Free Printable 3 PRECALCULUS

1.

What type of sequence is this?

5, 9/2, 4, 7/2, 3, 5/2, 2

a)

Arithmetic sequence

b)

Arithmetic series

c)

Harmonic sequence

d)

Geometric sequence

2.

The sum of the first n terms of an arithmetic series is -85.5. The first term of the series is -27/3 and the common difference is 1/2. How many terms are in the series?

a)

16

b)

17

c)

18

d)

20

3.

What is the sum of the first 35 terms in an arithmetic series with the first term 18, common difference -12?

a)

770

b)

775

c)

870

d)

875

4.

Find the sum of the first 105 terms in an arithmetic series with the first term 95876 is 7, 271, 880. Find the last term?

a)

6998

b)

6754

c)

7168

d)

72636

5.

Find the sum of the first 15 terms in a geometric series with the first term 81, 920 and the ratio 1/2.

a)

32/3

b)

5

c)

18

d)

1589/3

6.

Find the sum of the first 20 terms in a geometric series with the first term 9 and the common ratio -1.

a)

-20

b)

20

c)

15

d)

415/2

7.

Find the sum of the the following series

2+6+18+54+....

a)

-1

b)

1

c)

infinity

d)

No sum

8.

Find the sum of the following sequence

9, 13.5, 20.25, 30.375, ...

a)

-18

b)

18

c)

No sum

9.

Find the sum of the following series

2+4/3+8/9+16/27+ ...

a)

So sum

b)

6

c)

-6

10.

Expand the summation.

a)

-1800

b)

-1818

c)

-1825

d)

-1795

11.

Expand and simplify

a)

802

b)

1002

c)

1396

d)

1755

12.

Expand and simplify if possible.

a)

b)

c)

d)

13.

Write the expression in sigma notation

a)

b)

c)

d)

14.

Expand the expression

a)

b)

c)

d)

15.

Expand the expression

a)

b)

c)

d)

16.

a)

b)

c)

d)

17.

How many terms are there in the expansion

a)

100

b)

97

c)

99

d)

101

18.

a)

b)

c)

d)

19.

Which of the following is not an arithmetic sequence?

a)

11, 2, -8, -19, …

b)

-3, -5, -7, -9, …

c)

57, 51, 45, 39, …

d)

4, 7, 10, 13, …

20.

Which could be the graph of $\frac{\left(x-3\right)^2}{4}+\frac{y}{9}=1?$

a)

b)

c)

d)

21.

What is the coordinate of the center and radius of the circle whose equation is $\left(x-9\right)^2+\left(y+1\right)^2=4?$

a)

C(-9,1); r=2

b)

C(9,-1); r=2

c)

C(-9,1); r=16

d)

C(9,-1); r=16

22.

Find the equation of the circle graphed on the left.

a)

$x^2+y^2=4$

b)

$x^2-y^2=16$

c)

$x^2+y^2=16$

d)

$x^2+y^2=8$

23.

Which describe the graph of $\frac{x^2}{9}-\frac{y^2}{4}=1?$

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

24.

When graphed, which equation would produce a parabola?

a)

$y^2=25-x$

b)

$x^2-y^2=25$

c)

$x^2+4y^2=1$

d)

$x-y=25$

25.

Which of the following is the general term of the sequence 1, 4, 27, 256, …?

a)

$n$

b)

$n^2$

c)

$2^{n-1}$

d)

$n^n$

26.

An ellipse has a major axis of 20 and a minor axis of 12. A possible equation for this ellipse is______

a)

$\frac{x^2}{200}+\frac{y^2}{144}=1$

b)

$\frac{x^2}{20}+\frac{y^2}{12}=1$

c)

$\frac{x^2}{100}+\frac{y^2}{36}=1$

d)

$\frac{x^2}{10}+\frac{y^2}{6}=1$

27.

If the general term of a sequence is $\frac{n-1}{n+1}$ , find the 3rd term of the sequence.

a)

-2

b)

$\frac{1}{3}$

c)

$\frac{1}{2}$

d)

3

28.

1. The graph of $y^2=-4x^{ }$ is a parabola that _______

a)

opens to the right with a vertex at

(0, 0)

b)

opens to the left with a vertex at

(0, 0)

c)

opens upward with a vertex at

(0, 4)

d)

opens downward with a vertex at

(-4, 0)

29.

In an angle, the common end point is known as

a)

vertex

b)

point of intersection

c)

initial side

d)

terminal side

30.

A full revolution of a circle is equivalent to

a)

180\degree

b)

$2\pi\ radian$

c)

$360\ mm$

d)

$90\ rev$

31.

It refers to the length of a line that bounds a circle.

a)

arc

b)

radian

c)

circumference

d)

radius

32.

