Free Printable Precalc T1 Review

1.

How many years will it take an initial investment of $25,000 to grow to $80,000? Assume a rate of 6.8% interest compounded monthly.

a)

17.14 years

b)

9.64 years

c)

11.53 years

d)

23.50 years

2.

How many years will it take for an initial investment of $10,000 to grow to $25,000? Assume a rate of interest of 6% compounded continuously.

a)

3.73 years

b)

10.34 years

c)

7.80 years

d)

15.27 years

3.

John will be buying a used car for $15,000 in 3 years. How much money should he ask his parents for now so that, if he invests it at 5% compounded continuously, he will have enough to buy the car?

a)

$12,910.62

b)

$17,427.50

c)

$746.81

d)

$11,291.23

4.

Strontium-90 is a radioactive material that decays according to the function A(t)=A₀e^-0.0244t where A₀ is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500 grams of strontium-90. How much strontium-90 is left after 10 years?

a)

421.8g

b)

.05g

c)

110.1g

d)

391.7g

5.

Which equation matches the graph?

a)

y = 2x + 3

b)

y = -3

c)

y = 2x - 3

d)

y = -3x + 2

6.

Which graph matches the equation?

a)

A

b)

B

c)

C

d)

D

7.

Which of the following is false?

a)

A

b)

B

c)

C

d)

D

8.

Factor completely: x³ - 2x² - 4x + 8

a)

x = 2 and x = -2

b)

(x + 2)(x - 2)

c)

(x - 2)² (x + 2)

d)

(x - 2) (x + 2)²

9.

Give the range of F(x) = x² - 4

a)

x ε R

b)

F(x) ≥ -4

c)

F(x) ≥ 4

d)

x ≥ 4

10.

Solve : 2 log ₃ x = 8

a)

12

b)

81

c)

2

d)

64

11.

What is the core of Harry Potter's wand?

a)

Dragon Heartstring

b)

Unicorn Hair

c)

Phoenix Feather

d)

Troll Whisker

12.

In interval notation, –4 ≤ x < 0 is written:

a)

(0, –4]

b)

[–4, 0)

c)

[0, –4)

d)

(–4, 0]

13.

If 4x² – 1 = 0 , then x = ?

a)

(2x – 1)(2x + 1)

b)

(1 – 2x)(1 + 2x)

c)

± 1/2

d)

± 2

14.

What are the x-intercepts of the graph?

a)

(0,-3)

b)

(-3,0)

c)

(0,90)

d)

(5,0)

e)

(0,5)

15.

(a – b)² = ?

a)

a² – b²

b)

a² + b²

c)

a² – ab + b²

d)

a² – 2ab + b²

16.

If x²– 9x = 0, then x = ?

a)

3

b)

± 3

c)

0, 9

d)

0, 3, -, 3

17.

Pick the equation that matches the graph

a)

A

b)

B

c)

C

d)

D

18.

Given -4 is a zero, find all other zeros
f(x) = x³+4x²+9x+36

a)

x = -2, 2

b)

x = -3, 3

c)

x = -2i, 2i

d)

x = -3i, 3i

19.

Give the range of F(x) = x² - 4

a)

x ε R

b)

F(x) ≥ -4

c)

F(x) ≥ 4

d)

x ≥ 4

20.

Factor completely: x³ - 2x² - 4x + 8

a)

x = 2 and x = -2

b)

(x + 2)(x - 2)

c)

(x - 2)² (x + 2)

d)

(x - 2) (x + 2)²

21.

Find the domain of the function:
f(x)=3∛x-3

a)

[3,∞)

b)

(-∞,∞)

c)

[9,∞)

d)

(-∞,3)U(3,∞)

22.

5^3-2n = 125

a)

0

b)

5

c)

1

d)

5/3

23.

a)

x=2

b)

x=29

c)

x=7

d)

x=32

24.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

25.

a)

y = x

b)

y = x²

c)

y = x³

d)

y = |x|

26.

a)

y = x

b)

y = x²

c)

y = x³

d)

y = |x|

27.

a)

y = x²

b)

y = √x

c)

y = ∛x

d)

y = |x|

28.

a)

y = x²

b)

y = √x

c)

y = ∛x

d)

y = |x|

29.

a)

y = 2^x

b)

y = .5^x

c)

y = 1^x

d)

y = -2^x

30.

a)

y = x

b)

y = x²

c)

y = 1/x

d)

y = √x

31.

What is the increasing interval for this function?

a)

(-6, -2)

b)

(-∞, ∞)

c)

(-2, 6)

d)

(-1, 3)

32.

What is the domain of this function?

a)

(-∞ , ∞)

b)

(-2,∞)

c)

(0,∞)

d)

(3,5)

33.

What are the roots of this function?

a)

All real numbers

b)

x ≥ 2

c)

x > 0

d)

x = 3 and x = 5

34.

What is the range of this function?

a)

All real numbers

b)

y ≥ -4

c)

x = 1 and x = 5

d)

y ≥ 3

35.

$3-12x^2$ Factor completely:

a)

$3\left(-4x^2\right)$

b)

$3\left(1-12x^2\right)$

c)

$3\left(1-4x^2\right)$

d)

can't be factored

36.

$36x^2-108x+81$ Factor completely:

a)

$9\left(2x-3\right)^2$

b)

$36\left(x^2-3x+2.25\right)$

c)

$9\left(2x-3\right)\left(2x+3\right)$

d)

$3\left(4x-9\right)\left(3x-3\right)$

37.

$\frac{x}{3}+\frac{3x}{4}=2$ Solve:

a)

$x=\frac{24}{13}$

b)

$x=4$

c)

$x=\frac{12}{13}$

d)

$x=12$

38.

