Grade 10 Problems
Grade Ten Problems
1)
Natural and Whole Numbers.
A student at St. F. X. decided to become his own employer by using his
car as a taxi for the summer. It costs the student $693.00 to insure his
car for the 4 months of summer. He spends $452.00 per month on gas. If
he lives at home and has no other expenses for the 4 months of summer
and charges an average of $7.00 per fare, how many fares will he have
to get to be able to pay his tuition of $3280.00?
Need A Hint?
Answer
2)
If twenty people in a factory make 43 shoes in [(3)^.5] / 2 hours, then how
many shoes do they make in an eight hour day?
Need A Hint?
Answer
3)
Brendan went to Toronto to see a Blue Jays game. He had $650.00 for the
trip. It cost him $40.00 for his ticket to the game, $216.00 to stay 2
nights at a hotel, $329.00 for his flight and $29.00 for food. He met
a man on Young Street who was running a small casino. Brendan bet $5.00
in Black Jack and won an amount of money that was triple what he had left
after making the bet. He spent half of this at the ball game.
How much money did Brendan take home?
Need A Hint?
Answer
4)
The area of a trapezoid is given by the formula A = 1/2 (a + b) h.
If h = 1/2b and a = 1/3b.
a) What will be the value of b when a = 26 ?
b) What will be the value of h if a = 6? What will be the area of the
trapezoid?
Need A Hint?
Answer
5)
Joe was driving on the highway. A car ahead of him was driving far below
the speed limit so he decided to pass. In the first second he gained 5m
on the car and as he accelerated he gained 1.5 times as much distance in
each second as he had the second before. If there was 30m between Joe and
the car he was passing, then how long did it take him to pass?
Need A Hint?
Answer
6)
If a turntable rotates through 720 degrees in one second, how many
revolutions does it make in one minute.
Need A Hint?
Answer
7)
Two girls agree to go on a road trip together. They travel (x + 5)km on
the first day. On the second day they travel 2km more than half of the
distance they travelled on the first day. On the third day they drove
3 times as far as they did on the second day. If they drove 5000km
total, find the value of x.
Need A Hint?
Answer
8)
A rectangle has the following sides. One side must have an odd
integer length. Find the perimeter.
Need A Hint?
Answer
9)
If a tire rotates at 150 revs/min when the truck is travelling 40km/h,
what is the circumference of the tire?
Need A Hint?
Answer
10)
From the rectangle DEFG the square ABCD is removed, leaving an area of 92
square units. If AE is 4 and GC is 8 units, then use a polynomial
expression to find the original area of DEFG.
Need A Hint?
Answer
11)
Points A, B, C, D, are arranged in order on a line so that AB = 3, BC =
2CD what is BD as a fraction of AD?
Need A Hint?
Answer
12)
If (-2 + x^2)^5 = 1 then what can x be equal to in the set of positive
irrational numbers?
Need A Hint?
Answer
13)
Given the symmetric shape below with a known perimeter of 77, find the
area of the shape.
Need A Hint?
Answer
14)
A man in a speed boat which could only travel at 50km/h was driving his
boat up a river which flowed with a constant speed. As he was driving
his spare life jacket fell of the boat, 20 minutes later the man noticed
the jacket was gone and turned back to get it. He found it 3km away
from where he lost it. How fast was the river flowing?
Need A Hint?
Answer
15)
Find an odd number with 3 digits such that all the digits are different
and add up to 15. The difference between the first two digits equals the
difference between the last two digits. The hundreds digit is greater
than the sum of the tens and ones digits.
Need A Hint?
Answer
16)
The Jones family had a square patch of lawn in their backyard. Its
original area was x^2. They increased its length by 3 and its width
by 5. Write a polynomial to describe the new area.
Need A Hint?
Answer
17)
18)
How many minutes is it until 5:00 if forty minutes ago it was four times
as many minutes past 2 o'clock?
Need A Hint?
Answer
19)
Given a trapezoid of area 126 and a = 6, b = 8, use the formula
1/2 (ah) + h(a + b) / 2 + 1/2 (bh) = 126 to solve for variable h, then
find the perimeter of the trapezoid.
Need A Hint?
Answer
20)
21)
Mary and Gary graduated from university together. Gary became a teacher
and earned half what Mary earned for 5 years. Mary spent 1/3 of her
money; Gary spent 1/4 every year for those 5 years. Greg has $80,000
after 5 years. How much does Mary have?
Need A Hint?
Answer
22)
The cost of a lunch of 3 sandwiches, 7 cups of coffee and 1 donut is
$3.15. The cost of a lunch of 4 sandwiches, 10 cups of coffee and 1
donut was $4.20 at the same cafe.
