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WorksheetsMathematics Skills Assessment
Total questions: 219
Worksheet time: 6hrs 48mins
Approximate the value of π to two decimal places.
2.71
4.20
3.14
3.99
Find the sum of the vectors (3, 4) and (-1, 2).
(4, 2)
(2, 8)
(2, 6)
(5, 6)
Calculate the magnitude of the vector (5, -12).
8
17
13
10
Determine the decimal equivalent of the fraction 3/5.
0.6
1.2
0.8
0.3
What is the scalar multiplication of the vector (2, -3) by 4?
(10, -15)
(8, -12)
(3, -5)
(6, -9)
Solve the equation 2x - 5 = 11 for x.
x = 7
x = 8
x = 10
x = 3
If the probability of an event A is 0.3, what is the probability of the complement of A?
0.5
0.7
0.2
1.3
Find the difference of the vectors (7, -2) and (3, 5).
(10, 3)
(4, -7)
(1, -3)
(5, 7)
Express the decimal 0.75 as a fraction in simplest form.
1/2
2/3
5/6
3/4
Calculate the probability of rolling a 5 on a fair six-sided die.
1/4
1/2
1/3
1/6
Determine the components of the vector with magnitude 10 and direction angle 60 degrees.
The components of the vector are 4 and 6
The components of the vector are 5 and 8.66
The components of the vector are 6 and 8.66
The components of the vector are 3 and 4
Approximate the square root of 17 to the nearest whole number.
3
5
4
6
If vector A = (3, -1) and vector B = (2, 4), find the product A • B.
-2
7
2
12
Simplify the expression (3/4) ÷ (5/8).
5/6
6/5
3/20
2/3
What is the sum of the first 10 positive integers?
55
45
60
40
If vector C = (6, -3) and vector D = (-2, 7), find the sum C + D.
(4, 4)
(10, 4)
(3, 10)
(-8, 4)
Calculate the probability of drawing a red card from a standard deck of 52 playing cards.
0.25
0.75
1.0
0.5
Find the scalar multiple of the vector (4, -7) by -2.
(-2, 3)
(8, -14)
(-8, 14)
(4, 7)
Solve the equation 4x + 9 = 25 for x.
x = 2
x = 4
x = 6
x = 10
Determine the decimal equivalent of the fraction 7/9.
0.6666666666666666
0.5555555555555556
0.8888888888888888
0.7777777777777778
Convert fraction to a decimal
3/8
(a)
Convert fraction to a decimal
1/2
(a)
Convert fraction to a decimal
1/4
(a)
Convert fraction to a decimal
9/10
(a)
Convert fraction to a decimal
3/5
(a)
Convert fraction to a decimal
18/100
(a)
Convert fraction to a decimal
27/50
(a)
Convert fraction to a decimal
15/20
(a)
Convert fraction to a decimal
9/25
(a)
What is the place value of digit 6 in the number 71.263
hundredths
hundreds
tenths
tens
14.307 write in words
one four point three zero seven.
fourteen point three hundred and seven.
fourteen point three zero seven.
fourteen point three seven.
What is the value of the digit 7 in the number 8,123.37?
0.07
.7
7
70
What is the value of the tenths place in 564.67
.06
.6
60
6
.07
What is the decimal equivalent to 54/100?
5.4
0.54
54
540
What is the equivalent fraction for 0.3?
1/3
3/10
7/10
3/100
What is the decimal equivalent to 4/5?
0.8
0.45
4.5
0.4
Which statement is true about the fraction model above?
1/2 = 0.5
1/2 = 0.1
0.25 = 1/2
1.5 = 1/2
What is 0.75 written as a fraction?
75/1000
7/10
3/4
1/2
What is the fraction equivalency for 2/5?
4/10
8/10
3/4
4/100
What is the decimal equivalent for 1/2?
0.2
0.12
0.5
1.2
What is the fraction equivalent for 3/6?
1/10
2/5
3/10
1/2
What fraction and decimal is represented by the shaded amount in the image?
