Free Printable calculus

1.

What is the midpoint between (8, -3) and (2, 5)

a)

(5, 1)

b)

(10, 2)

c)

(-5, -1)

d)

(3, 4)

2.

What is the distance between (-5, 5) and (1, -2)

a)

9.2

b)

12.6

c)

14

d)

7.8

3.

Point M with coordinates (3,4) is the midpoint of the line AB and A has coordinates (-1,6). What are the coordinates of B?

a)

(1,5)

b)

(2,10)

c)

(7,2)

d)

(1,2)

4.

Find the slope of the line that goes through the points (-8,6) and (7,-3).

a)

1/3

b)

-1/3

c)

-3/5

d)

-5/3

5.

Use the equations given to determine if the following lines are parallel, perpendicular, neither or both.
y=4x-2
y-3=-1/4(x-8)

a)

parallel

b)

perpendicular

c)

neither parallel nor perpendicular

d)

both parallel and perpendicular

6.

What type of triangle is this?

a)

Equilateral triangle

b)

Scalene triangle

c)

Acute triangle

d)

Isosceles triangle

7.

What type of triangle is this?

a)

Scalene triangle

b)

Equilateral triangle

c)

Obtuse triangle

d)

Actue triangle

8.

What type of triangle is this?

a)

Acute triangle

b)

Obtuse triangle

c)

Equiangular triangle

d)

Right triangle

9.

What type of triangle is this?

a)

Acute triangle

b)

Equiangular triangle

c)

Obtuse triangle

d)

Right triangle

10.

Which of the following segments represents an altitude?

a)

BX

b)

AZ

c)

AC

d)

BZ

11.

The line inside this triangle is called

a)

an angle bisector

b)

a perpendicular bisector

c)

an altitude

d)

a median

12.

The line insider this triangle is called

a)

an altitude

b)

a perpendicular bisector

c)

a median

d)

an angle bisector

13.

What is true about the median.

a)

Cuts the side of a triangle into 2 equal parts.

b)

It is always inside the triangle.

c)

It passes through the midpoint of the side of the triangle and the opposite vertex.

d)

All of the above

14.

If you found the midpoint of line segment AB, what should you do next to find the equation of the perpendicular bisector?

a)

Use the midpoint and one of the points from AB to write the equation

b)

Use the midpoint and slope perpendicular to AB to write the equation

c)

Use the distance and midpoint to find the equation

d)

Use the midpoint and slope of AB to write the equation

15.

What is the equation of the line that passes through the points

(6, 5) and (4, -3)?

a)

y= 4x- 29

b)

y= 4x - 19

c)

y= 4x + 19

d)

y=-4x -19

16.

What is the equation of a line that is perpendicular to the line y = 3x + 2 and goes through the point (3, -4)?

a)

y = 3x - 2

b)

y = -1/3x - 5

c)

y = 3x - 4

d)

y = -1/3x - 3

17.

Points A(1,3) & B(-3,5) are the endpoints of a chord on a circle with centre not at the origin. What is the equation of the perpendicular bisector of chord AB?

a)

y = 2x + 4

b)

y = 2x + 6

c)

y = -2x + 6

d)

y = 2x - 6

18.

Triangle ABC has vertices at A(1,5), B(-2,-2) and C(7,-1). What is the length of the median from B the nearest tenth of a unit?

a)

2.5 units

b)

6.7 units

c)

7.2 units

d)

9.1 units

19.

What is the shortest distance (to the nearest tenth of a unit) between the origin and the line y = 2x - 10?

a)

3.8 units

b)

4.5 units

c)

5.0 units

d)

10.0 units

20.

What is the area of triangle ABC which has vertices at A(-3,6), B(5,2) and C(1,-6)?

a)

35 square units

b)

40 square units

c)

50 square units

d)

55 square units

21.

Simplify:

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

22.

x³(2x²+3x)=

a)

2x⁵+3x⁴

b)

2x⁶+3x³

c)

5x⁹

d)

5x

23.

Simplify the expression
(x - 3)²

a)

x² - 6x + 9

b)

x² + 9

c)

x² + 6x - 9

d)

x² + 6x + 9

24.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

25.

Multiply
(2x-1)(x+3)

a)

2x²+5x-3

b)

2x-3

c)

2x²+6x-3

d)

2x²-5x-3

26.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

27.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

28.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

29.

Factor
x² - 9x + 18

a)

A. (x - 6)(x - 3)

b)

B. (x + 6)(x - 3)

c)

C. (x - 9)(x - 2)

d)

D. (x - 6)(x + 3)

30.

Factor Completely: x²-17x+72

a)

(x-9)(x+8)

b)

(x-9)(x-8)

c)

x(x-3)

d)

(x+9)(x+8)

31.

Factor Completely:
x²-5x-14

a)

(x-9)(x+5)

b)

(x-14)(x+1)

c)

(x+7)(x-2)

d)

(x-7)(x+2)

32.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

33.

Factor Completely:
4x³+14x²-30x

a)

(4x²-6x)(x+5)

b)

(2x-3)(2x²+10x)

c)

2x(2x+3)(x-5)

d)

2x(2x-3)(x+5)

34.

Factor:
x² - 49

a)

(x + 7)(x - 7)

b)

(x + 7)²

c)

(x - 7)²

d)

(x+7)(x-1)

35.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

36.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

37.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

38.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

39.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

40.

Factor
9x²-6x-8

a)

(3x+2)(3x-4)

b)

(3x+2)(3x+4)

c)

(3x-2)(3x-4)

d)

(x-1)(9x+8)

41.

Write the explicit formula for the geometric sequence.

3, -12, 48, -192, ...

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

42.

Find the common ratio (multiplier): a₁ = 4 and a₄ = 256

a)

84

b)

64

c)

4

d)

8

43.

What is the 14th term of the geometric sequence?

3, 9, 27, 81, ...

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

44.

Find the partial sum $S_6$ for the geometric series.

$-\frac{4}{5}+8-80+...$

a)

$S_6$ = 21,845

b)

undefined

c)

undefined

d)

undefined

45.

Which of the series below is CONVERGENT?

a)

$a_1=4$
$a_n=a_{n-1}\cdot\left(1.5\right)$

b)

$a_n=-n^2-8n+106$

c)

$a_n=\left(\frac{5}{10}\right)^n$

d)

$a_n=5n+6$

46.

$\sum_{n=4}^{\infty}2\left(0.5\right)^{n-1}$

(a)

47.

$\sum_{k=1}^{\infty}\left(\frac{2}{5}\right)^k$ Find the sum

a)

$\frac{2}{5}$

b)

$\frac{2}{3}$

c)

0

d)

$\infty$

48.

What is row 5 of Pascal's Triangle?

a)

1, 2, 1

b)

1, 3, 3, 1

c)

1, 4, 9, 4, 1

d)

1, 5, 10, 10, 5, 1

49.

Expand $\left(2x+4y\right)^3$

a)

$8x^3+48x^2y+96xy^2+64y^3$

b)

$40x^3+160x^2y+320xy^2+320y^3$

c)

$32x^3+48x^2y+96xy^2+64y^3$

d)

$8x^3+16x^2y+32xy^2+64y^3$

50.

Calculate the coefficient of $a^4b^6$ in the expansion of $\left(a+b\right)^{10}$ .

(a)

51.

Find the binomial coefficient

(a)

52.

Consider the expansion of $\left(x+b\right)^{30}$ .
What is the 4th term's coefficient?

(a)

53.

Which of these is the first step in mathematical induction?

a)

Prove the statement is true for the first element in the set.

b)

Show that if the statement is true for the first k elements, then it is true for the (k+1)st case.

c)

Prove that the problem you are working on is the base to all proofs.

d)

None of these are correct.

54.

Which of the following is the induction step in mathematical induction?

a)

Show that if the statement is true for the first k elements, then it is true for the (k+1)st element in the set.

b)

Show that the statement is true for the first few elements in the set.

c)

Show that your math problem is different from all other math problems.

d)

None of these are correct.

55.

When using mathematical induction to prove : $\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ . In step #2, after you have made your assumption, what are you trying to prove? (What is your goal?)

a)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$

b)

$S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$

c)

$\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$

d)

$S_{k+1}=\left(k+1\right)^2$

56.

In the principle of mathematical induction, what is the term for the first condition?

a)

Base case

b)

First case

c)

Inductive case

d)

Introductory case

57.

What is the mathematical term for the second condition of the principle of mathematical induction?

a)

Base case

b)

First case

c)

Inductive case

d)

Introductory case

58.

What is the third step in Mathematical induction?

a)

P(1)

b)

P(k+1)

c)

P(k)

d)

n=k

59.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

On the basis of this assumption, [The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]

What must we show next?

a)

The statement is true for n = 1:

(2)(1) − 1 = 1²

b)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

60.

Let P(n) = 2n − 1. Evaluate:

a) P(k)

b) P(k + 1)

a)

a) P(k) = 2k − 1

b) P(k + 1) = 2n + 1

b)

a) P(k) = 2k + 1

b) P(k + 1) = 2(k + 1) - 1

c)

a) P(k) = 2k − 1

b) P(k + 1) = 2k + 1

61.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

To prove this by mathematical induction, what will be the induction assumption?

a)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

b)

The statement is true for n = 1:

(2)(1) − 1 = 1²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

62.

What is the first step in Mathematical Induction?

a)

P(k)

b)

n=k

c)

P(k+1)

d)

P(1)

63.

What do you call the statement to be prove?

a)

Inductive statement

b)

Structure

c)

Conjecture

d)

Given

64.

Find the first 6 terms of the sequence.

a)

13, 19, 25, 31, 37, 43

b)

7, 13, 19, 25, 31, 37

c)

1, 7, 13, 19, 25, 31

d)

7, 12, 17, 22, 27, 32

65.

Find an explicit rule for the nth term of the sequence.

a)

a_n= 15+(n-1)4

b)

a_n= -15+(n-1)4

c)

a_n= -15+(n-1)3

d)

a_n= 4n -19

66.

Use the formula S_n to find the sum of the first five terms of the geometric sequence.

a)

22

b)

2/3

c)

18

d)

21

67.

Find the sum of the arithmetic series using a formula.

a)

516, 240

b)

516,242

c)

116, 242

d)

506, 242

68.

Find the sum of the geometric series.

a)

248

b)

124

c)

120

d)

240

69.

a)

∞

b)

DNE

c)

3

d)

1

70.

Find the limit. Hint: Where is the horizontal asymptote?

a)

³/₇

b)

0

c)

$\infty$

d)

$-\infty$

71.

Find the limit

a)

⁶/₅

b)

0

c)

$\infty$

d)

$-\infty$

72.

Find the sum of the infinite geometric series, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$

a)

8

b)

8/5

c)

10

d)

Does not exist

73.

Find the sum of the infinite geometric series, if it exists. $\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+...$

a)

205

b)

19.5

c)

108.75

d)

Does Not Exist

74.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the first?

a)

The statement is true for n = 1.

b)

The statement is true for n = k.

c)

The statement is true for n = k+1.

75.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the second?

a)

The statement is true for n = k+1.

b)

If the statement is true for n = k, then it will be true for its successor, k + 1.

c)

The statement is true for n = 1.

d)

The statement is true for n = k.

76.

What is the formula to find the nth term of an arithmetic series?

a)

a_n = a_1 * (n-1)d

b)

a_n = a_1 + (n-1)d

c)

a_n = a_1 - (n-1)d

d)

a_n = a_1 / (n-1)d

77.

Find the sum of the arithmetic series: 2 + 5 + 8 + 11 + ... + 23, if there are 8 terms.

a)

132

b)

100

c)

78

d)

56

78.

Write the summation notation for the arithmetic series: 3 + 6 + 9 + ... + 27.

a)

∑(3n+3) from n=1 to 9

b)

∑(3n) from n=1 to 9

c)

∑(3 + 3n) from n=1 to 9

d)

∑(3n-3) from n=1 to 9

79.

What is the formula to find the sum of an arithmetic series?

a)

n(a - l)

b)

n(a + l)

c)

(n/2)(a - l)

d)

(n/2)(a + l)

80.

Find the sum of the arithmetic series: 10 + 15 + 20 + ... + 50, if there are 9 terms.

a)

275

b)

400

c)

240

d)

325

81.

Write the summation notation for the arithmetic series: 4 + 8 + 12 + ... + 40.

a)

∑(4 + 4n) from n=0 to 9

b)

∑(4 + 2n) from n=0 to 10

c)

∑(4 + 5n) from n=0 to 8

d)

∑(4 + 3n) from n=0 to 9

82.

What is the formula to find the nth term of a geometric series?

a)

a * r^(n-1)

b)

a * r^n

c)

a + r^(n-1)

d)

a * (r-1)^(n-1)

83.

Find the sum of the geometric series: 2 + 4 + 8 + 16 + ... + 256, if there are 6 terms.

a)

340

b)

768

c)

510

d)

1020

84.

Write the summation notation for the geometric series: 5 + 10 + 20 + ... + 320.

a)

∑(5 * 2^(n+1)) from n=1 to 7

b)

∑(5 * n) from n=1 to 7

c)

∑(5 * 2^(n-1)) from n=1 to 7

d)

∑(5 + 2^(n-1)) from n=1 to 7

85.

What is the formula to find the sum of a geometric series?

a)

S = a + r

b)

S = a / (1 - r)

c)

S = a * r

d)

S = a - r

86.

