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IB Mathematics: Applications and Interpretation SL · 12.5: Functions · 12.5.6

Functions: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) (1.8, 6.05)
    2. (b) (6.05, 1.8)
    3. (c) 1.8
    4. (d) They are inverse functions: the graph of g is the reflection of the graph of f in y = x
    1. (a) x = 5 and y = 7
    2. (b) b = 2, c = 6
    3. (c) \(f(x)\ne 7\)
    1. (a) (0.9, 7.94)
    2. (b) B is (7.94, 0.9); mirror line y = x
    3. (c) 0.900
    1. (a) t = −5 and S = 720
    2. (b) The number of subscribers gets close to 720 but never reaches or passes it.
    3. (c) 480
    1. (a) C(30) = 16.70; n = 40
    2. (b) 0 ≤ n ≤ 80, n a whole number; 3.2 ≤ C ≤ 39.20
    3. (c) x ≥ −2; g(x) ≥ −1
    4. (d) −3 ≤ h(x) ≤ 6

Section B: long questions

    1. (a) As t increases, k^(−t) tends to 0, so D tends to a; a is the total distance
    2. (b) b = −25
    3. (c) k = 1.47
    4. (d) 5.35 km
    5. (e) 6.55 hours
    1. (a) As t increases, \(k^{-t}\) tends to 0, so D tends to a; a = 40
    2. (b) b = −40
    3. (c) k = 1.60
    4. (d) 9.77 km
    5. (e) 9 hours
    1. (a) y-intercept −48; zeros x = 2 and x = 12; vertex (7, 50); the greatest profit is 50 euros, made at a price of 7 euros
    2. (b) T = 20; the temperature falls towards but never goes below 20 °C (the temperature of the studio); 89.6 °C
    3. (c) a = 240; N = 48; as p tends to 0, N grows without limit, so the graph never meets the N-axis (a price of 0 gives no value of N)
    4. (d) C(0) = 15; n = −6 and C = 5
    5. (e) Exponential; each value is 3 times the one before

jmaths.xyz · AI SL · 12.5.6 Unit review