1/4 and 0.25
3/4 and 0.75
1/2 and 0.5
1/10 and 0.1
What would 3/4 be as a decimal?
3.4
0.75
0.34
0.25
What would the equivalent fraction be for 4/5?
8/10
4/100
4/10
45/100
What would 4/8 be as a decimal?
4.8
0.48
0.4
0.5
What decimal is shown shaded green in the image above?
3.4
0.75
0.34
0.25
2/4 is equivalent to______
0.24
0.20
0.40
0.50
How is the fraction above represented as a decimal?
0.25
0.1
0.2
0.4
Round 0.813 to the nearest whole number.
(a)
Write 4.92 correct to 1 decimal place (d.p.)
(a)
Write 4.377 correct to 2 decimal places (2 d.p.)
(a)
How many significant figures are there in 0.0054 grams?
1
2
3
4
How many significant figures are there in 10.020 moles?
2
3
4
5
Identify, how many significant figures does the following number have?
(a)
True or False:
When writing
a number in standard form,
the first number must be
greater than 1 but less than 10.
FALSE
TRUE
What is 6.7 × 104 written
as an ordinary number?
67000
6700
670000
0.00067
What is 45,000 written in standard form?
45 × 103
4.5 × 104
4.5 × 103
What is 0.00051
written in standard form?
5.1 × 10-4
51 × 10-4
5.1 × 10-5
What is 3a+5b if a=4, b=6
40
42
44
46
Y=7, find the value of 2(y+4)
11
20
22
13
Simplifying the following expression
n-10+9n-3
-3
9n-3
n
10n-13
simplify 2(x + 4) + 3(x- 5) -2y.
x - 2y
8x - 2y -7
8x - 2x - 23
8x + 2x - 18
What is the value of 3x2-7
when x=-5
-57
43
-3x2 - 5x + 7 when x = -2
How many significant figures are there in 0.0054 grams?
1
2
3
4
How many significant figures are there in 10.020 moles?
2
3
4
5
Identify, how many significant figures does the following number have?
(a)
Write 4.377 correct to 2 decimal places (2 d.p.)
(a)
Write 4.92 correct to 1 decimal place (d.p.)
(a)
Round 0.813 to the nearest whole number.
(a)
The weight of a bag of potatoes is 25 kg, correct to the nearest kg.
What is smallest possible weight of the bag of potatoes?
A rectangular plot of land has sides with lengths of 38 m and 52 m correct to the nearest m.
Calculate the maximum possible values of the perimeter of the rectangle.
180 m
147 m
91 m
182 m
Hannah measures with a ruler that has marks every 0.1 cm. She says that the lengths of the side of a rectangle are 8.5 cm and 12 cm correct to 1 decimal place.
Calculate the minimum possible values of the area of the rectangle.
A metal pole is 500cm long, correct to the nearest centimetre. The pole is cut into rods each of length 5.8 cm, correct to the nearest millimetre.
Calculate the largest number of rods that the pole can be cut into.
The cost of making a chair is $28 correct to the nearest dollar.
Calculate the lower and upper bounds for the cost of making 450 chairs.
Determine the amplitude for the function
y=3sin21xAmplitude = 3
Amplitude = 21
Amplitude = −3
Amplitude = −21
Determine the period for the function
y=3sin21xPeriod = 4π
Period = 21π
Period = 2π
Period = π
Determine the vertical shift for the function
2y=sin(2x−2π)+22 units upward
2 units downward
1 units upward
2 units downward
Write the vector from A to B...
a
-a
b
-b
Write the vector from C to A...
a
-a
b
-b
Write the vector from B to D...
a
-a
b
-b
Write the vector from A to D...
a + b
-a + b
b - a
a - b
Write the vector from C to B...
a + b
-a + b
b + a
a - b
Write the vector from C to B...
y
-y
z
-z
Write the vector from E to D...
y
-y
x
-x
Write the vector from C to D...
y
-y
x
-x
Write the vector from A to C...
x + z
x + y
x - z
x - y
Write the vector from D to B...
