Before the midterm

A sign slip

The habit: Carry the sign through every line and check it against the sign the answer must have.

83 practice questions are built to catch it, in 17 topics.

What it looks like

A question from the definition of the derivative, with the answer this slip gives beside the right one.

Introductory2 marks · 3 min

A company’s weekly cost $C(x)$ of making $x$ bicycle helmets is a linear function of $x$ . A week in which it makes 200 helmets costs $5400, and a week in which it makes 350 helmets costs $7650. Find the company’s fixed cost: the weekly cost when no helmets are made.

Give the answer in dollars.

With the slip: $\displaystyle 8400$
Worked through: $\displaystyle C(x) = 15x + 2400;\quad \text{fixed cost } \$2400$

From 200 helmets down to 0 the cost falls: the 200 × $15 is taken off $5400, not added.

See the worked solution

Where it comes up

Power functions and first sketches4 questions
Functions, graphs and inverses5 questions
Limits4 questions
Continuity4 questions
The definition of the derivative10 questions
Differentiation rules6 questions
Exponential and trigonometric functions2 questions
The chain rule and logarithms5 questions
Implicit differentiation and inverse trigonometric functions8 questions
Curve sketching8 questions
Linear approximation4 questions
Taylor polynomials7 questions
Newton’s method1 question
Slope fields and Euler’s method7 questions
Logistic growth and phase lines1 question
Functions of two variables and partial derivatives6 questions
Optimization in two variables and Lagrange multipliers1 question

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
Let $f(x) = 3x^{2} - x^{5}$ . For very large positive $x$ , which term dominates, and what is the sign of $f(x)$ ?
Power functions and first sketchesIntroductory
02
The graph of $y = ax^{2} + bx^{4}$ is shown, where $a$ and $b$ are nonzero constants. What are the signs of $a$ and $b$ ?
Power functions and first sketchesIntroductory
03
Solve the equation below for $x$ . $\displaystyle \log(x + 1) - \log x = 1$
Functions, graphs and inversesIntroductory
04
For $x > 0$ , the expression below equals a single power $x^{k}$ . Find $k$ . $\displaystyle \frac{\left(x^{4}\right)^{3}}{x^{5}\sqrt{x}}$
Functions, graphs and inversesIntroductory
05
Which description fits the graph of $y = e^{x} - x^{3}$ ?
Power functions and first sketchesStandard
06
Let $y = kx^{2} + x^{3}$ , where $k$ is a nonzero constant. Which statement about the graph is correct for both signs of $k$ ?
Power functions and first sketchesCapstone

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