Precalculus Graphs of Trigonometric Functions Test with Point Values (PDF)

Precalculus math test: Graphs of Trigonometric Functions – Maths PDF

Cover of the book Precalculus Math Tests with Answer Keys (PDF)

Download as a PDFThe Precalculus tests book with answer keysPrintable PDFSee the book ›

Sommaire

This precalculus trig graphs test for Precalculus covers graphs of trigonometric functions (Common Core F-TF.B.5, F-IF.C.7e, F-TF.B.7), with a free PDF to print.

This 20-point test covers amplitude, period, phase shift, graphs of sine, cosine and tangent, and periodic models (F-TF.B.5, F-IF.C.7e). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Graphs of Trigonometric Functions
Standards: F-TF.B.5, F-IF.C.7e, F-TF.B.7
Time: 45 minutes
Total: 20 points

Precalculus trig graphs test: questions

Question 1 – Read the equation [2 pts]

For \(y=-3\sin\frac{\pi x}{2}+4\), state the amplitude, period and midline.

Question 2 – Phase shift [2 pts]

Write \(y=\cos\left(2x-\frac{\pi}{2}\right)\) in the form \(\cos(b(x-h))\) and give the period and phase shift.

Question 3 – Evaluate [2 pts]

Find \(y=4\cos\frac{x}{2}\) for \(x=0\), \(\pi\) and \(2\pi\).

Question 4 – Tangent [2 pts]

Find the period of \(y=\tan3x\) and the smallest positive \(x\) at which it has a vertical asymptote.

Question 5 – Read a trig graph [3 pts]

A cosine-shaped graph.

The graph shows \(y=a\cos(bx)+k\). (a) State the amplitude and period. (b) State the midline and the range. (c) Write the equation.

Question 6 – Write an equation [2 pts]

Write a sine function with amplitude \(4\), period \(6\pi\) and no shifts.

Question 7 – Range [2 pts]

Find the range of \(y=-2\sin x+3\).

Question 8 – Tide model [3 pts]

Depth of water in feet.

The depth is \(d(t)=6+2\cos\left(\frac{\pi t}{6}\right)\) feet, \(t\) in hours. (a) Find \(d(3)\). (b) State the period. (c) Find the times in \([0,12]\) when the depth is \(7\) ft.

Question 9 – Ferris wheel [2 pts]

Height of a rider.

A rider’s height is \(h(t)=25-20\cos\left(\frac{\pi t}{20}\right)\) feet. Find the greatest height and \(h(10)\).

Key facts behind this precalculus trig graphs test

Key facts

Amplitude = |a| = (max – min)/2; midline y = k = (max + min)/2.
Period of sine and cosine = 2 pi / |b|; period of tangent = pi / |b|.
Phase shift h moves the graph right when h is positive.
Tangent has vertical asymptotes at x = pi/2 + k pi.
Use cosine for a model that starts at a maximum and sine for one that starts at the midline.

How to use this precalculus trig graphs test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF