Free Printable IB Physics 2025 - Topic 0 - Math Skills & Measurement Worksheet

1.

What is the equation of the line from the table shown?

a)

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

b)

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

c)

$y=-2x-5$

d)

$y=-2x+5$

2.

What are the values of the slope and y-intercept?

a)

$m=1\ ;\ b=3$

b)

$m=\frac{1}{3};\ b=1$

c)

$m=3;\ b=-2$

d)

$m=3;\ b\ =1$

3.

What is the equation of the line from the table shown?

a)

$y=\frac{1}{3}x-2$

b)

$y=\frac{1}{3}x+2$

c)

$y=3x-2$

d)

$y=3x+2$

4.

What is the coordinate of the y-intercept?

a)

$\left(4,0\right)$

b)

$\left(0,4\right)$

c)

$\left(5,2\right)$

d)

$\left(-5,6\right)$

5.

Which equation can be used to determine the slope?

a)

$m=\frac{5-0}{2-4}$

b)

$m=\frac{4-2}{5-0}$

c)

$m=\frac{8-6}{-10-5}$

d)

$m=\frac{6-4}{-5-0}$

6.

Find the slope of the line that passes through
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

7.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

8.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

9.

What is the equation of this line?

a)

0

b)

undefined

c)

y = -2

d)

x = -2

10.

Write the equation of the line through the points (8, −7) and (−2, 8).

a)

y = 3/2x + 11

b)

y = −3/2x + 11

c)

y = −3/2x + 5

d)

y = 3/2x − 19

11.

What is the equation of the line graphed?

a)

x = -1

b)

y = -1

c)

y = -1x

d)

y = x - 1

12.

Write a slope intercept equation for a line containing the point (2,4) with a slope of $\frac{4}{3}$

a)

$y=-\frac{4}{3}x+\frac{4}{3}$

b)

$y=-\frac{5}{3}x+\frac{4}{3}$

c)

$y=\frac{4}{3}x+\frac{4}{3}$

d)

$y=x+\frac{4}{3}$

13.

Write a slope-intercept equation of the line containing the point (-3,5) and (4,3)

a)

$y=-\frac{2}{7}x+\frac{29}{7}$

b)

$y=\frac{2}{7}x+\frac{29}{7}$

c)

$y=\frac{29}{7}x+\frac{2}{7}$

d)

$y=\frac{3}{7}x+\frac{2}{7}$

14.

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

a)

y = 8x + 50

b)

C = 50m +8

c)

y = 50x + 8

d)

C = 8m + 50

15.

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

a)

y=15x

b)

y=15x+80

c)

y=x+15

d)

y=80x+15

16.

A camp charges families a fee of $625 per month for one child and a certain amount more per month for each additional child. Use the graph to write an equation in slope-intercept form to represent the amount a family with x additional children would pay.

a)

y = 625x + 225

b)

y = 225x

c)

y = 225x + 625

d)

y = 625

17.

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.

a)

h = 2C + 15

b)

C = 15h + 2

c)

h = 15C + 2

d)

C = 2h + 15

18.

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage. If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

a)

C = 15 + 0.20x

b)

C =15 (0.20x)

c)

C = 15 + x + 0.20

d)

C = 0.20 + 15x

19.

A car is timed around a race track for 8 laps. The laps are numbered in order. Look at the relationship between Lap Number and Lap Time (seconds).

What type of relationship is this?

a)

Direct

b)

Inverse

c)

Diagonal

d)

Horizontal

20.

In this graph, y increases ____ (relationship)

a)

exponentially as x increases

b)

directly as x increases

c)

as the root of x

d)

inversely with x

21.

What is the slope of this graph?

a)

20 cm

b)

0.1 s

c)

200 cm/s

d)

40 cm/s

22.

If the variables from the graph are position (s) and time (t), what is an appropriate physics equation to represent the trendline of the graph?

a)

s = (200 cm/s) * t

b)

s = (40 cm/s) * t

c)

t = (40 cm/s) * t

d)

t = (200 cm/s) * t

23.

