Transcript Find the area of the isosceles triangle whose congruent legs each

Find the sum of all of the prime numbers
between 50 and 70.
Answer: 240
If I reduce the length of a rectangle by 20%
and increase the width by 30%, what is the
percentage increase in area?
Answer: 4%
The mean of 4 numbers is 63.5. If I add a
fifth number the mean becomes 60. What
number did I add?
Answer: 46
I travel a distance of 100km at a speed of
80km/h. By how much must I increase my
speed in order to complete the same
journey in a time which is 27 minutes less
than before?
Answer: 45km/h
Given f(x)=2x3-3x2-2, find f(0.5).
Answer: -2.5
Find the difference between 35% of 25,
and 25% of 30.
Answer: 1.25
Find the area of the isosceles triangle
whose congruent legs each measure 12
and whose included angle measures
120.
Answer: 36sqrt3
Two brothers have a mean age of 16
years. The difference in their ages is 8
years. How old is the younger brother?
Answer: 12
In a class of 32 students, 20 of the
students are male. What percentage of the
students are female?
Answer: 37.5%
A bag contains 7 blue, 5 red and 3 yellow
discs. Two discs are drawn from the bag
simultaneously. What is the probability that
both discs are red? Your answer must be a
fraction in its simplest form.
Answer: 2/21
The side lengths of a triangle are 3 inches,
6 inches and 10 inches. One of the side
lengths of a similar triangle is 30 inches.
What is the minimum number of inches
possible in the perimeter of the second
triangle?
Answer: 57 inches
A rectangular garden has an area of 288
square metres. The length of the rectangle
is twice the width. A path one metre wide
surrounds the garden. What is the area of
the path?
Answer: 76 square metres
Tim chose an integer from the set
{1,2,3,4}, and Sheila chose an integer from
the set {5,6,7,8}. What is the probability
that the sum of their numbers is less than
10? Express your answer as a common
fraction in lowest terms.
Answer: 5/8
How many numbers from 1 to 100 have
the figure ‘4’, the figure ‘5’ or both in them?
Answer: 36
To make a new colour of paint, I mix red,
green and blue paint in a ratio 2:3:4. I
have 30 litres of red paint, 42 litres of
green paint and 50 litres of blue paint.
How many litres of the new paint can I
make?
Answer: 112.5 litres
How big is the acute angle between the
hands of a clock at 7:45?
Answer: 37.5 degrees
In a 25 question quiz, 5 points are
awarded for each correct answer, 2 points
are deducted for each wrong answer and
no points are awarded for an answer that
is missed out. Bob scored 35 points and
missed out 4 questions. How many
questions did he get wrong?
Answer: 10
The length of the hypotenuse of a right
triangle is 50 cm, and the length of one leg
is 14 cm. How many square centimeters
are in the area of the triangle?
Answer: 336
ABCD is a square. P and Q are points
outside the square such that triangles ABP
and BCQ are both equilateral. How big is
angle PQB?
Answer: 15 degrees
A high school has 517 students. 312
students are in Grade 10 or below. 321
students are in Grade 10 or above. How
many students are in Grade 10?
Answer: 116
You roll two dice, each with 2 red faces, 2
green faces and 2 blue faces. What is the
probability that that the dice will show
different colours?
Answer: 2/3
A cylindrical glass with radius 4cm and
height 12cm is filled with water to a depth
of 6cm. A spherical marble with radius r
centimetres is dropped into the glass and
sinks to the bottom. If the water level rises
by 2.25 centimetres, what is the radius of
the marble?
Answer: r = 3
Calculate (10!+8!) divided by 6!
Answer: 5096
The mean of x and y is 5y/6. What is
x/y+y/x?
Answer: 13/6
Given that x is an integer and that
f(x)=x2-x+19. What is the largest value of x
such that f(x) is a prime number less than
200?
Answer: x = 12
An equilateral triangle and a square have
the same perimeter. Find the ratio of the
area of the square to the area of the
triangle, expressing your answer as a
fraction with a rational denominator.
Answer: (3sqrt3)/4
A square has a diagonal of length 8 inches.
Find the perimeter, in inches, of this square.
Express your answer as a surd in simplest
form.
Answer: 16sqrt2
Anne, Bill and Fred receive a gift which
divide in a ratio of 3:4:8 respectively. Bill
receives $40 more than Anne. How much
was the original gift?
Answer: $600
What is the sum of the positive factors of
the square root of 256.
Answer: 31
One-seventh of one-sixth of one-fifth of
what number is 5?
Answer: 1050
If x*y is 2x2-3xy. Calculate 5*3 – 3*5.
Answer: 32
Calculate: (8-6)(48)(22)
Answer: 1
Tom and Mary are running towards each
other. Tom runs at a speed of 10 km/h and
Mary runs at a speed of 14 km/h. How far
apart are they two minutes before they
meet?