y - z
-x + y
-x - z
-y - z
Write the vector from F to D...
y - z
x + z
-x + z
z - x
Write the vector from A to E...
y + z
x + z
-x + y
y - x
Write the vector from A to D...
x + y + z
x - y + z
-x + y + z
x - y - z
Write the vector from B to E...
x + y + z
x - y + z
-x + y + z
x - y - z
Write the vector from F to C...
x + y + z
x - y + z
-x + y + z
x - y - z
Write the vector from A to B...
r
-r
s
-s
Write the vector from B to A...
r
-r
s
-s
Write the vector from C to A...
r
-r
s
-s
Write the vector from B to C...
r + s
-r + s
s + r
-s - r
Write the vector from C to B...
r + s
s - r
s + r
r - s
A vector includes ______ and ________.
direction, magnitude
magnitude, units
direction, units
scalars, scalars
A resultant vector is
equal to the sum of one vector.
equal to the sum of two or more vectors.
equal to the difference of one vector.
What is the resultant of these two vectors?
+17 m
+3 m
-17 m
-3 m
If two vectors to be added are at right angles, you will need to....
Multiply
Divide
Pythagorean Theorem
Use trigonometry
When using the head-to-tail method to draw a vector addition diagram, the resultant is drawn from the _____ .
head of the first vector to the tail of the last vector
tail of the first vector to the head of the last vector
head of the last vector to the tail of the first vector
tail of the last vector to the head of the last vector
Bob walks 2 miles north and turns west and walks 2 miles. What is Bob's general displacement?
4 miles northeast
4 miles northeast
3 miles northwest
3 miles southeast
Cameron (Cam for short) Per hikes to a campsite where he will spend the evening. He hikes 6.0 km, north and 3.0 km, west. The magnitude of Cam's displacement is ___km
3.0
4.5
6.7
45
What is the magnitude of the resultant vector, r?
3
4
5
7
Which of the following describes the vector above?
45 cm
45 cm at 30 degrees North of East
45 cm at 30 degrees East of North
45 cm North East
Describe the direction of the vector above.
30 degrees
30 degrees North East
30 degrees North of East
30 degrees East of North
If vector A has an y component of 12 units and a x component of 7 units, which would allow you to solve for the MAGNITUDE of vector A?
122−72
122+72
tan−1(712)
tan−1(127)
If vector A has an y component of 12 units and a x component of 7 units, which would allow you to solve for the DIRECTION of vector A?
122−72
122+72
tan−1(712)
tan−1(127)
What is the resultant for the following example?
(Part of the work is done, but not all)
24.6 km at 27 degrees north of east
24.6 km at 63 degrees north of east
33 km at 27 degrees north of east
33 km at 63 degrees north of east
An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h due east. What are the plane's speed with respect to the ground?
167.7 km/h at 26.6 degrees north of east
225 km/h at 26.6 degrees east of north
167.7 km/h at 63.4 degrees north of east
129.9 km/h at 63.4 degrees north of east
129.9 km/h at 26.6 degrees east of north
A Frisbee that flies at a speed of 1.8 m/s north relative to the air encounters a tailwind that travels at 1.2 m/s. What are the speed and direction of the Frisbee relative to the ground?
0.60 m/s north
0.60 m/s at an 45 degrees north of east.
3.0 m/s north
0.60 m/s south
3.0 m/s south
A Frisbee that flies at a speed of 1.8 m/s north relative to the air encounters a tailwind that travels at 1.2 m/s. What are the speed and direction of the Frisbee relative to the ground?
0.60 m/s north
0.60 m/s at an 45 degrees north of east.
3.0 m/s north
0.60 m/s south
3.0 m/s south
What is the resultant vector of the two labeled vectors?
+2 km
+14 km
-2 km
-14 km
What is the resultant of the two vectors shown above?
+5
-5
+15
-15
Bob walks 4 miles west and stops to rest. He then continues to walk another 3 miles west. What is his displacement?
7 miles west
1 mile west
12 miles west
7 miles east
Determine the magnitude of the vector <8, -2>
√12
√68
√60
√20
Find the magnitude.
0
5
-5
4
Find the magnitude.
4
5
3
square root of 5
direction
A deer running 15 meters per second due west
DISTANCE
Scalar
Vector
VELOCITY
Scalar
Vector
MASS
Scalar
Vector
SPEED
Scalar
Vector
WEIGHT
Scalar
Vector
ACCELERATION
Scalar
Vector
MOMENTUM
Scalar
Vector
DISPLACEMENT
Scalar
Vector
TEMPERATURE
Scalar
Vector
direction
A deer running 15 meters per second due west
DISTANCE
Scalar
Vector
VELOCITY
Scalar
Vector
MASS
Scalar
Vector
SPEED
Scalar
Vector
WEIGHT
Scalar
Vector
ACCELERATION
Scalar
Vector
MOMENTUM
Scalar
Vector
DISPLACEMENT
Scalar
Vector
TEMPERATURE
Scalar
Vector
There are 4 blue marbles, 5 red marbles, 1 green marble and 2 black marbles in a box. Suppose you select one marble at random. What is the probability that the marble chosen is blue?
21
31
32
41
There are 4 blue marbles, 5 red marbles, 1 green marble and 2 black marbles in a box. Suppose you select one marble at random. What is the probability that the marble chosen is red?
41.67%
50 %
8.33%
33.33%
There are 4 blue marbles, 5 red marbles, 1 green marble and 2 black marbles in a box. Suppose you select one marble at random. What is the probability that the marble chosen is green?
41.67%
16.67 %
8.33%
33.33%
There are 4 blue marbles, 5 red marbles, 1 green marble and 2 black marbles in a box. Suppose you select one marble at random. What is the probability that the marble chosen is black?
21
31
43
61
There are 4 blue marbles, 5 red marbles, 1 green marble and 2 black marbles in a box. Suppose you select one marble at random. What is the probability that the marble chosen is not green?
41.67%
91.67%
75%
8.33%
Sam rolled a number cube 50 times. A '3' appeared 10 times. Find the probability of getting '3'.
5010
5020
5040
5030
Sam rolled a number cube 50 times. A '3' appeared 10 times. Find the probability of getting numbers that are not '3'.
5010
5020
5040
5030
A coin is tossed 60 times. 27 times head appeared. Find the probability of getting heads.
55%
45%
0%
48%
A coin is tossed 60 times. 27 times head appeared. Find the probability of getting tail.
55%
45%
0%
48%
Christian Dayne drew a random set of cards from a well -shuffled deck of 52 playing cards. He recorded the suit of cards that he picked; results are shown in the table. Find the probability of selecting a spade?
3213
328
324
327
Christian Dayne drew a random set of cards from a well -shuffled deck of 52 playing cards. He recorded the suit of cards that he picked; results are shown in the table. Find the probability of selecting a diamond?
40.63%
25%
12.5%
21.88%
Christian Dayne drew a random set of cards from a well -shuffled deck of 52 playing cards. He recorded the suit of cards that he picked; results are shown in the table. Find the probability of selecting a red card?
3221
3211
3217
3215
direction
A deer running 15 meters per second due west
DISTANCE
Scalar
Vector
VELOCITY
Scalar
Vector
MASS
Scalar
Vector
SPEED
Scalar
Vector
WEIGHT
Scalar
Vector
ACCELERATION
Scalar
Vector
MOMENTUM
Scalar
Vector
DISPLACEMENT
Scalar
Vector
TEMPERATURE
Scalar
Vector
direction
A deer running 15 meters per second due west
DISTANCE
Scalar
Vector
VELOCITY
Scalar
Vector
MASS
Scalar
Vector
SPEED
Scalar
Vector
WEIGHT
Scalar
Vector
ACCELERATION
Scalar
Vector
MOMENTUM
Scalar
Vector
DISPLACEMENT
Scalar
Vector
TEMPERATURE
Scalar
Vector