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

a)

14

b)

10

c)

2

d)

-14

24.

x and y are in inverse variation

x=6 and y=7

Given y=k/x... Find k

25.

If y varies inversely as x, and y = 32 when x = 3, find x when y = 15.

a)

3/5

b)

8/5

c)

16/5

d)

32/5

26.

If x varies inversely as the square root of y, and x = 9 when y = 121, find x when y = 81. (a)

Choose from the below words

7

11

13

17

27.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

28.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?

a)

$394

b)

$443.25

c)

$472.80

d)

$512.20

29.

The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?

a)

175 atm

b)

200 atm

c)

225 atm

d)

275 atm

30.

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

a)

5.33 hours

b)

6.75 hours

c)

12 hours

d)

10 hours

31.

Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure when the volume is increased to 12 liters?

a)

39.8 cm Hg

b)

41.0 cm Hg

c)

43.2 cm Hg

d)

45.1 cm Hg

32.

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

a)

8 painters

b)

10 painters

c)

9 painters

d)

11 painters

33.

Determine the type of variation:

a)

Direct

b)

Inverse

c)

Neither

34.

What is the constant (k) in this inverse variation?

a)

12

b)

24

c)

48

d)

Not enough information given

35.

What is the equation for the axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

36.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

37.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

38.

Does y = -4x² have a maximum or minimum value?

a)

maximum

b)

minimum

39.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

40.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

41.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

42.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

43.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

44.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

45.

Solve.
n² - 5 = -4

a)

n = ±√9

b)

n = ±3

c)

n = ±1

d)

No real solution

46.

Find the zeros of the quadratic equation y=4(x+9)²-36

a)

x=-9+√6 & x=-9-√6

b)

x=3 & x=-3

c)

x=-6 & x=-12

d)

so solution

47.

Solve the following quadratic equation...

x² + 2x - 24 = 0

a)

x = 6

x = -4

b)

x = -6

x = 4

c)

x = -8

x = 3

d)

x = 8

x = -3

48.

Solve the following quadratic equation...

x² + 4x - 32 = 0

a)

x = 8

x = -4

b)

x = -8

x = 4

c)

x = -2

x = 16

d)

x = 2

x = -16

49.

Solve the following quadratic equation...

x² + 13x + 36= 0

a)

x = -2

x = -18

b)

x = -9

x = -4

c)

x = -3

x = -12

d)

x = -6

50.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

51.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

52.

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)

53.

How many significant figures does the following number have?
0.00345

a)

6

b)

5

c)

3

d)

Ambiguous: 3,4,5, or 6

54.

How many significant figures does the following number have: 0.00204

a)

6

b)

4

c)

3

d)

2

55.

How many significant figures does the following number have?1.2500 x $10^3$

a)

5

b)

3

c)

Ambiguous: 3 or 5

d)

7

56.

How many significant figures does the following number have: 100.00210

a)

7

b)

8

c)

10

d)

Ambiguous: 7 or 8

57.

Round 1289 to three significant figures

a)

1290

b)

130

c)

1300

d)

1.29x10³

58.

What is 98.907 rounded to 1 significant figure?

a)

98.9

b)

90

c)

100

d)

1x10²

59.

How many significant figures are there in 1008 grams?

a)

1

b)

2

c)

3

d)

4

60.

How many significant figures: 0.001 g

a)

4

b)

3

c)

2

d)

1

61.

How many significant figures are there in 0.020 meters?

a)

1

b)

2

c)

3

d)

4

62.

What is 78.5 rounded to one significant figure?

a)

8

b)

70

c)

79

d)

80

63.

Round 0.010229 to four significant figures

a)

1022

b)

1023

c)

0.01023

d)

0.01022

64.

Round 1047.78 to three significant figures.

a)

104

b)

105

c)

1050

d)

1050.00

65.

What is 375.6523 to four significant figures.

a)

375.0

b)

375.00

c)

375.7

d)

375.6

66.

