Download MYP 10 Mathematics End of Year Review Sheets

MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 1: Number Sequences
1.
What are the next two terms in the arithmetic sequence 58,52, 46 .
2.
What is t6 of the arithmetic sequence 14, 23,32,......?
3.
In an arithmetic sequence, the 3rd term is 2 and the 6th term is 10 . Find the 10th term.
4.
Find the expression tn for the arithmetic sequence 48, 43,38,...?
5.
A later term in the arithmetic sequence 7, 3,1,......... is 21. Which term is it?
6.
For the arithmetic series 72  69  66  ....... , what is the sum of the first 10 terms?
7.
What is the sum of the arithmetic series 4  9  14  .............  104 ?
8.
The numbers of cans arranged in layers form an arithmetic sequence. There are 46 cans in the
bottom layer and 16 cans in the top layer. There are 6 layers. How many cans are in the display?
9.
Which number can be inserted between 28 and 7 so the 3 numbers form a geometric sequence?
10.
What are the first 3 terms of a geometric sequence in which the 2 nd term is 10 and the 5th term is 80?
11.
What is the 5th term of the geometric sequence 3, 12, 48,.......?
12.
What is the sum of the first 10 terms of the geometric series 3, 12, 48 .
13.
A ball is dropped from a height of 4 m. After each bounce, it rises to 75% of its previous height.
What height does the ball reach after the second bounce?
14.
Simplify:
16.
Evaluate:  x 4 y  x 2 y 3  , when x  3 and y  4 .
m 2 n 1
m4 n
15.
Simplify:  x3 y 5 
4
MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 2: Real Numbers
2
3
1.
Simplify: 64 2
3.
The mass of a cat is about 3.6 kg. Use the formula b  0.001m0.7 , where b represents the body mass.
What is the approximate mass of the cat’s brain?
4.
A rectangular field is 150 m long and 90 m wide. How much shorter is the diagonal distance than the
distance around half the perimeter?
5.
Which type of number cannot be expressed in the form
6.
2.
Simplify: 4 3
A. A natural number
m
, where m and n are integers, and n  0 ?
n
B. An integer
C. A whole number
D. An irrational number
E. A rational number
Which phrase describes the set of real numbers?
A. The set of natural numbers and the set of integers
B. The set of integers and the set of rational numbers
C. The set of rational numbers and the set of irrational numbers
D. The set of irrational numbers and the set of natural numbers
E. The set of natural numbers and the set of rational numbers
7.
Which number is irrational?
A.
8.
C. 7
B. 7
7
D. 0
E.
1
7
Which number is rational?
A.
B. 
7
C. 0.12112111211112....... D. 7.23
3 . What is the longer leg?
9.
In a 30-60-90 triangle, the shorter leg is
10.
Write
48 in its simplest form.
11.
Write
486 in its simplest form.
12.
Write 2 12  5 20  3 15 in its simplest form.
13.
Write
14.
Write 2 3
12 40
8 45

in its simplest form.

