Exercises for Question Type 5: Finding values through substitution of values

Question 1

Skill question

For $y = a sin (4 x) + 1$ , if $y = 5$ when $x = \frac{π}{2}$ , determine $a$ .

Question 2

Skill question

In the exponential model $y = A e^{k x}$ , suppose $y (0) = 5$ and $y (2) = 20$ . Find $A$ and $k$ .

[5]

Question 3

Skill question

In the sinusoidal model $p (t) = P cos (ω t) + 3$ , given $p (0) = 8$ and $p (\frac{π}{2}) = 3$ , find the value of $P$ and of $ω$ .

[5]

Question 4

Skill question

Given $y = 2 x^{2} + b x + 3$ passes through $(2, 15)$ , find $b$ .

[3]

Question 5

Skill question

For the model $y = a cos (3 x) + 9$ , when $x = 0$ and $y = 11$ , find the value of $a$ .

[3]

Question 6

Skill question

Find $a, b, c$ if the quadratic $y = a x^{2} + b x + c$ passes through $(1, 4)$ , $(2, 9)$ and $(3, 16)$ .

[6]

Question 7

Skill question

Finding parameters of a trigonometric function given specific points on the curve.

For $p (x) = A sin (B x) + 2$ , given $p (\frac{π}{2}) = 5$ and $p (π) = 2$ , determine $A$ and $B$ .

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Question 8

Skill question

The line with equation $y = m x + 5$ passes through the point $(2, 11)$ . Find the value of $m$ .

[2]

Question 9

Skill question

The model $y = 3 a sin (3 x) + d$ passes through $(0, 7)$ and $(\frac{π}{6}, 3)$ . Determine $a$ and $d$ .

[5]

Question 10

Skill question

The question requires determining the value of a parameter $a$ in a trigonometric function $y = a sin (2 x) + k$ given a specific point on the curve.

Given the curve $y = a sin (2 x) - 5$ , and the point $(x, y) = (\frac{π}{4}, 3)$ lies on the curve, find the value of $a$ .

[3]

Question 11

Skill question

Find the values of $m$ and $c$ for the line $y = m x + c$ passing through the points $(1, 3)$ and $(4, 9)$ .

[3]

Question 12

Skill question

For $y = 10 e^{k x}$ , if $y = 20$ when $x = 1$ , determine $k$ .

[3]

IB Mathematics Applications & Interpretation Question Type 5: Finding Values Through Substitution of Values Exercises