Round 345 000 to 1 s.f

a)

400 000

b)

3

c)

300 000

d)

350 000

67.

How many significant figures are in the result for the following calculation?

$6.08\ kg\times5.0\ \frac{m}{s}$

a)

3 significant figures

b)

1 significant figure

c)

2 significant figures

d)

4 significant figures

e)

5 significant figures

68.

How many significant figures are in the result for the following calculation?

$\frac{65.3\ J}{50.085\ s}$

a)

5 significant figures

b)

2 significant figures

c)

1 significant figure

d)

3 significant figures

69.

What is the result for the following calculation? Ensure that the correct number of significant figures are included in the calculated result.

$25.085\ m\ +\ 16.2\ m$

a)

41.3 m

b)

41.2085 m

c)

41.285 m

d)

41.2 m

70.

What is the result of the following calculation? Ensure that the correct number of significant figures are included in the calculated result.

$12.582\ s\ -\ 5.23\ s$

a)

7.360 s

b)

7.36 s

c)

7.35 s

d)

7.352 s

e)

7.350 s

71.

For significant figures, which term is the limiting term in the following calculation?

$17.2\ g\ +\ 9\ g\ +\ 36.333\ g\ +\ 0.58\ g$

a)

17.2 g

b)

9 g

c)

36.33 g

d)

0.58 g

72.

Which set of measurements demonstrates accuracy and precision if the true value is equal to 25.0 cm?

a)

19.9 cm

20.0 cm

20.1 cm

20.2 cm

b)

24.8 cm

24.9 cm

25.0 cm

25.1 cm

c)

17.2 cm

18.9 cm

19.8 cm

20.0 cm

22.0 cm

d)

23.5 cm

24.9 cm

25.0 cm

26.3 cm

26.5 cm

73.

Use the correct significant figure to calculate the final answer of this question.

$3.02\times2.3=$

a)

6.946

b)

6.95

c)

6.9

d)

7.0

74.

What is $1\ x\ 10^6$ ( $7\ x\ 10^8$ )?

a)

$8\ x\ 10^{48}$

b)

$7\ x\ 10^{48}$

c)

$7\ x\ 10^{14}$

d)

None of the Choices

75.

Give the answer to the correct number of significant figures to

3.419 + 3.912 + 7.0518 + 0.00013

a)

14.383

b)

14.382

c)

14.3829

d)

14.38293

76.

Give the answer to the correct number of significant figures to

247.89 ÷ 43.5

a)

5.70

b)

5.7

c)

5.699

d)

5.69

77.

Solve and give your answer with the correct number of significant figures
129.6/3

a)

43.0

b)

43

c)

4x10¹

d)

40.0

78.

Solve and give your answer with the correct number of significant figures
(12.470)(271)

a)

3366.9

b)

3.370x10³

c)

3400

d)

3370

79.

Calculate 1.23 m x 0.89 m and give your answer with the appropriate number of significant figures.

a)

1.0 m²

b)

1.1 m²

c)

1.0947 m²

d)

1.09 m²

80.

How many grams are in a kilogram

a)

1,000 grams

b)

100 grams

c)

10 grams

d)

1 gram

81.

Convert 10000g to Kg.

a)

10

b)

100

c)

1000

d)

10000

82.

How many millimeters are in 7 centimeters?

a)

7

b)

7 thousand

c)

700

d)

70

83.

Convert 525 ml to cl

a)

52.5 cL

b)

5.25 cL

c)

0.525 cL

d)

0.0525 cL

84.

42 L - _______mL

a)

4200

b)

0.0042

c)

4.2

d)

42,000

85.

350 grams (g) will convert to how many kilograms (Kg)?

a)

.035 Kg

b)

.35 Kg

c)

35 Kg

d)

350000 Kg

86.

2349800 micrometers will convert to _ meters (m)

(a)

87.

Convert 45 mm to dm

a)

450 dm

b)

.45 dm

c)

450000 dm

d)

34 dm

88.