$270\degree$ is equivalent to?

a)

$\pi$

b)

$2\pi$

c)

$\frac{3\pi}{2}$

d)

$\frac{\pi}{4}$

33.

$\frac{\pi}{9}$

Convert the angle measure into degrees

a)

$20\degree$

b)

$30\degree$

c)

$35\degree$

d)

$60\degree$

34.

What is the measure of a given angle in radians if its arc length is 4π and the radius has a length of 12 ?

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}$

c)

$\frac{5\pi}{2}$

d)

$3\pi$

35.

It is the measure of an angle formed when the initial side rotates all the way around its vertex until it reaches its initial position.

a)

arc length

b)

revolution

c)

circumference

d)

area

36.

Which of the following is not an example of coterminal angles?

a)

$45\degree\ and\ -315\degree$

b)

$30\degree,\ 390\degree,\ and\ -330\degree$

c)

$\frac{\pi}{3}\ and\ -5\frac{\pi}{3}$

d)

$\frac{\pi}{6}\ and\ \frac{7\pi}{6}$

37.

What is the reference angle of the 135 degrees?

a)

$10\degree$

b)

$15\degree$

c)

$35\degree$

d)

$45\degree$

38.

Which of the following is an example of a quadrantal angle?

a)

$45\degree$

b)

$60\degree$

c)

$135\degree$

d)

$360\degree$

39.

There are 5-steps in solving a non-linear inequality, which of the following is the correct sequence?

P: Critical Values

Q: Solving Method (Number line method/Table sign method)

R: Rewrite the inequalities so that RHS is 0

S: Solution

T: Linear factor(s) of the variable/unknown

a)

R, Q, P, T, S

b)

R, P, T, Q, S

c)

R, T, P, Q, S

d)

R, P, T, Q, S

40.

|x| ≥ 10

a)

x ≥ 10 or x ≤ -10

b)

x ≥ -10 or x ≤ 10

c)

-10 ≤ x ≤ 10

d)

10 ≤ x ≤ -10

41.

The figure shows the steps to solve a rational inequality

\frac{x-8}{x-2}\le0

. What is the solution of the inequality?

a)

$x<2$

b)

$x\le8$

c)

$2\le x\le8$

d)

$2<x\le8$

42.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

43.

Choose the best solution for $\frac{-2-i}{11+i}$ .

a)

$\frac{-2-i}{11+i}\times\frac{-2-i}{11-i}$

b)

$\frac{-2-i}{11+i}\times\frac{11-i}{11-i}$

c)

$\frac{-2-i}{11+i}\times\frac{-2+i}{-2+i}$

d)

$\frac{-2-i}{11+i}\times\frac{-11-i}{-11-i}$

44.

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

45.

Which is f ^-1(x)?

a)

f^-1(x) = 5x + 3

b)

f^-1(x) = 5x - 3

c)

f^-1(x) = 5x - 15

d)

f^-1(x) = 1/5(x) + 3/5

46.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

47.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

48.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

49.

Find tan(θ).

a)

tan(θ) = 5/13

b)

tan(θ) = 12/13

c)

tan(θ) = 12/5

d)

tan(θ) = 5/12

50.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

51.

The correct way to convert 5.6 rad to degree is......

a)

$5.6\times\frac{180}{\pi}$

b)

$5.6\times\frac{\pi}{180}$

c)

$5.6\div\frac{180}{\pi}$

d)

$5.6\div\frac{\pi}{180}$

52.

The correct method to convert $56^{\degree}$ to radian is.........

a)

$56+\frac{180}{\pi}$

b)

$56\times\frac{180}{\pi}$

c)

$56\times\frac{\pi}{180}$

d)

$56+\frac{\pi}{180}$

53.

Which of the following figure is refering to area of sector?

Yang manakah rajah di bawah menunjukkan luas sektor?

a)

b)

c)

d)

54.

Solve for x:
log₃3^x = 5

a)

5

b)

4

c)

3

d)

243

55.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

56.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

57.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

58.

For the function $y = \sin(2x + \pi)$ , what is the phase shift?

a)

$\frac{\pi}{2}$ to the right

b)

$\pi$ to the right

c)

$\frac{\pi}{2}$ to the left

d)

$\pi$ to the left

59.

Find the inverse of $g\left(x\right)=\sqrt[]{x-3}$

a)

$g^{-1}\left(x\right)=\left(x+3\right)^{2\ }$

b)

$g^{-1}\left(x\right)=\left(x-3\right)^{2\ }$

c)

$g^{-1}\left(x\right)=\left(x\right)^2+3$

d)

$g^{-1}\left(x\right)=\left(x+3\right)^{\ }$

60.

Solve $\sqrt[]{x-3}=x-5$

a)

9

b)

11

c)

7

d)

5

61.

