Precalculus Conic Sections Test with Point Values (PDF)

Precalculus math test: Conic Sections – Maths PDF

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This conics test for Precalculus covers conic sections (Common Core G-GPE.A.1, G-GPE.A.2, G-GPE.A.3), with a free PDF to print.

This 20-point test covers circles, parabolas, ellipses, hyperbolas and a satellite dish model (G-GPE.A.1 to G-GPE.A.3). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Conic Sections
Standards: G-GPE.A.1, G-GPE.A.2, G-GPE.A.3
Time: 45 minutes
Total: 20 points

Conics test: questions

Question 1 – Circles [2 pts]

(a) Write the equation of the circle with center \((-1,4)\) and radius \(3\). (b) Find the center and radius of \(x^{2}+y^{2}+8x-2y+8=0\).

Question 2 – Parabola parts [2 pts]

The parabola x² = -16y.

Find the focus and directrix of \(x^{2}=-16y\).

Question 3 – Parabola from focus and directrix [2 pts]

Write the equation of the parabola with focus \((-2,0)\) and directrix \(x=2\).

Question 4 – Ellipse foci [2 pts]

Write \(16x^{2}+25y^{2}=400\) in standard form and find the foci.

Question 5 – Read an ellipse [3 pts]

The ellipse x²/36 + y²/20 = 1.

For \(\frac{x^{2}}{36}+\frac{y^{2}}{20}=1\): (a) State \(a\) and \(b\). (b) Find \(c\) and the foci. (c) Find the length of the major axis.

Question 6 – Hyperbola parts [2 pts]

For \(\frac{x^{2}}{25}-\frac{y^{2}}{144}=1\), find the vertices and the equations of the asymptotes.

Question 7 – Hyperbola from vertices and foci [2 pts]

Write the equation of the hyperbola with vertices \((0,\pm3)\) and foci \((0,\pm5)\).

Question 8 – Satellite dish [3 pts]

Cross-section of a 6 foot dish.

A parabolic dish is \(6\) ft across and \(1.5\) ft deep. (a) Write its equation as \(x^{2}=4py\) with the vertex at the origin. (b) Find the focus. (c) Find the depth \(2\) ft from the center.

Question 9 – Classify conics [2 pts]

Identify each conic: (a) \(3x^{2}+3y^{2}=27\); (b) \(\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\).

Key facts behind this conics test

Key facts

Circle: (x – h)^2 + (y – k)^2 = r^2.
Parabola: (x – h)^2 = 4p(y – k); focus is p from the vertex and the directrix is on the opposite side.
Ellipse: x^2/a^2 + y^2/b^2 = 1 with c^2 = a^2 – b^2; the foci lie on the major axis.
Hyperbola: x^2/a^2 – y^2/b^2 = 1 with c^2 = a^2 + b^2 and asymptotes y = plus or minus (b/a) x.
Complete the square to find the center or vertex.

How to use this conics 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.

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