Math 9 Midterm REview
Demonstrate an understanding of powers with integral bases (excluding base 0) and whole
number exponents by:
• representing repeated multiplication, using powers
• using patterns to show that a power with an exponent of zero is equal to one
• solving problems involving powers.
Demonstrate the differences between the exponent and the base by building models of a given
power, such as 23 and 32. Draw 23 and 32
 Explain, using repeated multiplication, the difference between 103 and 310.
 Express 45as a repeated multiplication.
Express (-5)(-5)(-5)(-5) as a power.
 Explain the role of parentheses in powers by evaluating a (–2)4, (–24 ) and –24.
 a0 =
Evaluate 32, 83
Evaluate: 94 + 32 X 43
Demonstrate an understanding of exponent laws
Q/Examples of exponent laws
(a5)(a7)
(x8) / (x5)
(d5)6 (d4)
(e5)6
(e3)
(y7)3
(-32)(-37)
(-32)3(-33)
Q/52 + 53
Q/ 43 – 42 x 52
Q/Solve for x:
(x4)2 = 256
Q/Susan needs to wrap two gift boxes in the shape of cubes. She has a sheet of wrapping paper 140cm by 30cm. One
box is 7cm by 7cm by 7cm. Each side of the other box has an area of 529cm 2. Does she have enough wrapping
paper to wrap both gift boxes?
Q/Evaluate:
Identify the error(s) in a given simplification of an expression involving powers.
Demonstrate an understanding of rational numbers
Order 3/5, -0.666….,0.5, -5/8, 3/2 by placing them on a number line
-->Identify three rational numbers that is between -2/3 and -4/5
 Solve a given problem involving operations on rational numbers in fraction or decimal form
Q/Add/Subtract/Multiply/Divide Fractions:
3/8 – 2 ¾
-3 ¼ - (-2/7)
Q/Convert to decimal: 28/40
(2/3)(-4/9)
(3/4) / (5/6)
Convert to fraction: 0.84
Q/If x = –1.25 and y = 2.5, evaluate 2y + 3x.
Q/What is the value of
?
Q/Margaret takes 1 ¼ h to complete her English assignment and 2/3 h to complete her math assignment. How much
longer does it take Margaret to complete her English assignment than her math assignment? Answer in minutes.
 Identify the error in applying the order of operations in a given incorrect solution.
Q/Evaluate: 1.6 – (2.4 – 5.6) – (4)2 + (4)(-6)
7(3 – 8) - 24
Q/Evaluate
.
 Determine the square root of a given positive rational number that is a perfect square.
Q/What is the square root of 36?
 Identify the error made in a given calculation of a square root
Q/is 3.2 the square root of 6.4?
 Determine an approximate square root of a given rational number that is not a perfect square,
using a calculator.
Q/What is the square root of 7rounded to the nearest hundredth.
Q/What is the perimeter of a square if the area is 144cm2
Shape and Space
(3-D Objects and 2-D Shapes)
Determine the area of overlap in a given composite 3-D object
Determine the surface area of a given composite 3-D object
 Solve a given problem involving surface area.
 Q/Calculate the surface area
Similar Polygons
Determine if the polygons in a given pre-sorted set are similar, and explain the reasoning.
 Draw a polygon similar to a given polygon, and explain why the two are similar.
Determine the scale factor for a given diagram drawn to scale (for enlargement and reduction)
Solve a given problem that involves the properties of similar triangles
Q/This kite is reduced by a scale factor of ¾. What will the side lengths of the reduced kite be?
Q/On a map, 3 cm represents 5 km. The distance between two towns is 90 km. What is the distance between the two
towns on the map?
Q/The scale on a map of a region shows that 2 cm represents 5 km. City of Westwood Heights is 12 cm from the
Town of Southgate on the map. How far apart are Westwood Heights and Southgate?
Q/ John would like to determine the height of a maple tree. He is 1.5 m tall and his shadow is 4.0
m long. The shadow of the tree at the same time of day is 80.0 m long. What is the height of
the tree?
Q/What is the length of CD?
Q/What is the length of AB?
Linear Relations (Ch.5)
 Describe the pattern found in a given graph.
 Graph a given linear relation, including horizontal and vertical lines.
Match given equations of linear relations with their corresponding graphs.
Extend a given graph (extrapolate) to determine the value of an unknown element.
Interpolate the approximate value of one variable on a given graph, given the value of the other
variable.
Solve a given problem by graphing a linear relation and analyzing the graph.
Write an expression representing a given pictorial, oral or written pattern.
Write a linear equation to represent a given context.
Write a linear equation representing the pattern in a given table of values, and verify the
equation by substituting values from the table.
REVIEW QUESTIONS:
p.150 #1-18; p.360 #1-8;
Chapter Reviews and Chapter Self-Test for Ch. 1,2,3,4;
Practice Tests: http://www.nelson.com/mathfocus/grade9/student/tryout.html (note: this link is on
Mr.Semaka’s homework website)