You know 16 cups = 1 gallon. Convert 3.5 gallons into cups.

a)

56 cups

b)

0.21875 cups

c)

19.5 cups

d)

48 cups

89.

48 inches = _______ feet

a)

16

b)

1 1/2

c)

4

d)

144

90.

How many hours are in a year?
(Hint: 365 days = 1 year)

a)

8760 hrs

b)

8670 hrs

c)

525,600 hrs

91.

There are 60 seconds in a minute. How many seconds are in 5 minutes?

a)

65

b)

60

c)

240

d)

300

92.

Convert this number into scientific notation: 0.068

a)

6.9 x 10⁶

b)

6.8 x 10^-9

c)

6.8 x 10^-2

d)

None of the above

93.

Convert this number to standard notation: 1.4 x 10^-2

(a)

94.

Convert this number into scientific notation: 950,000

a)

9.5 x 10⁵

b)

9.5 x 10^-9

c)

9.5 x 10²

d)

None of the above

95.

Write 6,700 in scientific notation.

a)

6.7 x 10³

b)

6.7 x10^-3

c)

67 x 10²

d)

67 x 10^-2

96.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

97.

Change from standard form to scientific notation: 0.000398

a)

39.8 x 10^-5

b)

3.98 x 10^-5

c)

3.98 x 10^-4

d)

39.8 x 10^-6

98.

How would you write 50,000 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

99.

Try to change the number back to standard form: 6.79 x 10⁴

a)

679,000

b)

6,790

c)

67,900

d)

6,790,000

100.

How would you write -5.6 x 10^-3 in standard form?

a)

0.0056

b)

-5,600

c)

0.00056

d)

-0.0056

101.

(2 x 10^-5)+ (7 x 10^-5)

a)

9 x 10^-10

b)

14 x 10^-5

c)

9 x 10^-5

d)

1.4 x 10^-4

102.

(8 x 10⁴) - (2 x 10⁴)

a)

16 x 10¹⁶

b)

16 x 10⁸

c)

6 x 10⁸

d)

6 x 10⁴

103.

Subtract withing scientific notation
(7.32 x 10⁶) - (4.01 x 10⁸)

a)

-3.937 x 10⁸

b)

3.937 x 10⁸

c)

3.937 x 10⁷

d)

3.937 x ⁻²

104.

Add withing scientific notation
(5.2 x 10⁷) + (3.01 x 10⁴)

a)

5.20301 x 10¹¹

b)

.520301 x 10⁷

c)

5.20301 x 10⁷

d)

5.20301 x 10⁸

105.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

106.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

107.

(9.6×10^-8)÷(2×10^-15)

a)

-4.8×10⁷

b)

4.8×10⁷

c)

4.8×10^-7

d)

-4.8×10^-7

108.

Multiply:
(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

109.

(2 x 10⁹)(4 x 10^-4)

a)

8 x 10¹³

b)

8 x 10³⁶

c)

8 x 10⁵

d)

8 x 10^-36

110.

Complete the statement:

5.0 cm/min = ______ m/day

(100 cm = 1 m)

a)

72

b)

840

c)

7.2

d)

5,040,000

111.

A bicycle has a speed of 6.00 m/s. What is its speed in km/h?

a)

21.6 km/h

b)

16.67 km/h

c)

2.16 km/h

d)

1.67 km/h

112.

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?

1 mile = 5,280 feet

a)

45 miles per hour

b)

46 miles per hour

c)

47 miles per hour

d)

48 miles per hour

113.

Ann Proctor won the 2007 World Waterski Racing Championship race in her category when she finished the 88-kilometer course in 51.23 minutes. What was her average speed in miles per hour? (Hint: 1 km= 0.62 miles)

a)

23.66 mph

b)

63.90 mph

c)

46.59 mph

d)

51.23 mph

IB Physics 2025 - Topic 0 - Math Skills & Measurement Worksheet

Total questions: 113

Worksheet time: 3hrs 29mins

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