Answer: 800m (0.8km)
What is the first prime number larger than
63 – (53 + 33)?
Answer: 67
One-third of one-fifth of K equals four fifths
of 90. Find K.
Answer: 1080
I am thinking of a number less than 200.
The number is 4 less than a multiple of 10
and is 4 more than a multiple of 7. What is
the largest possible value of the number?
Answer: 186
When 0.216216216…. is expressed as a
fraction of the form a/b, what is the value
of a+b?
Answer: 1215
In how many different ways can 5 students
sit in a row of 5 seats if the oldest student
cannot sit at the beginning or end of the
row?
Answer: 72
Of the 104 students in Grade 11, 55 play
soccer, 51 play tennis, and 12 have never
played either soccer or tennis. How many
students play soccer and tennis?
Answer: x=14
When training for a running race, Paul ran
for 8 minutes on the first day of training.
Each day he ran for 2 minutes longer than
the previous day. How many minutes had
he ran for in total during the first 20 days
of training?
Answer: 540 minutes
The difference between the squares of two
positive integers is 57. The product of the
two integers is 88. What is the sum of the
two integers?
Answer: 19
The point (2,5) is rotated 90 degrees
clockwise about the origin to a point A.
Point A is then reflected in the y-axis to a
point B. What is the product of the
coordinates of B?
Answer: 10
How many square numbers between 1
and 1000 (including both numbers) are
divisible by 2?
Answer: 15
Find the product of the lengths of the
longest and shortest diagonals in a regular
hexagon with side length 2 centimetres.
Answer: 8sqrt3
ABCD is a quadrilateral with AB=AD=25
centimetres, and CB=CD=52 centimetres.
Given DB=40 centimetres, find AC.
Answer: 63
The probability that David remembers to
take his medicine is 0.7. If he remembers
to take his medicine, the probability he
becomes ill is 0.2. If he forgets to take his
medicine the probability he become ill is
0.9. Calculate the probability that David
becomes ill.
Answer: 0.41
2x – 2x-2 = 192. What is the value of x?
Answer: x=8
The first two terms of a sequence are a
and b. From then on, each term is equal to
the negative of the previous term plus the
term before that. What is the sixth term?
Answer: 5b-3a
How many prime numbers between 10
and 99 remain prime when their digits are
reversed?
Answer: 11
A shopkeeper increases the price of an
article by x%. Some time later he reduces
the new price by y% and notices that the
price is now the same as it was originally.
What is the value of 1/y-1/x?
Answer: 1/100
What is the smallest possible integer of
the form prqqrp where p, q and r are distinct
integers?
Answer: 12
One of the sides of a rectangle is 3
centimetres long. The perimeter of the
rectangle in centimetres is equal to the
area of the rectangle in square
centimetres. What is the length of the
other side of the rectangle?
Answer: 6 centimeters
What are the two solutions to the equation
2x2 - 2x – 2 = 2
Answer: x=2 and x=-1
You are given x and y are positive integers
defined as follows:
0<x<6 and 1<y<7
One number from each set is selected at
random, find the probability that the sum of
the numbers is an odd number.
Answer: 13/25
The line y = mx – 4 intersects the line
y = -3x at the point where x=-2. What is
the value of m.
Answer: -5
Find the sum of the first ten terms of the
series: -6, -1.5, 3…….
Answer: 142.5
What is the area of the triangle whose
vertices are (0,-3), (0,2) and (2,4)?
Answer: 5
Calculate 2((2((2!)!))!)
Answer: 48
• Calculate the sum of the solutions to the
equation 6x2=13x-6
Answer: 13/6
A train 70m long traveling at a speed of
30m/s enters a tunnel 2km long. After how
many seconds will the train have passed
completely through the tunnel?
Answer: 69 seconds
Polly is taking a science test consisting of
60 questions. She gets 3 of the first 7
wrong. How many of the remaining
questions must she get correct so that
overall she get 3 times as many answers
correct as wrong?
Answer: 42
Alice drops a ball from a height of 50m.
After each bounce the ball reaches 80% of
the maximum height it had after the
previous bounce. What is the maximum
height the ball will reach after the third
bounce?
Answer: 25.6m
A circle has area 32o square centimeters.
Find the area of a rectangle with one side
equal to the diameter of the circle, and the
other side 10cm.
Answer: 80 sqrt2 square centimeters
Factorize x2-4x+4-y2+6x-9
Answer: (x-y+1)(x+y-5)
Three sisters are of different ages. The
youngest 2 sisters have a mean age of
13.5. The oldest 2 sisters have a mean
age of 18.5. The mean age of the oldest
and youngest sister is 17. How old is the
youngest sister?
Answer: 12
Calculate (1 – tan30sin60cos30tan60). All
angles are given in degrees
Answer: 0.25