$6x^2+3x=0$ Solve:

a)

$x=0$

b)

$x=\frac{1}{2}$

c)

$x=-\frac{1}{2}$

d)

$x=0,\ -\frac{1}{2}$

39.

$2x^2=12$ Solve:

a)

$x=6$

b)

$x=\pm6$

c)

$x=\pm\sqrt{12}$

d)

$x=\pm\sqrt{6}$

40.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

41.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

42.

What type of function is shown?

a)

Exponential, f(x) = e^x

b)

square root, f(x) = √x

c)

quadratic, f(x) = x²

d)

cube root, f(x) = ∛x

43.

a)

-4.5

b)

2.9

c)

2.8

d)

24

44.

Solve for x: $\frac{2}{x-3}+\frac{1}{x}=\frac{x-1}{x-3}$

a)

x = 3

b)

x = 1

c)

x = 0

d)

x = 4

45.

Which equation matches the graph?

a)

y = log₃(x + 1) – 2

b)

y = log₃(x – 2) – 1

c)

y = log₃(x + 2) + 1

d)

y = log₃(x – 1) + 2

46.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

47.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

48.

G(x)=2x²+2x. Find G(4).

a)

26

b)

40

c)

30

d)

29

49.

Describe the transformations.

a)

Translate Right 2, Down 4

b)

Translate Left 2, Down 4

c)

Translate Left 2, Up 4

d)

Translate Right 2, Up 4

50.

What is the equation of the graph?

a)

y = √(x - 3)

b)

y = √(x) + 3

c)

y = √(x - 5) + 4

d)

y = √(x + 5) + 4

51.

Where is the decreasing?

a)

( −∞, −2.55) , (0, 2.55)

b)

(∞, −6.25) , (36, −6.25)

c)

(−∞, ∞)

d)

(−∞, 0)

52.

Find the asymptote for the following.

a)

x = -1

b)

x = 1

c)

y = 5

d)

y = -5

53.

Solve for r:
3^-3r = 3⁵

a)

-4

b)

-5/3

c)

2

d)

8

54.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

55.

Solve 5e^{3x - 2} + 15 = 35

a)

1.13

b)

1.29

c)

1.10

d)

0.87

56.

Find the roots of 0=x³-4x²+2x-8

a)

±2,4

b)

±2i,4

c)

±i√2,4

d)

±√2,4

57.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

58.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

59.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

60.

The pilot of a traffic helicopter sights an accident at an angle of depression of 18 degrees. The helicopter’s altitude is 1560 ft. What is the horizontal distance from the helicopter to the accident? Round to the nearest foot.

a)

543 ft

b)

1756 ft

c)

4801 ft

d)

5404 ft

61.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

62.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

63.

What is the degree of the polynomial?

a)

2

b)

3

c)

4

d)

5

64.

What are the local maxima of this graph?

a)

local maximum at (2.2, 3.9)

b)

local maximum at (-8, 5)

c)

local maximum at (5, -8)⋃(3.9, 2.2)

d)

local maximum at (-8, 5)⋃(2.2, 3.9)

65.

If the degree of the function is even, the graph starts and ends in the ____________ direction.

a)

same

b)

opposite

66.

When is this function increasing?

a)

-2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

-5 < x < 0

67.

a)

± 1/4

b)

± 9/36

c)

± 1/2

d)

No real solution

68.

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

69.

a)

4

b)

-4

c)

2

d)

-2

70.

Which of the following intervals has the largest average rate of change?

a)

[13,14]

b)

[13, 17]

c)

[16, 17]

d)

[16, 19]

71.

What was the average rate of change in the population from 1900 to 1990?

a)

175 million people/year

b)

1.94 million people/year

c)

2.13 million people/year

d)

-1 million people/year

72.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

73.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

74.

Find the slope from the graph

a)

0

b)

undefined

c)

5

d)

-5

75.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

76.

Find the excluded value(s).

a)

3

b)

-3

c)

0

d)

-1

77.

Find the vertical asymptote(s).

a)

None

b)

x = 0

c)

x= 4

d)

x = -4, 4

78.

Describe the parent graph transformation

a)

h. stretch, left 1, down 3

b)

h. shrink, right 1, down 3

c)

v. shrink, left 1, down 3

d)

v. stretch, right 1, down 3

79.

Describe the transformation from the parent graph.

a)

h. stretch by factor of 2, left 5

b)

h. shrink by factor of 2, up 5

c)

v. stretch by factor of 2, down 5

d)

v. shrink by factor of 2 right 5

80.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

81.

Over the interval (−1, 2), the graph of the polynomial shown could be described as

a)

decreasing

b)

increasing

c)

quadratic

d)

complex

82.

Fully Factor the Following
4x²-16

a)

(2x-4)(2x+4)

b)

(4x-4)(4x+4)

c)

4(x-2)²

d)

4(x-2)(x+2)

83.

Solve for the missing angle

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

84.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

85.

cot 45

a)

0.1

b)

1

c)

1/2

d)

2

86.

Given sin $\theta$ = 3/4, find cot $\theta$

a)

4/3

b)

$\frac{\sqrt{7}}{3}$

c)

$\frac{\sqrt{7}}{4}$

d)

$\frac{3\sqrt{7}}{7}$

87.

What are the asymptotes?

a)

x=-3, y=1

b)

x=3, y =1

c)

x=-3, y =-1

d)

x=3 y=-1

88.

What is the horizontal asymptote of the function?

a)

y=0

b)

none

c)

y=1

89.

Solve

a)

A

b)

B

c)

C

d)

D

Precalc T1 Review

Total questions: 89

Worksheet time: 5hrs 26mins

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