2 2  3


8  98 in its simplest form.
E.
1
2
MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 3: Coordinate Geometry: Line Segments
1.
Write down the formula for the distance between two points.
2.
Calculate the lengths of the sides of ABC with vertices A  4,0  , B  4, 3 and C 1, 5 .
3.
What kind of triangle is the triangle in question 2?
4.
What is the perimeter of the triangle in question 2?
5.
Write down the formula for the coordinates of the midpoint of a line segment.
6.
Calculate the coordinates of the midpoint of a line segment with end points A  1, 3 and B  2,7  .
7.
Plot the vertices A  0, 3 , B  7, 1 , C 10, 4 and D  3, 2 . Do all calculations needed to show as
much information about this shape that you can. What is the shape?
8.
The midpoint of the line segment joining P  4, 7  and Q  x, y  is M 5, 1.5 . Calculate the
coordinates of Q .
9.
Plot the following points to make line segments: X  2,7  and Y  3, 2  to make XY , K  4,9 and
L  4,3 to make KL , P  4, 2 and M  2, 2 to make PM , G  3, 1 and F  6, 2 to make GF and
J  0, 6  and H  2, 2  to make JH .
10.
For each line segment, calculate the slope of the line.
11.
For each line segment, calculate the midpoint.
12.
Identify some special lines and state their properties.
MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 4: Coordinate Geometry: The Straight Line
1.
Two points on a line are A  1, 2  and B  3, 4  . What is the slope of the line?
2.
A line has slope 3 . It passes through the points P  2, k  and Q 1, 4 . What is the value of k ?
3.
3
If y   x  2 , what is the slope and the coordinates of the y -intercept?
4
4.
On a Cartesian plane, plot the following lines.
a) y  3x  3
b) y 
3
x3
2
3
c) y   x  3
2
d) y 
2
x3
3
5.
For the line y  4 x  b , that passes through the point P  2,3 . What is the value of b ?
6.
Find the equation of the line with slope
7.
For the equation 5x  2 y 18  0 , find the slope and x -intercept of this line.
8.
Write the equation of the line perpendicular to the line 5x  4 y  7  0 , passing through the point
3, 2 in the form
9.
Ax  By  C  0 .
Write the equation of the line perpendicular to the line 2x  5 y  8  0 , passing through the point
 4,0
10.
5
passing through the point Q  4, 1 .
7
in the form Ax  By  C  0 .
Write the equation of the line perpendicular to the line 7 x  3 y 15  0 , passing through the point
 0, 5
in the form Ax  By  C  0 .
MYP Grade 10 Mathematics
Final Exam Review Material
Chapter 6: Polynomials.
1.
Simplify: 7xy 12 yz  8 yz  21xy .
2.
Simplify:
3.
Simplify: 5  a 2  7a  3  2  5a  9  10a 2  .
4.
Simplify:  2 x  3   3x  5  7 x  1 .
5.
Factorize: x2  4x  4 .
6.
Factorize: x2 13x  48 .
7.
What value can q take to make the expression x 2  2 x  q factorize?
8.
What value can k take to make the expression x2  kx 12 factorize?
9.
Factorize: 6 x 2  13xy  5 y 2 .
10.
Factorize: 16a 4 y 2  49 .
11.
Factorize: 6x2 19x  7 .
12.
Factorize: 4x2  3x 10 .
13.
Solve: 6x2 13x  6  0 .
14.
Solve: 4x2  29x  7  0 .
15.
Solve: 10x2  x  3  0 .
16.
Solve: 12 y 2  16 y  5  0 .
 2 x y  3xy  .
3
4
5
12 x10 y10
2
Semester 2 2006-2007
MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 8: Trigonometry
1.
A ladder of length 6 m leans against a vertical wall so that the base of the ladder is 2 m from the wall.
Calculate the angle between the ladder and the wall.
2.
In PQR , Pˆ  90 , PQ  3.2 cm and QR  5.7 cm . Find Q̂ and R̂ .
3.
Find Â
4.
C
Find x
M
20
6.7
x
B
A
L
18
5.
43
N
A is the point 1,1 , B is the point  4,5 and C is the point  5,3 . Find
a) the angle between AB and a line parallel to the y - axis
b) the angle between BC and a line parallel to the y - axis.
ˆ .
c) Hence find ABC
6.
In  XYZ , Xˆ  90 , XY  2.5 cm and XZ  3.2 cm . Find YZ and Ŷ .
7.
In  ABC , Cˆ  90 , AB  4.3 cm and Aˆ  54 . Find B̂ and AC .
8.
The diagram represents two ships at P and Q that are 35.0 km apart. Angle P is 69.0 and angle Q
is 41.0. How far is each ship from a lighthouse at R?
Q
P
R
9.
A helicopter hovers directly above the landing pad on the roof of a 125-m high building. A person is
standing 145 m from the base of the building. The angle of elevation of the helicopter from this person is
58. Assume the landing pad is at the edge of the roof closest to the person on the ground. How high is the
helicopter above the landing pad?
MYP Grade 10 Mathematics
Final Exam Review Material
Semester 2 2006-2007
Chapter 9: Statistics and Probability
1.
The median of x  4 , x , 2x and 2 x  12 is 9, where x is a positive integer. Find the value of x .
2.
The table shows the results of a short test.
Mark
number of students
0
1
1
3
2
10
3
x
4
6
5
3
The mode of the marks is 2 and the median is 3. Find the possible values for x .
3.
Answer the whole question on a sheet of graph paper. The table shows the amount of money, $ x , spent on
books by a group of students.
Amount spent ($ x )
0  x  10
10  x  20
20  x  30
30  x  40
40  x  50
50  x  60
Number of students
0
4
8
12
11
5
a) Calculate an estimate of the mean amount of money per student spent on books.
b) Use the information above to make a cumulative frequency table.
c) Use a scale of 2 cm to represent 10 units on each axis, draw a cumulative frequency diagram.
d) Use the diagram to estimate the mean amount spent, the upper and lower quartiles and therefore calculate
the inert-quartile range.
4.
Give each of your answers to this question as a fraction.
Peter has 10 geranium plants. He knows that five will flower red, three pink and two white.
a) Make a tree diagram for the first, second and third flowerings.
b) What is the probability that the first plant to flower is pink?
c) What is the probability that, of the first two plants to flower:
(i) both are red,
(ii) one is red and the other is pink,
(iii) at least one is pink?
d) What is the probability that the first three plants to flower are all white?