. (d) 65 to 135 tickets
1. (a) 1.5 m
2. (b) 8.85 m after 1.22 s
3. (c) 2.57 s
4. (d) 1.77 s

jmaths.xyz · AI HL · 12.4.8 Unit review