We can use SOH-CAH-TOA for...

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

87.

sin A = ?

a)

7/25

b)

24/25

c)

7/24

d)

25/7

88.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

89.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

90.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

91.

Which trigonometric ratio you would use to find side AB?

a)

Sin 60 = 10/AB

b)

Sin 60 = AB /10

c)

Cos 60 = 10 / AB
Cos 60 = 10 /AB

d)

tan 60 = AB /10

92.

Which trigonometric ratio you should use to find the height(h)?

a)

sin 60 = h/1000

b)

cos 60 = h / 1000

c)

cos 60 = 1000/h

d)

tan 60 = h / 1000

93.

Find the ratio for sinA. (Reduce the fraction)

a)

36/27

b)

4/5

c)

36/45

d)

3/5

94.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

95.

Solve for x.

a)

24.20

b)

4.92

c)

290.4

d)

29.75

96.

$\cos\ 45^o\ =\ ....$

a)

$\frac{1}{2}\sqrt{2}$

b)

$\frac{1}{2}\sqrt{3}$

c)

$\frac{1}{2}$

d)

$\frac{1}{3}\sqrt{3}$

97.

$\cos\ 60^o\ =\ ....$

a)

$\frac{1}{2}\sqrt{2}$

b)

$\frac{1}{2}\sqrt{3}$

c)

$\frac{1}{2}$

d)

$\frac{1}{3}\sqrt{3}$

98.

$\cos\ 30^o\ =\ ....$

a)

$\frac{1}{2}\sqrt{2}$

b)

$\frac{1}{2}\sqrt{3}$

c)

$\frac{1}{2}$

d)

$\frac{1}{3}\sqrt{3}$

99.

tan²x + 1 =

a)

csc²x

b)

sec²x

c)

sec²x - 1

d)

cscx

100.

1 - sin²x =

a)

cos²x

b)

cos²x+1

c)

csc²x

d)

tan²x

101.

Simplify (sec²x)(1 - sin²x)

a)

-cos(x)

b)

1

c)

-1

d)

-sin(x)

102.

Simplify (Hint: you will need to FOIL first)

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

103.

Simplify...

$\frac{\cot\left(\theta\right)\sin\left(\theta\right)}{\cos\left(\theta\right)}$

a)

$\sec\left(\theta\right)$

b)

1

104.

Simplify...

\cos\left(\theta\right)+\sin\left(\theta\right)\tan\left(\theta\right)

a)

$\sec\left(\theta\right)$

b)

$\csc\left(\theta\right)$

105.

$\frac{\tan x}{\sec x}$

a)

$\cos x$

b)

$\csc x$

c)

$\cot x$

d)

$\sin x\$

106.

Is this a pythagorean identity?
tan²x + 1 = secx

a)

Yes

b)

No

107.

Please select the correct solution
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

108.

What is the length of the side opposite ∠X?

a)

16

b)

30

c)

34

109.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

110.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

111.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

112.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

113.

Arccos(sin 5π/4)

a)

3π/4

b)

π/2

c)

π/6

d)

π/3

114.

Cos^-1(√3/2) =

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

115.

Sin^-1[cosπ]

a)

0

b)

π

c)

π/2

d)

-π/2

116.

Cos^-1(0) =

a)

½π

b)

π

c)

1

d)

none of these

117.

What range of angles can you get from the principal value of inverse cosine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

118.

What range of angles can you get from the principal value of inverse sine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

119.

Evaluate the function: Arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

120.

Arcsin(0)

a)

0

b)

1

c)

1/2

d)

3/2

121.

Arcsin (-1)

a)

π/2

b)

-1

c)

-π/2

d)

1

122.

Arctan (0)

a)

1

b)

0

c)

-1

d)

0.5

123.

Arccos (-√3/2)

a)

5π/6

b)

7π/4

c)

-√3/2

d)

-5π/6

124.

Arcsin(cos π/6)

a)

π/6

b)

π/3

c)

-π/6

d)

π/4

125.

Tan ( Arctan -1)

a)

-1

b)

0

c)

π/6

d)

-π/4

126.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

33°

b)

49°

c)

39°

d)

41°

127.

Find the measure of the angle. Round to the nearest tenth.

a)

30.8

b)

32.1

c)

34.3

d)

36.9

128.

Find the measure of the missing angle.

a)

49^o

b)

50^o

c)

41^o

d)

33^o

129.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

49°

b)

57°

c)

45°

d)

54°

130.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

calculus

Total questions: 130

Worksheet time: 10hrs 40mins

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