Chapter 1 Symmetry and Surface Area Squares Everywhere  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0070973407/645442/image002.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>]]>
What is the sum of the surface areas of all of the squares?
The side length of the smallest squares measures 1 cm. Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 2 Rational Numbers Oasis  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0070973407/645442/image004.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>]]>
Twenty caravans are travelling across the desert one day apart. The first
caravan reached an oasis, and the camels drank half of the water in the pool. On the second
day, the second caravan reached the oasis, and the camels drank one-third of the water that
was left. On the third day, the camels in the third caravan drank one-quarter of the water
that was left. On the first day, the pool contained 1050 m3 of water. How much was
left after the 20th caravan passed through?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 3 Powers and Exponents Exponent Power You have four 3’s. Develop an expression using all four 3’s that is as large as possible when evaluated. Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 4 Scale Factors and Similarity Pong Soccer
Rachel held out a soccer ball and a ping pong ball from the window of a tall building such
that their centres were at the same level. She dropped both balls at the same time and each
fell straight down. Which ball will travel the farthest distance before hitting the ground?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 5 Introduction to Polynomials Polly Wolly Doodle Each of the letters a, b, c and d represents a single digit from 0 to 9. If cd – ab = bb, determine a possible value for each letter. Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 6 Linear Relations Pattern Puzzle Each row in this table of numbers uses the same pattern. What is the missing number?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 7 Multiplying and Dividing Polynomials Magic Polynomials
A polynomial consists of powers of x. All the numerical coefficients are single
digits from 0 to 9. If x = 10, the value of the polynomial is 2351. What is the
polynomial?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 8 Solving Linear Equations DaVinci Goes Linear
A code is based on the linear equation y = x + 3. Assign a number to each
letter in the alphabet. Calculate the corresponding value of y, and use it to
replace the letter in a message. For example, if C is letter 3, the corresponding value of
y is 6. So C becomes an F.
To decode a message, reverse the process. What message does the code PHHWDWVLA indicate? Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 9 Linear Inequalities Present for Damian  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0070973407/645442/image006.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (8.0K)</a>]]>
It is Damian’s birthday. His friends Anwar, Grace, Colin, Diana, and Evan went to the store
to buy a present. Each had an integral number of dollars. They found a suitable item whose
price was an integer. Anwar was $15 short, Graeme was $14 short, Colin was $13 short, Dieter
was $12 short, and Ewan was $11 short. Even when they pooled all of their funds, they could
not buy the item. What was the cost of the item?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 10 Circle Geometry On a Tangent  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0070973407/645442/image008.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (13.0K)</a>]]>
Allan tied a ball to a string and whirled it around in a circular path, as shown. He let go
of the string when the ball was at point P. Which of his friends is most likely to catch the ball?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Chapter 11 Data Analysis Deserted Island  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0070973407/645442/image010.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (6.0K)</a>]]>
A passenger plane makes an emergency landing on a deserted island with
120 persons on board. The cargo included enough food to last for 15 days. On the morning of
the sixth day, before the daily rations were handed out, a ship sank close to the island. All
30 ship passengers made it to shore. How long can the two groups survive, assuming that
rations per person remain the same?
Click here for a hint Click here for the solution Note: Brain teasers are often open to more than one interpretation, and multiple answers may be possible.
Sample solutions are shown.
Hints Teaser | Hint | Squares Everywhere | Consider similar squares of all possible different sizes. | Oasis | Calculate how much is left after each of the first three drinks. Look for a pattern. | Exponent Power | You may use multiplication, division, or exponents. | Pong Soccer | Consider the different sizes of the balls. | Polly Wolly Doodle | Look at the last digit in each term to determine a relation between d and b. | Pattern Puzzle | Think in terms of mathematical operations such as adding, subtracting, multiplying and dividing. | Magic Polynomials | Consider equivalent fractions with the same denominator. | DaVinci Goes Linear | Use the linear relation to write out each letter and its corresponding code. | Present for Damian | Let x represent the price. Use the data given to set an upper and a lower limit for x. | On a Tangent | Consider the direction in which the ball is going when it is at point P. | Deserted Island | Determine how many units of daily rations were on the plane when it landed. |
Solutions
Teaser | Solution | Squares Everywhere | There are four types of squares with side lengths that measure 1 cm, 2 cm, 3 cm and 4
cm. The table summarizes the area of each type of square. Type of Square | Number | Surface Area (cm2) | 1 cm | 16 | 16 | 2 cm | 9 | 36 | 3 cm | 4 | 36 | 4 cm | 1 | 16 | Total Surface Area: | 104 | |
The total surface area is 104 cm2. | Oasis |
The first caravan left half of the water. The second caravan left  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0070973407/645442/image012.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0070973407/645442/image014.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]>
of the water. Continuing the pattern, the 20th caravan leaves  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0070973407/645442/image016.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]>
or 50 m3 of water.
| Exponent Power |
You can use some 3’s for the base and some for the exponents. Using a calculator to
help you, show that the largest number occurs when you develop the expression 33 × 3 × 3.
| Pong Soccer | The ping pong ball has a smaller radius than the soccer ball.
Therefore, it must fall farther before it hits the ground. | Polly Wolly Doodle | You can start by noticing that d – b = b. Therefore,
b must be half of d. Try each case: 8 and 4, 6 and 3, 4 and 2, and 2
and 1. One possible solution is a =1, b = 4, c = 5, and
d = 8. Are there any others? | Pattern Puzzle | Divide the number in the first column by the number in the second column. Then,
multiply by 3. The missing number is 18. | Magic Polynomials | Represent the polynomial as ax3 + bx2 + cx + d. If x = 10, this becomes 1000a + 100b + 10c + d. Comparing this to 2351, the polynomial must be 2x3 + 3x2 + 5x + 1. | DaVinci Goes Linear | Replace each letter by the letter that is 3 to its left in the alphabet. For example, P
becomes M. The decoded message is MEETATSIX. | Present for Damian | Let x represent the cost of the item. The table summarizes the provided data. Friend | Costx | Anwar | x – 15 | Grace | x – 14 | Colin | x – 13 | Diana | x – 12 | Evan | x – 11 |
The cost of the present must be greater than the total amount of dollars of the five friends. x > x – 15 + x – 14 + x – 13 + x – 12 + x – 11 x > 5x – 65 x < 16.25 Since Anwar is $15 short, x > 15. The only integer that satisfies both
inequalities is 16. Therefore, the present cost $16. | On a Tangent | When Allan lets the string go, the ball will continue along a tangent to the circle.
Deirdre is most likely to catch the ball. | Deserted Island | The number of rations available when the plane landed on the island was 120 × 15 = 1800. At the end of five days, 120 × 5 = 600 rations had been used. So, there were 1800 – 600 = 1200 rations remaining.  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0070973407/645442/image018.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]>
Dividing the rations among 150 people, there will be enough rations for 8 more days. |
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