Let $p\left(x\right)=3x^3+9x^2-3x-9$ and state the maximum number of real zeros and the maximum number of relative extrema.

a)

Maximum number of real zeros: 2; Maximum number of relative extrema: 3.

b)

Maximum number of real zeros: 1; Maximum number of relative extrema: 1.

c)

Maximum number of real zeros: 4; Maximum number of relative extrema: 0.

d)

Maximum number of real zeros: 3; Maximum number of relative extrema: 2.

62.

Find the zeros of $p\left(x\right)=3x^3+9x^2-3x-9$

a)

x = 1, x = 1, x = -3

b)

x = 1, x = -1, x = -3

c)

x = 1, x = -1, x = 3

d)

x = -1, x = -1, x = -3

63.

Divide $2x^5+3x^4-15x-2$ by $x+1$

a)

$2x^4+x^3+x^2+x-16\ R.14$

b)

$2x^4+x^3-x^2+x+16\ R.14$

c)

$2x^4+x^3-x^2+x-16\ R.14$

d)

$2x^4-x^3-x^2+x-16\ R.14$

64.

Use the Remainder Theorem to find the remainder when $p\left(x\right)=x^5+3x^2-10$

is divided by $x+2$

a)

34

b)

50

c)

-30

d)

10

65.

Use Descartes’s Rule of Signs to describe the possible number of positive and

negative zeros of $p(x)=3x^4−6x^3+15x^2+10x−8.$

a)

Positive zeros: 3 or 1; Negative zeros: 1.

b)

Positive zeros: 1; Negative zeros: 2 or 0.

c)

Positive zeros: 4; Negative zeros: 0.

d)

Positive zeros: 2 or 0; Negative zeros: 3.

66.

Write a standard form polynomial of least degree with integral coefficients

that has the given zeros for the polynomial p(x) has rational coefficients and zeros of 3 and 1 + √ 2 .

a)

x^3 - 5x^2 + 5x + 3

b)

x^3 - 3x^2 + 3x + 5

c)

x^3 - 6x^2 + 9x - 2

d)

x^3 - 4x^2 + 2x + 1

67.

Find all the zeros of $p\left(x\right)=x^3+x-10$

a)

$x=2,\ -1\pm2i$

b)

$x=2,\ 1\pm2i$

c)

$x=-2,\ -1\pm2i$

d)

$x=-2,\ 1\pm2i$

68.

Identify any asymptotes and

point discontinuities of $g\left(x\right)=\frac{1}{x-2}+1$

a)

Vertical asymptote at x = 1; horizontal asymptote at y = 0; point discontinuity at x = 2.

b)

No vertical asymptote; horizontal asymptote at y = 1; point discontinuity at x = 2.

c)

Vertical asymptote at x = 3; horizontal asymptote at y = 2; no point discontinuities.

d)

Vertical asymptote at x = 2; horizontal asymptote at y = 1; no point discontinuities.

69.

Solve $4x-3=\frac{x+13}{x+1}$

a)

x = 0

b)

x = 3 or x = -3

c)

x = -1 or x = 1

d)

x = 2 or x = -2

70.

Which of the following relations are functions? List all correct answers.

a)

A

b)

B

c)

C

d)

D

71.

Write the slope-intercept form equation of the line passing through (3, −4) and

perpendicular to $y=-\frac{1}{2}x-5$

a)

y = -2x + 2

b)

y = -2x - 10

c)

y = 2x - 10

d)

y = 2x + 10

72.

Find the center and length of a radius of a circle whose diameter has endpoints (0, 6)

and (8, −2).

a)

Center: (2, 4), Radius: 3

b)

Center: (4, 2), Radius: 4√2

c)

Center: (4, 4), Radius: 5

d)

Center: (6, 0), Radius: 4

73.

Write a function rule for the illustrated transformation of f (x) = ∣x∣.

a)

f(x) = 2|x + 1| + 3

b)

f(x) = -2|x + 1| + 3

c)

f(x) = -2|x - 1| + 3

d)

f(x) = -x

74.

If $f\left(x\right)=\sqrt[]{x-6}$ and $g\left(x\right)=x^2+7$ write a function rule for $\left(f\circ g\right)\left(x\right)$

a)

$f\left(g\left(x\right)\right)=\sqrt[]{x^2-1}$

b)

$f\left(g\left(x\right)\right)=\sqrt[]{x^2+1}$

c)

$f\left(g\left(x\right)\right)=\sqrt[]{x^2}+1$

d)

$f\left(g\left(x\right)\right)=\sqrt[]{x^2}-1$

75.

Are $f\left(x\right)=x^2+1$ and $g\left(x\right)=\sqrt[]{x^2-1}$ inverse functions?

a)

Yes

b)

No

76.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

77.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

78.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

3 PRECALCULUS

Total questions: 78

Worksheet time: 3hrs 36mins

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