Precalculus Practice Test
36 questions from 12 lessons · 110 minutes · percent score and grade · step-by-step answers
How it works
- 36 questions, about 110 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 4 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Precalculus formula sheet.
1 Question 1
Vector from (1, 2) to (4, 6)Type the answer.
2 Question 2
Vector from (−2, 1) to (2, −2)Type the answer.
3 Question 3
Vector from (0, −2) to (5, 0)Type the answer.
4 Question 4
u = <3, −2>, v = <−1, 4>, find u + vType the answer.
5 Question 5
u = <4, 1>, v = <1, 3>, find u − vType the answer.
6 Question 6
u = <−1, 2>, v = <2, 1>, find 3u + vType the answer.
7 Question 7
OA = a, OB = b, find ABType the answer.
8 Question 8
OA = a, OB = b, M is the midpoint of AB, find BMType the answer.
9 Question 9
OA = a, OB = b, P divides AB in the ratio 2 : 1, find BPType the answer.
10 Question 10
Magnitude and direction of <3, 3>Type the answer.
11 Question 11
Unit vector of <0, −5>Type the answer.
12 Question 12
Unit vector of <8, 15>Type the answer.
13 Question 13
Calculate <3, 4> • <2, 1>Type the answer.
14 Question 14
Dot product of <6, 2> and <−1, 3>Type the answer.
15 Question 15
Angle between <6, 8> and <3, 4>Type the answer.
16 Question 16
Graph x2 = 8y- A) −2
- B) 4
- C) 2
- D) 8
17 Question 17
Graph y2 = −8x- A) −2
- B) 12
- C) −8
- D) 2
18 Question 18
Graph (y + 2)2 = −4(x − 1)Type the answer.
19 Question 19
Graph x225 + y29 = 1Type the answer.
20 Question 20
Graph x24 + y29 = 1Type the answer.
21 Question 21
Graph (x + 1)2/4 + (y + 3)2/9 = 1Type the answer.
22 Question 22
Graph x216 − y29 = 1Type the answer.
23 Question 23
Graph 9x2 − 4y2 = 36Type the answer.
24 Question 24
Graph (x − 3)2/4 − y24 = 1Type the answer.
25 Question 25
Which conic is 4x2 + 9y2 = 36Type the answer.
26 Question 26
Which conic is x2 + y2 − 6x − 7 = 0- A) 9
- B) −16
- C) 7
- D) 16
27 Question 27
Which conic is 4x2 − 9y2 + 8x + 36y − 68 = 0Type the answer.
28 Question 28
Polar (4, 60°) to rectangularType the answer.
29 Question 29
Convert (4, 7π/4) to rectangularType the answer.
30 Question 30
Convert r = −2 sin θ to rectangularType the answer.
31 Question 31
Write 2(cos 60° + i sin 60°) in rectangular formType the answer.
32 Question 32
Simplify (√3 + i)6- A) 64
- B) −64
- C) 30
- D) 2
33 Question 33
Simplify (−√3 + i)3Type the answer.
34 Question 34
Graph x = t + 1, y = 2tType the answer.
35 Question 35
Graph x = t, y = t2 − 3Type the answer.
36 Question 36
Graph x = 5 cos t, y = 3 sin tType the answer.