How much will 1 sandwich, 1 cup of coffee and 1 donut cost?
Need A Hint?
Answer
23)
Brendan and Shawn were out for a bike ride when the tire fell off
Brendan's bike. They were 20km from home. They decide that Brendan will
walk for a while and Shawn will take the bike, leaving it further along
and walking the rest of the way. When Brendan reaches the bike, he will
bike home. Brendan walks at 5km/h and rides at 12km/h. Shawn walks at
4km/h and rides at 10km/h. How far should Shawn ride the bike for both
to arrive home at the same time?
Need A Hint?
Answer
24)
25)
Thales of Miletus proved that any triangle inscribed in a semicircle will
be a right triangle.
Given a circle of radius a and a smaller circle of radius b = 1/2a, find
the ratio of the areas of the triangles ABC and DEC. Both triangles have
altitudes intersecting their base at 1/4 the length of their bases.
h1 = (b (b + a))^.5
h2 = (1/2 (1/2 b + b))^.5
Need A Hint?
Answer
26)
Given a circle with center A and radius 2. If ABCD is a parallelogram,
find the area of the shaded region. Area parallelogram = b*h
Need A Hint?
Answer
27)
The distance from an observation point to a comet at a given time is
known to be 3.5 million kilometers. Given that a line drawn from the
comet to the observation point is parallel to a line going through the
center of the earth, find the values of x and y.
Need A Hint?
Answer
28)
a = 2 * (3^0.5) c = 2
d = 3^0.5 b = (28^0.5)/2 = 7^0.5
How far apart will the flag poles be?
Need A Hint?
Answer
29)
Given a figure with squares ABCD and EFGD not equal, and knowing CE = CD
and angle DEC = 40 degrees, find angle BDG.
Need A Hint?
Answer
30)
31)
The algebraic equation of a circle with its center at (0,0) is
x^2 + y^2 = r^2. Given a circle of radius 4 and a chord of this circle
which is the perpendicular bisector of a radius, find the length of a chord.
Need A Hint?
Answer
32)
Given a triangle of area 5 perform a series of reflections to create a
solid figure of area 40 (want 360 degrees about point 0) using only the
x and y axes and the line y = x.
Need A Hint?
Answer
33)
The lookout on a pirate ship is keeping his eyes open for land. From his
perch 6m above the water he can only look down at a 60 degree angle.
He cannot see the land (x) from his position at t = 0 but in 3 seconds it
comes
into view. What was the distance from the ship's position at t=0 to land?
Need A Hint?
Answer
34)
Given the following information find the area of triangle AEB.
Lines:
The length of AE is not equal to the length of AD
EB is parallel and equal in length to DC
The length of AD=the length of DC
The area of triangle ADC =8
The area of triangle BDC=3
Angle DAB is a right angle
Need A Hint?
Answer
35)
The Egyptians used a hexagon (all sides equal) incribed in a
square to approximate the area of a circle. If the radius of the
circle is 2 and the circle is tangent to all four sides of the square,
find the area of the circle, without the use of pi, assuming that the
hexagon trisects each side of the square.
Need A Hint?
Answer
36)
In a soccer tournament the average of 8 goals scored in Caratine's first
5 games was 6.4. The average of her next five games was 6.5. If there
were 9 goals scored in the tenth game what was the overall average.
Need A Hint?
Answer
37)
In a class of four students there are four marks given to students
A, B, C, and D. The average of the first two marks is 50. The average of
the second and third marks is 75 and the average of the third and fourth
marks is 70. What is the average of the first and fourth marks?
Need A Hint?
Answer
38)
A right triangular prism has edges in the ratio 3:4:5:10. If the volume
is 202.5 units find the actual length of the longest side.
Need A Hint?
Answer
39)
A woman who runs two breakfast cafes wants to know how much it will cost
to supply each if one uses 1066 slices of bread per week and 48L of
orange juice and the other uses 988 slices of bread per week and 56L of
orange juice. One slice of bread costs 1.5 cents and 1 L of orange juice
costs 99 cents. Use matrices to solve this problem.
Need A Hint?
Answer
40)
Form a quadratic equation with rational coefficients having
2 - 4(3)^.5 as one of its roots.
Need A Hint?
Answer
41)
The average age of a group of teachers and professors is 40. If the
teachers average 35 years and the professors 50 years, then what is the
ratio of the number of teachers to professors?
Need A Hint?
Answer
42)
The graph of y = (x+2) * (x-3) intersects the x axis at points A and B.
Find the length of AB.
Need A Hint?
Answer
